InSAR Technique for Earthquake Studies

Transcription

1 InSAR Technique for Earthquake Studies By Youtian Liu A thesis submitted to The University of New South Wales in partial fulfilment of the requirements for the Degree of Master of Engineering Geoscience and Earth Observing Systems Group (GEOS) School of Civil and Environmental Engineering Faculty of Engineering The University of New South Wales Sydney, NSW 2052, Australia August 2015

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5 Abstract An earthquake could be a devastating disaster that leads to losses of human lives. Direct observation of slip distribution at the earthquake source is almost impossible, therefore indirect measuring methods are commonly applied. The research in this thesis focuses on mapping earthquake affected areas with the Interferometric Synthetic Aperture Radar (InSAR) technique, and utilises the surface deformation observations as input for the slip inversion process in order to model the earthquake. Using InSAR to map earthquakes can obtain dense ground deformation observations with metre-scale resolutions at centimetre accuracy. The deformation of the typical area during a certain time period is observed by repeat-pass InSAR, where in this research is the two-pass Differential InSAR (DInSAR). The displacement map generated from the InSAR result will be the main source for this procedure; the subsequent steps include the forward modelling and slip distribution inversion using the sampled surface deformation observations from the displacement map. These dense observations support the slip inversion using an elastic model named the Okada model. The Levenberg-Marquardt algorithm is applied for nonlinear inversion while the damping value is utilised for linear inversion. Four case studies are presented in this work. The first two are the Sichuan earthquake using ALOS PALSAR data and the L Aquila earthquake using ENVISAT ASAR data respectively, showing the different capabilities of L-band and C-band mapping of the earthquakes. The third case study is the 2010 Darfield earthquake using both C-band and L-band observations to map and model the event. The fourth case study is the 2015 Gorkha earthquake in Nepal using ALOS-2 data to invert the slip distribution of the earthquake, and a combining inversion with ScanSAR and Stripmap is conducted. This work reveals the ability of L-band and C-band radar interferometry to map a large earthquake area and demonstrates the possibility of using contour expansion for emergency response. i

6 Acknowledgement This study was performed in the Geoscience and Earth Observing Systems Group (GEOS), School of Civil and Environmental Engineering at the University of New South Wales (UNSW Australia), Sydney, Australia. There are many people who supported me during my research, and they deserve my most sincere thanks. I want to begin by thanking my supervisor Associate Professor Linlin Ge, for supervising and supporting my Master s research. He has given me advice on various aspects and I have gained a lot of scientific knowledge from him during this two-year research. I will always be grateful for his contribution to this research work. Moreover, I would like to thank Dr Xiaojing Li for her encouragement, suggestions and support which have provided me with an excellent atmosphere for doing research. I express my gratitude towards all academics and staffs of this Masters by Research program. My close colleagues in GEOS are worthy of my sincere gratitude, including Alex Hay-Man Ng, Xin Wang, Wendi Peng, Liyuan Li, Rattanasuda Cholathat, Xiaofeng Chang, Qingxiang Liu, Zheyuan Du and Yan Wang. I would particularly like to thank Dr Alex Hay-Man Ng, for sharing his knowledge in the field of SAR interferometry and modelling. I would also thank Dr Simone Atzori in Roma for his excellent support in using SARscape, and Dr Henriette Sudhaus in Germany for her suggestions in my research. JAXA (Japan Aerospace Exploration Agency) is acknowledged for providing ALOS PALSAR and ALOS-2 PALSAR-2 imagery used in my research. The European Space Agency (ESA) is acknowledged for providing ENVISAT ASAR imagery. Finally, I would like to express my deep gratitude to my parents for their generous financial support, positive encouragement and selfless love; without their support I could not have completed my research so successfully. Thanks to all the people who love me and whom I love. ii

7 List of Publications LIU, Y., GE, L., LI, X. & WU, J. Phase Unwrapping for Interferometric Synthetic Aperture Radar Technique. In: WAYNE, S. & IVER, C., eds. Proceedings of the 13th Australian Space Science Conference, 30 Sep. - 2 Oct Sydney LIU, Y., GE, L. & LI, X. Coseismic Deformation Inferred from DInSAR and Model Results for 2008 Sichuan and 2009 L Aquila Earthquakes In: SHORT, W. & CAIRNS, I., eds. Proceedings of the 14th Australian Space Research Conference 29 Sep. - 2 Oct Adelaide, Australia Linlin Ge, Alex Hay-Man Ng, Xiaojing Li, Youtian Liu, Zheyuan Du & Qingxiang Liu (2015): Near real-time satellite mapping of the 2015 Gorkha earthquake, Nepal, Annals of GIS, DOI: / iii

8 List of Abbreviations ALOS: Advanced Land Observation Satellite AOI: Area of Interest ASAR: Advanced Synthetic Aperture Radar CMT: Centroid Moment Tensor DEM: Digital Elevation Model DInSAR: Differential Interferometric Synthetic Aperture Radar ESA: European Space Agency ENVISAT: Environmental Satellite ERS: European Remote Sensing InSAR: Interferometric Synthetic Aperture Radar JAXA: Japan Aerospace Exploration Agency LOS: Line of Sight PALSAR: Phased Array type L-band Synthetic Aperture Radar SAR: Synthetic Aperture Radar SRTM: Shuttle Radar Topography Mission iv

9 List of Figures Figure 1.1 Four seismic stages: Red line shows the inter-seismic stage, black dash line shows the pre-seismic stage, green line depicts the co-seismic stage, and orange dash line the post-seismic stage... 3 Figure 2.1 Satellite SAR geometry sketches Figure 2.2: Multilook Geometry Figure 2.3: Multilook example (ENVISAT): (a) the original interferogram intensity image, (b) multi-looked intensity image showing phase overlapped Figure 2.4: Filtered example images of Christchurch area from ALOS dataset Figure 2.5 (a) original interferogram with phase ramp (L Aquila) (b) Refined by polynomial correction Figure 2.6 ScanSAR image assists Stripmap boundary example (2015 Gorkha earthquake) Figure 2.7 The flow chart of Contour Based Modelling Figure 2.8 Linear Regression of Ascending and Descending Observations at same points Figure 2.9 The Sampling area and the modelled Interferogram Figure 3.1 Fault plane and parameters Figure 3.2 Fault Geometry and contributions to surface deformation (Adapted from (Okada, 1985)) Figure 3.3 LOS and 3D deformation projection Figure 3.4 Triangular inversion (a) and rectangular inversion (b) for simulated earthquake Figure 3.5 Laplacian Operator Smooth on patches, where i,j indicates the i th patch in strike direction and j th patch in dip direction Figure 3.6 An illustration of the L-curve method Figure 3.7 Quadtree subsampling (left) and Uniform subsampling (right) Figure 4.1 (a) Interferogram of ALOS PALSAR for Sichuan earthquake (Track 475)52 Figure 4.2 DInSAR measurement and Modelling result comparison Figure 4.3 Slip distribution of the Sichuan YB fault Figure 4.4: (a) Slip distribution estimated for L Aquila earthquake in 2009 of track 79. (b) Slip distribution estimated from track v

10 Figure 5.1 New Zealand seismic sequence: focal mechanisms of main earthquakes from GCMT. Aftershocks from USGS until 10 th Mar Figure 5.2 Overlapping area for ENVISAT and ALOS sensor Figure 5.3 ENVISAT interferogram (Left) and ALOS interferogram (Right) comparison in radar coordinate system Figure 5.4 LOS displacement measured by ENVISAT and ALOS for 2010 Darfield earthquake Figure 5.5 Slip distributions from ENVISAT for the 3 rd September 2010 (UTC) Darfield earthquake Figure 5.6 Slip distributions from ALOS for the 3 rd September 2010 (UTC) Darfield earthquake Figure 6.1 Seismic events occurred in the first 24 hours Figure 6.2 Seismic events happened from Main shock to the first 24 hours of 12 th May Event Figure 6.3 Time line of image captured in the first month of Gorkha Earthquake occurred Figure 6.4 GPS locations and Nepal earthquakes sequence sketch Figure 6.5 Forward modelled 3D components (U E is East component, U N is North movement, and U Z is vertical deformation) Figure 6.6 Modelled interferogram and Observed LOS interferogram Figure 6.7 Comparison between modelled and measured coseismic deformation Figure 6.8 Slip distribution of 2015 Gorkha Earthquake Figure 6.9 Gorkha Main Shock Fault Geometry in 3D Figure 6.10 Modelled Displacement Map (a) and Wrapped Phase (b) Figure 6.11 Observed (a), modelled (b), residual displacement maps (c) of ALOS-2 PALSAR-2 ScanSAR interferogram relating to the 12 th May Event. (d) is the profile plotting of (a) and (b) Figure 6.12 Slip distribution of the Second Major Shock on 12 th May Figure 6.13 Observed result of both events, the red stars are the epicentre Figure 7.1 Stripmap image covering Kathmandu area, the white dot lines are the preliminary fault Figure 7.2 Coverage of Stripmap and ScanSAR images Figure 7.3 Relationship between ascending and descending tie points Figure 7.4 Sampling points vi

11 Figure 7.5 Gaussian Kernel based sampling histogram Figure 7.6 Modelling semivariogram and coherence Figure 7.7 Final LOS displacement map generated from contour map Figure 7.8 Clipped area for comparison Figure 7.9 Comparison of modelled and Stripmap results Figure 7.10 Slip distribution of the 2015 Gorkha Earthquake from combined modelling List of Tables Table 2-1 Satellite Sources comparison Table 3-1 Range of each angle parameter Table 4-1 Images for Interferometric Pairs Used Table 4-2 Nonlinear Results for 2008 Sichuan earthquake and 2009 L Aquila earthquake Table 5-1 Darfield Earthquake Data Sets Table 5-2 Source parameters of Darfield earthquake Table Nepal Earthquake Data Sets Table 6-2 Focal mechanism solutions for Gorkha Main Shock (USGS, 2015b) Table Gorkha Earthquake Nonlinear Inversion Table 6-4 Moment tensor solutions Table 7-1 Source parameter for 2015 Gorkha Earthquake vii

12 Table of contents Abstract... i Acknowledgement... ii List of Publications... iii List of Abbreviations... iv List of Figures... v List of Tables... vii Table of contents... viii Chapter 1 Introduction Seismic deformation mapping with InSAR method Co-seismic slip distribution modelling based on InSAR results Current research problem and challenges Thesis objectives and contributions Thesis structure... 6 Chapter 2 Co-seismic deformation observed from InSAR Earthquake mapping from InSAR observations DInSAR displacement map generation procedure Interferogram generation Multilook, filtering procedure and coherence Generation Phase unwrapping Refinement and re-flattening process Phase to displacement map and geocoding Discussion on limitations of InSAR observation Multi-frame method Contour assisted coverage expansion Concluding remarks Chapter 3 Earthquake modelling methodology Forward modelling and non-linear modelling strategy Fault geometry definitions Okada forward modelling Non-linear inversion procedure LOS and 3D displacement Linear inversion procedure Green s function and unweighted slip distributions Laplacian operator constraint Weighting strategies Inversion with weight and ramp consideration Concluding remarks and future works Chapter 4 InSAR coseismic deformation mapping for 2008 Sichuan and 2009 L Aquila earthquakes Introduction DInSAR data analysis Modelling method Discussion Concluding remarks Chapter 5 Deformation detection by InSAR of 2010 Darfield earthquake Introduction for Christchurch area DInSAR results analysis InSAR data processing InSAR deformation detection Modelling procedure and result analysis Concluding remarks Chapter 6 The 2015 Nepal earthquake sequence modelling by ScanSAR results Background introduction InSAR data analysis Modelling strategy and processing viii

13 6.4 Discussion of the main shock on 25 th April, Discussion of the second major shock on 12 th May Concluding remarks Chapter 7 The ScanSAR assisted Stripmap expansion for emergency response Limitation of Stripmap Coverage Contour generation for coverage expansion Discussion of the results Concluding remarks Chapter 8 Conclusions and future research Conclusions Recommendations for future research References ix

14 Chapter 1 Introduction Natural hazards such as earthquake disasters can cause loss of life or property damage. Unfortunately, reliable predictions of devastating earthquakes are not currently possible (Shearer, 2009), and short-term earthquakes cannot be predicted even in a seismically active area such as Japan (Uyeda, 2015). However, researchers are making efforts to improve understanding of the mechanism of underground earthquakes. To alleviate the adverse impact of earthquakes, various kinds of geophysical techniques are utilised for earthquake mechanism research. Ground or space based techniques such as seismographs which record the seismic wave, levelling measurements of relative deformation of the surface and the GNSS (Global Navigation Satellite System) such as GPS (Global Positioning System) that offers vertical and horizontal movement information are commonly used to monitor earthquakes. Network continuous GPS receivers in seismically active regions also provide continuous temporal coverage monitoring the region. 1.1 Seismic deformation mapping with InSAR method Geodetic measurements like levelling and GPS results are accurate but discrete observations may suffer from the spatial density limitation problem (Rosen et al., 2000). It is usually time consuming and costly to carry out a very dense spatial observation. Interferometric Synthetic Aperture Radar (InSAR) technology obtains large scale surface deformation of the Earth with a centimetre-level accuracy in a certain time period, thus providing an unprecedented way of evaluating the natural geophysical phenomena that causes or is derived from surface deformation (Atzori and Salvi, 2014). With the penetration ability of the 1

15 radar beam from space to the Earth s surface, InSAR technology generates an interferogram of certain areas in a acceptable time duration using repeat-pass interferometry. Through phase interferometry methods, surface subsidence on Earth such as urban subsidence, landslide and seismic deformation are detected in the line of sight (LOS) direction. The active microwave radar intrinsically has the all-weather, day and night capability to map the Earth s surface, with applications such as the Digital Elevation Model (DEM) generation, surface deformation detection, volcano deflation, glacier movement monitoring and many other applications (Massonnet and Feigl, 1998). As Figure 1.1 depicts, an earthquake cycle is usually divided into three or four stages. Observations of surface deformation can be utilised to constrain and model slow strain changes which are found in seismically active regions. Seismic cycles are commonly defined as interseismic, co-seismic and post-seismic (Shearer, 2009) or even a theoretical preseismic cycle. The sudden surface change occurring in the region is termed as co-seismic change and following this co-seismic cycle the stage before the next earthquake occurrence is defined as post-seismic (Shearer, 2009). The seismic cycles are depicted in figure

16 Figure 1.1 Four seismic stages: Red line shows the inter-seismic stage, black dash line shows the pre-seismic stage, green line depicts the co-seismic stage, and orange dash line the post-seismic stage Considering the temporal baseline of the satellite SAR data, InSAR has the advantage of mapping the inter-seismic, co-seismic change and the postseismic stage of an earhtquake. The two-pass radar interferometry is a powerful technique to map the co-seismic deformation by using an interferogram generated from an image taken both before and after the earthquake. This work utilises a C-band satellite ENVISAT (Advanced Synthetic Aperture Radar) ASAR and L-band ALOS (Phased Array type L-band Synthetic Aperture Radar) PALSAR datasets. With InSAR observations, co-seismic slip distributions are inverted and analysed (Pedersen et al., 2003, Wang et al., 2007). The co-seismic slip distributions are then utilised to drive sophisticated modelling simulations of the earthquake and this information can be used to assess the risk to the area. To obtain the fault slip distribution occurred during an earthquake, displacement 3

17 maps can be obtained through InSAR processing, followed by data inversion based on some ad hoc geophysical model. More details of the basics of DInSAR displacement map generation are discussed in Chapter Co-seismic slip distribution modelling based on InSAR results The first scientific publication utilising InSAR to map an earthquake was written by Massonnet et al. (1993) mapping the Landers (California) earthquake in In geophysical modelling, good results can be obtained by approximating the Earth to an elastic half space, exploiting the analytic solution proposed by Okada (1985). After much research and many observations, the focal mechanism of the 1992 Landers earthquake inverted from the InSAR result was published by Feigl et al. (1995). Massonnet and Feigl (1998) summarised the procedure of slip distribution inversion in two stages: (1) Find the best fit parameters with the observations by non-linear inversion and (2) Obtain the slip vector by linear inversion. Moreover slip distributions on the fault plane subdivided into patches assuming uniform slip cannot be simply inverted due to the complicated fault geometry and data error. The InSAR data errors come from many different sources. The first one is the radar instrument itself which causes problems like speckle noise, and the other data errors arise from the wave path through the atmosphere and the reflection of the surface (Hanssen, 2001). In order to tackle these problems, data weighting utilising variance covariance matrix and smoothing constraints for the inversion steps e.g. (Jonsson, 2002, Lohman, 2004, Sudhaus, 2010). 4

18 1.3 Current research problem and challenges Geodetic data such as GPS and satellite data have been utilised by earthquake researchers and geologists around the world to study the Earth s tectonic plate movements. The slip distributions are inverted by a modelling method using the geodetic data. Geoscientists are most interested in the slip distributions to estimate catastrophic quakes. However, to respond to the earthquake event as soon as possible, and to validate the reliability of the results, images taken in different modes are analysed. The challenge for satellite obtaining good results from is the balance between resolution and coverage. The higher the image resolution is, the smaller area the image covers. Large scale earthquakes such as the 2008 Sichuan earthquake and the 2015 Nepal earthquake impacted large areas and generated long fault lines, thus a single track or single frame image will not be sufficient to cover the entire seismic zone. Due to the revisit time limitation for a satellite, methods using multi-frame images in earthquake research are applicable but not ideal for an emergency response in practice. 1.4 Thesis objectives and contributions This research work is based on using DInSAR data to invert a co-seismic fault plane on the rectangular geometry and to find slip distributions for geoscientific analysis using SARscape and Matlab. The first objective is to generate optimised DInSAR results. Both C-band and L- band satellite InSAR data are used and studied to optimise the displacement map generation, such as reducing the influence from orbit, terrain correction and phase unwrapping. The 2008 Sichuan earthquake in China, the

19 L Aquila earthquake in Italy, the 2010 Darfield earthquake in New Zealand and the 2015 Nepal earthquake have been selected as case studies where there have received a lot of recent research attentions. To capture large scale earthquakes such as the 2008 Sichuan earthquake, a multi-frame of interferograms are mosaicked to carry out inversion for the slip distributions. The second objective is to model the slip distributions of the earthquakes listed above. The inversion algorithm based on Okada forward modelling constrained by the Levenberg-Marquardt algorithm is utilised for non-linear inversion. Second order Laplacian smoothing is applied to the slip value division constraints and a non-negative least square condition is imposed for linear inversion to obtain the slip distribution. The third objective is to invert the slip distributions using ScanSAR data and Stripmap data and to demonstrate the possibility of combining the datasets. The contributions of this research are: Working on C-band and L-band datasets to illustrate the advantages and disadvantages for each source of data; Modelling results of the 2015 Nepal earthquake using ScanSAR data were generated; Combining Stripmap and ScanSAR datasets for inversion to obtain high resolution image for possible quick response to earthquake events. 1.5 Thesis structure There are 8 chapters in this dissertation. Following the introductory chapter, the rest of the thesis is organised as followes. 6

20 In chapter 2, an introduction of the use of InSAR to map the co-seismic area is given. This chapter provides the InSAR theory and procedure of displacement map generation. Case studies such as the 2008 Sichuan earthquake and the 2009 L Aquila earthquake are discussed with consideration for different phase contributions to optimise the DInSAR result. A possible extended modelling interferogram method combining Stripmap and ScanSAR data is introduced. Chapter 3 presents the modelling method for earthquake studies, particularly the parameters for the Okada model. Their impacts are discussed, and the nonlinear inversion is conducted with constraints for the fault geometry. The data weighting and covariance sampling method will be discussed for the linear inversion process and the smoothing procedure to construct Green s function is deduced. In chapter 4, the co-seismic studies of the 2008 Sichuan earthquake and the 2009 L Aquila earthquake are analysed. The deformations of the two events were obtained from L-band and C-band interferogram for co-seismic research for each event respectively. The non-linear inversion applies a cost function based constraint to retrieve the source parameters of the fault plane. This defined fault geometry is then applied in the linear inversion procedure with a damping value. These two earthquake events are modelled by rectangular fault geometry and slip distributions are given, showing mosaicked L-band image capability and C-band ability for deformation detection and co-seismic modelling for each specific case. In chapter 5 the 2010 Darfield earthquake subsidence is analysed using L-band and C-band satellite resources. The distributed slips which are inverted from the source present the trend and risks of the possible triggering mechanism for the 7

21 second event which happened in A multi-faults modelling method is utilised for the Darfield earthquake, and it is found that a three faults system has the best-fit for both L-band and C-band observations. This chapter shows the Stripmap image for modelling procedure of the same event with different datasets from different wavelengths. In chapter 6, ScanSAR interferograms for the 2015 Nepal earthquake sequence were analysed and utilised for slip inversion. Both the M w 7.8 main shock and M w 6.3 second major shock were captured in the ALOS-2 ScanSAR data. Based on the observations, the modelling results were analysed. Single fault models were utilised for both events, indicating the dip-slip thrust fault with slightly right-lateral trend for the fault planes. In chapter 7, a new method was developed to model an earthquake event with high resolution images derived from Stripmap and ScanSAR images. The high resolution Stripmap image cannot fully cover the city of Kathmandu in the 2015 Gorkha earthquake, while the coarse resolution ScanSAR image achieved this. Combining the two modes of observation resulted in an extended interferogram using contour. It showed use of the implemented contour method is possible to expand and estimate the impacted area of the main shock. In chapter 8, the main findings are summarised and the potential future work on the co-seismic modelling from InSAR observations are outlined to conclude this thesis. 8

22 Chapter 2 Co-seismic deformation observed from InSAR This chapter focuses on the principles of the InSAR technique, the steps followed and methods of overcoming its limitations. Section 2.1 discusses the development of InSAR using in mapping earthquake, and section 2.2 introduces DInSAR procedure, while section 2.3 explains how contour works in expanding observing area. 2.1 Earthquake mapping from InSAR observations Since the very early research on the 1992 Landers earthquake (Massonnet et al., 1993), geophysicists have benefited greatly from using DInSAR data to describe the surface crustal changes due to earthquakes or inflation of a volcano. With a nominal 5.6 cm C-band wavelength ability, satellite sources such as ERS or ENVISAT were acquired to map seismic changes. By tracking the observed displacement at different time intervals for the Landers area, the focal mechanism was inverted (Feigl et al., 1995). This early research was the first publication describing where remote sensing, rather than an instrument on the ground, determined the focal mechanism. Later researchers applied ERS data to seismic events such as the 1997 Umbria-Marche sequence earthquake (Salvi et al., 2000), the strong motion of 1999 Izmit earthquake in Turkey (Delouis et al., 2002), and 1999 Hector Mine earthquake in California, USA (Fialko et al., 2001, Jonsson, 2002, Put, 2008). ENVISAT is the continuity of ERS, with its data enhanced resolution and effective performance in arid areas, it supported many observations and analyses of co-seismic events such as the 2003 Bam 9

23 earthquake in Iran (Talebian et al., 2004, Funning et al., 2005) and the 2009 L Aquila earthquake in Italy (Atzori et al., 2009, Wang et al., 2010, Guerrieri et al., 2010) Apart from C-band resources, L-band resources, such as JERS, ALOS and many others with their 23 cm long wavelength ability of penetration in certain areas, are recommended to alleviate influences such as vegetation. Large earthquakes which easily cause phase saturation, will lead to co-seismic deformation being underestimated, like the 2008 Sichuan earthquake, are better observed using L-band resources (Ge et al., 2008, Li et al., 2008, Chini et al., 2010). In the meantime comparison with C-band radar, GPS work is also provided (Guglielmino et al., 2009, Wei et al., 2010). Co-seismic deformation can be captured by multi-pass method, or two-pass radar interferometry with an external DEM available.in this work, Shuttle Radar Topography MissionDEM (SRTM) is utilised to eliminate the topographic phase influence. The procedure used to generate the displacement map and result optimisation is discussed in section DInSAR displacement map generation procedure In this section, we outline the basics of DInSAR processing. At present, both spaceborne and airborne radar systems are utilised to form interferograms. Spaceborne resources have the advantages such as global coverage with less turbulence impact and easier trajectory control (Massonnet and Feigl, 1998). This section focuses on spaceborne DInSAR result generation. 10

24 2.2.1 Interferogram generation The phase change of an electromagnetic signal wave variation is caused by the Earth s physical change. However, to form an interferogram, at least two acquisitions are needed; coregistering the two images is the fundamental step before interferogram generation. Ideally, the following conditions should be met: the same sensor, same area appropriate the same sensor location and the same view geometry (Figure 2.1 (a)). However, it is difficult to beam the wave at the same sensor location every time. A critical interferometric baseline then is applied, which will be discussed in later sections. (a) (b) Figure 2.1 Satellite SAR geometry sketches We process the interferogram from Single Look Complex (SLC) data, after the coregistration step, following the general equation (2.1) to obtain an interferogram (Massonnet and Feigl, 1998). I = f(m)f(s )exp (2πiG) f(m) 2 f(s) 2 (2.1) where M, S and G are implicit functions of the image point coordinates, M is the master image, S is the slave image while the asterisk denotes complex 11

25 conjunction, and G is the function of eliminating the phase differences due to orbits and topography. The phase of I in equation (2.1) is the interferogram. Phase difference can be simply defined as MS, and the filter f applied to both master and slave images to increase the Signal Noise Ratio (SNR) of the fringes. The change in surface deformation can cause a phase change in the obtained radar data. This observed phase information is limited or wrapped in the interval [ π, π), which is a part of the signal components of interferogram. The interferogram formed from SLC data is usually referred to as raw interferogram, in other words, an interferogram contains all the phase information, and is generated with the function model as follows (Kampes, 2006): ϕ k k p = W{ϕ p,topo k + ϕ p,defo k + ϕ p,obj k + ϕ p,atmo k + ϕ p,orbit k + ϕ p,noise } (2.2) where W{.} indicates the wrapped phase function, k is the number of the k interferogram, p is the point of target cell, ϕ p,topo is the phase contribution from the topography of the k th k interferogram, ϕ p,defo is the phase caused by k displacement of a target point between the acquisition periods, ϕ p,obj is the object scattering phase related to the travelled path of the wave in the pixel cell, k k ϕ p,atmo is the influence of atmospheric phase consideration, ϕ p,orbit is the phase k coming from imprecise SAR sensor orbit data, and ϕ p,noise is the noise term from the SAR system and other additives. Considering the DInSAR procedure, after the interferogram flattening, the dominant phase components of DInSAR comprise topography and deformation impacts as illustrated in Figure 2.1 (b) are shown in equation (2.3) (Hanssen, 2001) and depict the topography and deformation impact respectively: 12

26 φ p = 4π λ (D defo + B,p R p sin θ p 0 H p ) (2.3) Here λ is the wavelength, D defo is LOS surface deformation, B,p is the perpendicular baseline, R p is the range from the scatter p to the sensor, θ is the looking angle and H p is the height of the cell point. With the assistance of an external DEM, the topography term (equation (2.4)) (Ferretti et al., 2007) can be subtracted and the deformation can be obtained. φ(p) = 4πB,p λr p [ΔR(p)] (2.4) Here φ(p) is the topographic phase computed on a regular grid, B,p is the perpendicular baseline, λ is the wavelength of the microwave, ΔR(p) is slant distance between sensor-target Multilook, filtering procedure and coherence Generation The phase obtained in the raw interferogram is usually rather noisy, especially in the two-pass interferogram due to temporal decorrelation. Multilook and filtering can increase the SNR. One simple method is by averaging adjacent pixels in the complex interferogram. There are several implemented ways to generate multi-looked interferogram, but a fixed mask is the most efficient and simplest. The simple multilook number calculation is illustrated in Figure

27 Figure 2.2: Multilook Geometry The illustration depicts the slant range relation in terms of ground range. The cross mark is the flight path, Δr g is the ground spacing in range direction, Δr is slant range spacing, and θ is the incidence angle. The ground resolution is then calculated as: Δr g = Δr/ sin θ (2.5) Taking ALOS PALSAR FBS (Fine Mode Single Polarisation) SLC data as an example, if the azimuth resolution is 3.17 m and ground resolution is 7.49 m, the possible multilook number could be 2 in terms of range and azimuth direction ratio. A similar calculation can be applied to ENVISAT ASAR satellite data to give a possible azimuth to range compression ratio of 1:5 (Figure 2.3). 14

28 Figure 2.3: Multilook example (ENVISAT): (a) the original interferogram intensity image, (b) multi-looked intensity image showing phase overlapped The raw interferogram can be flattened by subtracting an Earth ellipsoid. The flattened interferogram can also utilise external DEM to perform further topography phase reduction. In addition, the complex multilook procedure reduces uncorrelated noise due to temporal, baseline and volume, but is not able to remove spatial-correlated artefacts (Ferretti et al., 2007). The adaptive 15

29 filter (Goldstein and Werner, 1998) is applied in this study due to its effectiveness to increase SNR (Figure 2.4). (a) (b) (c) (d) Figure 2.4: Filtered example images of Christchurch area from ALOS dataset (a) Raw interferometric phase (b) Filtered interferometric phase (c) Original intensity (d) Filtered intensity 16

30 The interferograms in figure 2.4 are wrapped phase information. From the phase information, an estimated coherence of the two images can be generated (equation (2.6)). The coherence value demonstrates another powerful way to measure the interferogram quality (SNR). Estimated from 0 to 1, the higher coherence value indicates the better measurement or higher SNR of the pixel (Gatelli et al., 1994). u 1 (x)u 2 (x) γ x = (2.6) u 1 (x) 2 u 2 (x) 2 Here u i (x) is the single look complex number of the target on the SAR image, u i (x) is the conjugate of the corresponding target, and i indicates the master and slave image when it equals to 1 or 2 respectively. The estimated coherence could be extracted either from the original interferogram or the filtered interferogram. In my research the coherence map generated from the filtered interferogram is based on several considerations: (1) the coherence decreases linearly with the baseline, becoming zero when it reaches the critical length of the baseline ( B cr ) ; (2) the coherence intuitively shows the temporal decorrelation between the master and slave acquisitions with a longer time baseline; (3) the systematic spatial decorrelation of the two images Phase unwrapping As discussed in section the obtained phase is wrapped, due to the measurement of the phase cycles which can only be of modulo 2π; hence any phase larger than 2π will be wrapped. Phase unwrapping is a procedure to resolve the phase ambiguity and rebuild the relative phase difference in equation (2.7). Ψ = φ + 2π n (2.7) 17

31 Where Ψ is the unwrapped phase, φ is the phase modulo, while n is the integer ambiguity between the unwrapped phase and the wrapped phase. If prior information such as ambiguity integer n is obtained, the phase can be rebuilt. Phase attributions as described in equation (2.2), such as the inherent speckle noise, atmosphere or other artefact influences like topographic residual, will impact the final results and cause problems, if not eliminated. To overcome the problem, algorithms are developed such as branch-cut (Goldstein et al., 1988), minimum least square (Ghiglia and Romero, 1996), Minimum Cost Flow (Flynn, 1997, Costantini, 1998), SNAPHU (Chen and Zebker, 2000), multi baseline (Lachaise et al., 2007). Many significant developments in understanding the interferogram phase unwrapping theory have been made but they have some drawbacks when dealing with real datasets (Gens, 2003). Since we have no prior information about the integer part to rebuild the absolute phase, phase unwrapping is based on the assumption that the correct unwrapped phase field is smooth and the gradient varies slowly. More precisely, the gradients between neighbour pixels are limited in π radians, or half cycle of the phase. However, the integral of the estimated phase gradient is influenced by the noise, atmosphere and other artificial factors. The decisive issue for phase unwrapping is to deal with the phase integration exceeding the limitation, such as a defined residual. A residual can be calculated easily by summing the wrapped phase differences around the closed paths of the neighbouring four pixels. Either a positive (+1) or negative (-1) sign is assigned to wherever the summation is non-zero (Goldstein et al., 1988). Connecting the residuals in terms of zero summations, a branch-cut algorithm avoids the integration of any path through the branches carried out by the algorithm. Minimum cost flow 18

32 considers the discontinuity and is more efficient for dealing with large datasets (Zhang, 2011). In essence, these algorithms are required to apply or combine on a case by case basis to get optimal results. In the case of earthquake interferogram interpretation, a large area could have low coherence due to the spatial decorrelation or phase saturation, thus MCF can give a more robust result. The area where coherence is lower than a threshold, which covers most of this study at 0.2, is masked out. From the interferogram, some empirical aspects can be considered such as the dark surface defined as lakes, and bright crests are usually suspected to generate ghost lines during the phase unwrapping procedure (Massonnet and Feigl, 1998) Refinement and re-flattening process At this stage the interferogram is generated, but before transforming the phase into displacement and geocoding, the residual orbital contribution in the interferogram can be removed as much as possible through refining the orbital correction. This process refines the orbit and calculates the phase offset or remove the possible phase ramp. It is a crucial process because the phase difference is relative rather than absolute. Ground Control Points (GCPs) are needed for the refinement processing, which is also named Orbital GCPs. Without GPS information, the GCPs will be regarded as zero velocity at the selected area on the DEM. Two methods are generally utilised for this process in my research. Method one is orbital refinement. The GCPs are used in the orbital model to correct the inaccuracies, though it is not feasible to apply this to all corrections. Massonnet et al. (1998) 19

33 provided a method of tuning the slave orbit by choosing the four corner points of the interferogram and performing refinement. The orbit of the slave image is tuned and the phase in the interferogram then reflattened. Method two is to apply a polynomial approximation to remove the residual phase (equation (2.8)). K = a + bx + cx 2 (2.8) Several technical issues are considered for choosing the refinement and reflattening method: (1) A-priori RMS is larger than achievable RMS or a-posteriori RMS; (2) A-priori check is larger than the minimum baseline; (3) Selected number of GCP is lower than 7. The Residual Phase Refinement method is applied to situations that meet any of the conditions above; otherwise the orbital refinement correction is used. However, if an obvious phase ramp presents in the interferogram, a polynomial of order 1 is suggested to remove the ramp (Figure 2.5). Figure 2.5 (a) depicts the displacement map from a ramped interferogram; figure 2.5 (b) gives the comparison to a ramp removed interferogram. 20

34 (a) (b) Figure 2.5 (a) original interferogram with phase ramp (L Aquila) (b) Refined by polynomial correction Phase to displacement map and geocoding The final step in DInSAR result generation is transferring the unwrapped phase into displacement and geocoding the result from azimuth-slant range coordinate to the Geographic Coordinate System. As SAR detects the deformation on LOS direction, the increase of terrain slope will influence the ground resolution cell on SAR images. Three effects are needed to consider when geocoding the final InSAR product: (1) Foreshortening, which is caused by the increase of terrain slope, will increase the ground resolution cell dimension; (2) Layover, when the slope exceeds the radar off-nadir angle, will reverse the scatterers imaged and super imposed on the contribution calculated from other areas; (3) Shadowing, when the terrain is parallel to the LOS, will make all the information in shadow not collectable (Ferretti et al., 2007). More importantly, the earthquake modelling is based on an elastic half-space model, which transforms the coordinates between the model and interferogram measurement in terms of 21

35 Cartesian Coordinate System (CCS) to the Geographic Coordinate System (GCS). Universal Transverse Mercator (UTM) projection is the fundamental map projection used in this research. 2.3 Discussion on limitations of InSAR observation The InSAR technique is used in monitoring the subsided area with superior dense observations, with the cost of short time baseline; in other words, discontinue observation time period between each repeat observations. The revisiting time of different satellites is varied due to different operating modes (Table 2-1). The narrow swath cannot fully cover the co-seismic area with a single track or frame when the earthquake is devastating and powerful. For example, the 2008 M w 7.9 Sichuan earthquake in China and 2015 M w 7.8 Gorkha earthquake in Nepal, both generated a fault line of hundreds of kilometres. Table 2-1 Satellite Sources comparison Satellite ALOS ALOS 2 ENVISAT Revisit time 46 days 14 days 35 days Spatial Resolution Stripmap: 10 m Stripmap: 3 m/ 6 m/ 10 m Image mode: 28 m 28 m ScanSAR: 100 m ScanSAR: 100 m Wide Swatch mode: 150 m 150 m Spotlight: 1 m 3 m Global Monitoring: 950 m 980 m When an earthquake happens, the satellite can capture the co-seismic image at each revisit time concentrating on the damaged area. However, as discussed above, if the fault line is longer than the width of the single image swath, then we need to consider other image availabilities to fully cover the area. 22

36 2.3.1 Multi-frame method The classic method using multiple tracks and frames is developed to capture the whole seismic area when the fault is longer than the satellite swath. Ge et al. (2008), Chini et al. (2010) and Tong et al. (2010) utilised 6 tracks of ALOS data from Track 471 to 476 to cover the full length of the coseismic area of the 2008 Sichuan earthquake, and analysed the mosaicked DInSAR interferograms results. De Michele et al. (2010) processed the same tracks and used subpixel correlation to invert the 3-D displacement of the event. Similar works were done for the 2010 Christchurch earthquake sequence in New Zealand. Beavan et al. (2011), Stramondo et al. (2011) and Salvi et al. (2012) utilised the ALOS image of 2 paths of ascending images and 1 path of descending images to cover the whole area. Multiple frames can cover the seismic area, but there are assumptions that during the revisiting period the interferograms are consistent with each other, and any deformation detected in each track is dominantly contributed by the main shock. These assumptions are based on the situation where there were no significantly large aftershocks between each capture Contour assisted coverage expansion However, the stripmap images are not always available when an earthquake occurs. ScanSAR images cover much larger areas, and usually can cover the whole seismic fault, but with coarse resolution. One possible solution is to combine the two resources together. Based on the high resolution stripmap image, with the assistant information from ScanSAR, we can generate contour lines of the interferogram, thereby remodelling an interferogram that is 23

37 expanded to cover the whole seismic area with accuracy dominantly consistent with a stripmap image. (a) Difficulties to Overcome To incorporate a Stripmap dataset with a ScanSAR source, several conditions should be met to overcome difficulties and satisfy the final results. The first condition is, to ensure accuracy, the Stripmap images selected should cover more than half the cycle of each fringe, which contains the most interferogram information. Figure 2.6 shows the example of the 2015 Gorkha earthquake, a narrow high resolution Stripmap image was captured and covered the dominant fringes in the interferogram. Figure 2.6 ScanSAR image assists Stripmap boundary example (2015 Gorkha earthquake) 24

38 The background image is the ScanSAR result, while the red lines indicate the sampling ScanSAR area for contour generation. The selected ScanSAR areas provide the trend information of the interferogram. While it is obvious that the Stripmap covers dominant properties of the fringes, the ScanSAR can define the trends using the Stripmap image accurately. From Figure 2.6 the trend is depicted and contours can be extracted and generated. The second difficulty to be considered is the ascending and descending LOS displacement of the two datasets. Ideally both images are taken from the same direction of view, but in this research looking from the ascending and descending viewpoints lead the LOS displacement to be slightly different. The third challenge is the sampling density of points for contour generation, considering the workstation capacity for Kriging algorithm. (b) Methodology The flowchart for the proposed approach is illustrated as below (Figure 2.7): 25

39 Figure 2.7 The flow chart of Contour Based Modelling Besides the slip distribution modelling (which is discussed in Chapter 3), the modelled contour for interferogram generation is illustrated in the flow chart. With the ScanSAR image s larger coverage to model the interferogram, the contour generated based on the Stripmap image can approach over the image boundary limitation (Figure 2.6). When two InSAR image pairs are available, the contour can then be generated. To deal with the ascending and descending LOS viewing problem, considering the image resolution is 10 metre verses 100 metre, the vertical component is the main component to be calculated. Taking the vertical deformation for each 26

40 observation pairs, the relationship between the ascending observations at the same location to the descending observations is shown in equation (2.9). D Asc = f(d Des ) (2.9) Here D Des is the descending observations from InSAR images, D Asc is the ascending observations in respect to the same points, and f is the function handle between the two observations. To reveal the function f, it is not simply a matter of projecting or shifting the data. The first step to consider is the geometry should be implemented using trigonometric functions, and then applying linear regression to best fit the two datasets (Figure 2.8). The assumption here is that the contribution of horizontal movements to LOS in each pixel can be ignored, due to the multi-looked pixel size being large enough. Figure 2.8 Linear Regression of Ascending and Descending Observations at same points Referring to the third difficulty, generating an accurate contour for modelling, this is more related to a hardware issue. The Stripmap originally has 3 m in azimuth resolution and after applying multilook, the image is down-sampled to 27

41 10 m resolution. The whole co-seismic area covered in the Stripmap image will have appropriately 10 million points, which imposes heavy computation in addition to the ScanSAR points. The strategy here is to sample the areas of interest with dense observations and other areas with fewer observations. To preserve the 10 m resolution information obtained in the Stripmap interferogram, the sampling points in the deformation area reach 104,438, then adding the ScanSAR points shown in Figure 2.6 selected along the red line, they reach a total number of 113,588 points. After resolving the problems and difficulties, the Contour Map is produced and the Kriging modelled interferogram can be utilised for further analysis (Figure 2.9). Figure 2.9 The Sampling area and the modelled Interferogram 28

42 2.4 Concluding remarks DInSAR, with its ability to measure the surface deformation of the seismic area at centimetre accuracy, has shown its superior advantages to detect subsidence. With wide coverage and remote access to the target area, the relative displacement accuracy is obtained through the wrapped phase. The MCF method for phase unwrapping presents its superior fast and accurate ability to process large satellite datasets (for example a pair of ALOS data can be as large as 3 GB in single polarization mode). Multi looking of the interferogram can increase the processing speed but sacrifices the image resolution. Nevertheless, nowadays with new satellite sensors, SAR images can be obtained at higher resolution, which counteracts this impact and increases the processing speed. Phase information obtained from the DInSAR technique shows the scale of damage and a geoscientist can analyse the deformation and assess the risks. Whether the deformation is captured by a single track, multi frame, or with the ScanSAR combined Stripmap modelling method, observation which fully covers the fault line is always achieved and prepared for further analysis or modelling. 29

43 Chapter 3 Earthquake modelling methodology After obtaining the surface deformation from the InSAR result, an elastic model can be applied to research earthquakes. This chapter is introducing the modelling procedure. The two main steps are introduced. Section 3.1 is the forward modelling procedure and Section 3.2 discusses the linear inversion algorithms. 3.1 Forward modelling and non-linear modelling strategy An earthquake can cause surface deformation and even rupture of the earth surface. Geoscientists use a variety of models to describe an earthquake fault with many parameters; these parameters are explained in Section Utilising these parameters to model the surface deformation is called forward modelling (Massonnet and Feigl, 1998) Fault geometry definitions An earthquake can be modelled by fault planes which are based on various seismic theories. The parameters to illustrate a fault plane are shown in Figure

44 Figure 3.1 Fault plane and parameters A fault plane (shaded area in Figure 3.1) is usually described first by its strike angle φ, which is defined as the azimuth of the fault, calculating from North to the fault strike direction where it intersects either the horizontal surface or the fault top edge. The dip angle δ is calculated from horizontal to the fault plane. This research follows the right hand rule for dipping direction, which along the strike direction, the hanging wall dips at right side. Rake is the angle calculating the slip value for hanging wall movement, which is set as the angle between the slip vector and the strike direction. Here the slip value is the distance that the hanging wall moves with respect to the foot wall. Each angle has a specific range and is defined in Table 3-1. The array of black arrows between hanging wall and foot wall in Figure 3.1 show the dilation, or as other literature described, the opening distance, between the hanging wall and the foot wall. 31

45 Table 3-1 Range of each angle parameter Parameter Range( ) Strike (0, 360) Dip (0, 90) Rake (-180, 180) Through the angles, the fault geometry is defined. When the rake angle increases from horizontal upwards, it is termed reverse fault, with an angle ranging from 0 to180. When the angle is counted downward, defined as 180 to 0, it is called a normal fault. Furthermore, reverse faults that dip less than 45 are named thrust fault, and nearly horizontal thrust faults are termed as over thrust faults (Shearer, 2009). The earth can be regarded and modelled as an elastic model, and the surface deformation caused by the fault can be inverted based on the theory of half space (Steketee, 1958). While geoscientists are most interested in the slip distributions on the fault plane, different theories have been established. For example either a rectangular (Okada, 1985) or triangular (Barnhart and Lohman, 2010) slip dislocation is assumed on the isotropic half space. In this research, the half-space model from finite rectangular source is utilised, as the patch geometry and compute efficiency can be achieved easier and more accurately Okada forward modelling This dislocation theory in seismology was introduced by Steketee (1958), and then further analysed and deduced by Okada (1985). The rectangular fault can be described by the parameters addressed in section Strike angle, dip angle, rake angle, slip vector and dilation value can define the basic geometry of the fault. Furthermore, with the fault plane coordinates, the geolocation of the fault can be defined. Due to the interest in slip value as well as slip directions, 32

46 the fault geometry usually can be described with up to 10 parameters, namely strike (φ), dip (δ), rake (λ), strike-slip (U 1 ), dip-slip (U 2 ), fault width (W), fault length (L), dilation (dia), East coordinate of the source point (E) and North coordinate of the source point (N). The process that utilises the parameters to model the earth s surface deformation is called forward modelling. The surface deformation is derived based on fault geometry on Cartesian coordinate system (CCS) and then transformed to Geographic Coordinate System (GCS). These parameters are the initial value used to deduce the surface deformation (Figure 3.2). Figure 3.2 Fault Geometry and contributions to surface deformation (Adapted from (Okada, 1985)) These parameters on the fault plane affect the seismic area, which can only be validated by a huge number of observations. Before the InSAR technique was established, this model was usually theoretically proved Non-linear inversion procedure Once the surface deformation can be obtained, the parameters of a fault can be inverted to approach the deformation obtained from forward modelling. While 33

47 there are 10 parameters for a single fault, the inverted surface deformations are heavily dependent on the fault geometry. This procedure is a non-linear process. If the modelling is perfectly approached, the inverse problem then can be presented as equation (3.1). g(p) = d Obs (3.1) Here p is the parameters of the fault, d Obs is the surface deformation observed from DInSAR results, and g is the function model to transfer the parameters to deformation. In the elastic half-spacemodelling, it is assumed that the two lame s moduli, λ and μ, are equal because the rigid crust being determined as a Poisson solid. The Poisson s ratio can be deduced to 0.25 with equation (3.2) (Sheriff, 1974). ν = λ 2(λ+μ) (3.2) And substituting equation (3.2) into the function model gives: μ = μ+λ λ λ+μ λ+μ = 1 λ λ+μ = 1 2ν (3.3) To invert the parameters p in equation (3.1), an iterative linearised leastsquares scheme is utilised by Feigl et al. (1995) since the problem is not a sharply non-linear problem. To constrain the non-linear problem, a prior model value p 0 which comes from seismological focal mechanism can be utilised. To avoid the local minima (Atzori and Antonioli 2011), a downhill simplex algorithm using Monte Carlo restarts can be implemented in the uniform slip model (Wright et al., 2003, Wang et al., 2007). Another alternative algorithm is Levenberg-Marquardt s minimization algorithm (Marquardt, 1963), which is an algorithm mixed with Gauss-Newton s algorithm and the gradient descent 34

48 method. This algorithm can be implemented with multiple restarts to ensure convergence of the Cost Function as defined in Atzori and Antonioli (2011) LOS and 3D displacement The non-linear inversion approaches DInSAR observations and minimises the difference between the modelled deformation g(p) and d, which is in LOS (Line of Sight) direction. However, the forwarded modelling deformation is in 3D dimensions, depicting horizontal dislocation (East and North) and the vertical dislocation components. As discussed in Chapter 2, the InSAR observations are in the LOS direction, so the 3D crustal movements are projected into the radar LOS direction (Equation (3.4)). D east Coef east + D north Coef north + D up Coef up = g(p) (3.4) Where D east, D north and D up are the dislocations modelled from the non-linear inversion respectively. The Coef east, Coef north and Coef up are the coefficients from the radar incidence angle and azimuth angle. The geometry is illustrated in Figure 3.3, which is an example of an ascending track. 35

49 Figure 3.3 LOS and 3D deformation projection In Figure 3.3, α is the heading angle, θ is the incidence angle, and ΔR is the LOS deformation in DInSAR measurement. Regarding the coefficients, it is a trigonometric function from the view of LOS with respect to 3D dislocations (Fialko et al., 2001, Ng et al., 2011). The results are described in equation (3.5). [ sin θ cos α sin θ sin α cos θ] [ D east D north D up ] = d Mod (3.5) The question now turns to finding the parameters that minimise the difference of g(p) d Obs 2. Geoscientists are more interested in the slip distributions on the fault plane. This requires a linear inversion procedure, which is explained below. 36

50 3.2 Linear inversion procedure Green s function and unweighted slip distributions The linear inversion usually follows the nonlinear inversion results. The parameters are linearly related to the surface displacement, as occured with the slip vector on strike and dip direction respectively, and the dilation component for the Okada model (Atzori and Salvi, 2014). The fault plane can be subdivided into triangular (Barnhart and Lohman, 2010) or rectangular (Atzori et al., 2009) samples for slip inversion (Figure 3.4). The fault is divided into numbers of patches, which in the latter case are along the strike and dip directions. (a) (b) Figure 3.4 Triangular inversion (a) and rectangular inversion (b) for simulated earthquake This inversion can be set up in a matrix form as equation (3.6), which is a linear expression: d Obs = G U (3.6) Here d Obs are the displacements from geodetic measurement, which in this research it is the DInSAR LOS results. U is the slip vector along strike or dip direction, and G is a matrix consisting of Green s function that relates the slip 37

51 distributions (U 1 and U 2 ) on the fault to the surface deformation d LOS. There are two ways to construct the Green s function, either based on stress tensor (Hardebeck and Michael, 2006) or from the Okada model (Okada, 1985). This research utilises the latter to form the Green s function matrix, and equation (3.6) can now be described as equation (3.7). To specify the slip vector, here we use U ss, U ds instead of U 1, U 2. [ P1 G ss1 P1 G ssn Pn Pn G ssn G ss1 P1 P1 G ds1 G dsn ] Pn Pn G ds1 G dsn [ 1 U ss N U ss 1 U ds U N ds ] = [ 1 d Obs n d Obs ] (3.7) Pn Where there are n observations and the fault is divided into N patches. G ssn is the Green s function along strike direction to the n th point ( Pn ), which is contributed from the N th patch; G Pn dsn is the Green s function along dip direction to the n th point, which is contributed from the N th patch; U ss N is the strike slip on the N th N patch; U ds is the dip slip on the N th n patch; and d Obs is the observation at the n th point. As the observations are always more than the number of unknown slip vectors U, solving the problem generally requires solving the over-determined equations. The simplest case utilises the least square sense on data for modelling slip U Mod as equation (3.8): U Mod = G g d Obs (3.8) Here G g is the generalised inverse of G, and its expression in terms of G is deduced from different methodologies (Menke, 2012). Utilising the Green s function directly to construct G g is shown in equation (3.19) (Lohman, 2004, Atzori and Salvi, 2014). 38

52 G g = [G T G] 1 G T (3.9) This defined the generalised Green s function. Apart from uniform sampling, a resolution matrix can be obtained to subsample the geodetic dataset (Atzori and Antonioli 2011): R = G g G (3.10) However, to obtain the resolution matrix, Singular Value Decomposition (SVD) can also be utilised as equation (3.11) to form G g (Atzori and Antonioli, 2011, Reeves, 2013). G g = f(g) = V Λ 1 T U svd (3.11) Assuming G g is a matrix of M N dimensions, here V is a matrix of M M containing the individual orthonormal vectors with V V T = I. Λ is a matrix of N M diagonal eigenvalue matrix, where the diagonal elements are non- T negative. To avoid the ambiguity, U svd is specifically defined as an N N matrix of eigenvectors spanning the data space. Thus equation (3.10) is rewritten as: R = (V Λ 1 U T svd ) (U svd Λ V T ) = V V T (3.12) Laplacian operator constraint However, in practice, the slip values obtained from equations (3.8) and (3.9) are generally unrealistic. This is due to unconstraint or weak control distributions from the InSAR measurement to the physical fault parameters. To avoid high values or oscillations in the results, a common method using Laplacian Operator (equation (3.13)) minimizing the two-dimensional second derivative of slip distribution is applied in equation (3.6) to constrain the fault slip (Jonsson, 2002). 39

53 [ d Obs 0 ] = ( G κ 2 2) U (3.13) Where the Green s functions now are the G in equation (3.6) with extended Laplacian operator 2 on the modelled parameters and the Laplacian operator is weighted with the Lagrange multiplier κ 2 (Jonsson, 2002, Wright et al., 2003). To construct the Laplacian operator, the rectangular fault plane is subdivided into N patches along the strike and dip direction (Figure 3.5). Figure 3.5 Laplacian Operator Smooth on patches, where i,j indicates the i th patch in strike direction and j th patch in dip direction. The value is defined in terms of the patch area and the slip values in the neighbours (equation (3.14)): i,j = U i 1,j 2U i,j +U i+1,j ( l 1 ) 2 + U i,j 1 2U i,j +U i,j+1 ( l 2 ) 2 (3.14) The patches out of the boundary are assumed to have zero slip (Put, 2008), and this reduces the length and form of the Laplacian operator. Substituting the Laplacian operator equation (3.14) into (3.12), the matrix form of equation (3.13) which is similar to (3.7) then becomes equation (3.15) and equation (3.16: 40

54 [{ 0 1 ( l 1 ) ( l 1 ) 2 1 ( l 1 ) 2 0}] [ 1 U ss N U ss 1 U ds U N ds ] = [ 0] (3.15) { 0 1 ( l 2 ) ( l 2 ) 2 1 ( l 2 ) 2 0} [ 1 U ss N U ss 1 U ds U N ds ] = [ 0] (3.16) If we add equation (3.15) with equation (3.16), the 2 along the strike direction is obtained, and a procedure is then applied for the dip direction. The smoothed function model of (3.13) is now implemented as equation (3.17): G ss G ds 2 0 ( κ 2 ss ) U = [ d Obs 0 κ ] (3.17) ds The variables inside parentheses are the smoothed Green s function, and the same symbol G is used for presenting the smoothed Green s function with constrained equation. By substituting equation (3.17) with equation (3.8), the modelled slip vectors will be inverted. Choosing the κ 2 value according to j R i method (Lohman, 2004, Barnhart and Lohman, 2010) or from the corner of L-curve (Harris and Segall, 1987) are popular methods for obtaining the optimised result, where the bottom right corner in (a) is the best smooth factor, while (b) shows the standard deviation. 41

55 (a) (b) Figure 3.6 An illustration of the L-curve method This research utilises the procedure by trial and error process for damping value κ 2, usually beginning from a small value, then approaching to the best solution for smoothness of curve vs empirical fit (Atzori and Salvi, 2014) Weighting strategies The above inversion strategies have made an assumption that the InSAR data is correct without a ramp or noise. However, considering data quality and Area of Interest (AOI), this assumption could lead to biased modelling results at high noise or low coherence datasets. 42

56 (a) Weighting different data resources Due to different data resources and AOI, the weight for each dataset is defined differently. The most commonly used geodetic data with InSAR are GPS. Salvi et al. (2000) modelled the parameters by utilising GPS constrained InSAR resources, while Jonsson (2002) assigned 22% weight for GPS data, 75% for InSAR dataset, and 3% for SAR image offset dataset respectively. InSAR resource is weighted by a variance-covariance matrix, while GPS data is weighted for east, north and vertical directions respectively, constituting a unit matrix. (b) Weighting InSAR Resources As discussed in Section 2.2, InSAR source data is impacted by its inherent speckle noise, atmospheric turbulence and other noisy contributions. Assigning the weight is effective in eliminating or reducing the influence of noise. Because a Stripmap interferogram can contain about 20 million observations, directly processing the full image is computationally prohibitive. Subsampling the image can preserve the information as much as possible, so it is then reasonable to sample the interferogram into hundreds of thousands of observations. Different sampling methods are based on different sampling priorities, so there are several different methods for weighting the InSAR observations. The weighting strategy is directly related to the algorithm that subsamples the image data. Uniform grid sampling and quad-tree partitioning are two commonly used algorithms (Figure 3.6). 43

57 Figure 3.7 Quadtree subsampling (left) and Uniform subsampling (right) The subsampled datasets are then assigned with weight obtained from the variance-covariance matrix. To obtain this variance-covariance matrix from the covariance function, Sudhaus and Sigurjón (2009) sampled the semivariograms γ (h) to evaluate the InSAR variance and utilised covariogram C (h) for covariance. With the isotropic characteristics of a homogeneous random field, the direction of the step function in equation (3.18) is not important, but depends critically on the length h. C (h) = 1 N d(r 2N i=1 i) d(s i ) (3.18) Where the covariance C (h) is related with the displacements sampled between the distance of point r i and s i. Where the correlation length h equal 0, the covariance is estimated by the autocovariance of the image (Hanssen, 2001). The images may have higher error variance with less multilooking. The overall linear ramp is removed first when the random data-points pairs are picked. The variance can be obtained by a similar definition as equation (3.19) shows: 44

58 γ (h) = 1 2N [d(r i) d(s i )] 2 N i=1 (3.19) The variance and covariance are then utilised to estimate the error of the InSAR images for data weighting. The subsampled result determines the corresponding covariance matrix directly. (1) If subsampled uniformly, in other words, by sampling points on a regular grid, the variance-covariance matrix is constructed as follows: the diagonal is the variance estimated from equation (3.19), whereas the off-diagonal values are defined directly, e.g. the covariance of sampled points 15 and 52 is given by equation (3.18). (2) If the subsample method is a quadtree algorithm, the pixel value is averaged. The covariance values for each pixel in the quadtree is given by equation (3.20) (Sudhaus and Sigurjón, 2009). Σ i,j = 1 N i N j C N i N kl j k=1 l=1 (3.20) Inversion with weight and ramp consideration After the observations are weighted, the ramp needs to be calculated, either in linear or in bilinear subtraction. The full matrix of equation (3.7) then becomes: W 1 G ss W 1 G ds κ 2 2 ss 0 ( 0 κ 2 2 ds 1 0 0) [ U a ] = [W 2d Obs ] (3.21) 0 Where W 1 stands for the weight from variance-covariance, W 2 is the weight of different data resources, a represents the ramp ambiguity. The general weighted Least Squares Estimation of equation (3.21) will then finally be deduced as: 45

59 U = (G T WG) 1 G T Wd Obs (3.22) Non-negative least-squares can also be introduced as a further condition, to increase the reliability of slip vector on the same fault (Atzori and Salvi, 2014). This is because the slip value on the same fault should avoid the back-slip to preserve the same geo phenomenon. 3.3 Concluding remarks and future works In this chapter the earthquake modelling method utilizing InSAR resource was developed. Forward modelling is the basic idea for nonlinear inversion. The nonlinear inversion is constrained by the surface deformation obtained from InSAR observations together with the cost function. This research utilises the Levenberg-Marquardt algorithm to solve the nonlinear problem. Obtaining the fault geometry from a nonlinear result, the slip distributions are inverted from InSAR observations through the linear inversion procedure with the constraint of damping value. Constraints such as smoothing factor and weights are applied to optimise the results. The advantage of the variance-covariance matrix is that it describes the data error and assigns higher weight to the useful data. However, the ramp has to be removed as much as possible to ensure the sampling variograms deliver the correct result. Hence future studies could consider GPS and Azimuth Offset ( AZO) data to enhance the results. Other resources such as field survey of levelling is also an auxiliary data for weighting, but when considering the time baseline for disaster mitigation, the weight should be smaller than GPS. 46

60 Chapter 4 InSAR coseismic deformation mapping for 2008 Sichuan and 2009 L Aquila earthquakes In this chapter, L-band and C-band case studies for different earthquake events were carried out to demonstrate the abilities of InSAR in earthquake studies. This chapter will depict the Sichuan earthquake study and the L Aquila earthquake and compare the difference for the L-band and C-band in different cases. 4.1 Introduction Techniques such as ground surveying, seismometers, and a GPS network are commonly employed in studying earthquake activities. Nevertheless, these methods have their advantages and disadvantages. For example, seismometers respond to the earthquake very quickly, and can capture the seismic event due to its vast range. However, seismometers cannot provide surface deformation for analysis and assessment. The GPS network gives continuous observations offering East, North and vertical movements of the observed site, but due to the cost of GPS site construction, the density is usually not satisfactory for monitoring seismic events, or finite element modelling. To overcome these problems, and improve the efficiency and accuracy on deformation measurement over a large seismic area, the Interferometric Synthetic Aperture Radar (InSAR) technique has been increasingly utilised. This technique has the benefits of substantial coverage, all weather working capability, and acceptable accuracy. 47

61 In this chapter, L-band satellite imagery are used to study the devastating Mw 7.9 earthquake which occurred on 12th May 2008 in Sichuan, China, while C- band satellite imagery are used to study the Mw 6.3 earthquake which struck the region of Abruzzo in central Italy on 6th April The study of the ground surface deformation, especially the co-seismic deformation of these two events, not only can provide a better understanding of the two earthquakes, but also can assist geoscientists further on forecasting for future events. The change of ground surface before and after an earthquake is termed coseismic deformation. Compared to conventional surveying methods, the Differential InSAR (DInSAR) technique turns out to have superior advantages for co-seismic deformation measurement, such as the capabilities of accessing remote areas, providing dense observations and covering large areas. More specifically, DInSAR delivers accurate measurements with much higher spatial density, e.g.100 or more measurements per square kilometre (Ferretti et al., 2007). These dense DInSAR observations proved the elastic dislocation model at half-space is reliable. For the first case study, the Sichuan earthquake occurred along the Longmen Shan (LMS) thrust system. It bounds the eastern margin of the Tibetan plateau, and consists of three SW-NE striking faults (namely, Wenchuan Fault, Yinxiu- Beichuan Fault and Guanxian-Anxian Fault). The main shock took place on 12th May 2008, and deformed a large area of about 300 km E-W and 250 km N-S. This means a single frame or a single path ALOS PALSAR (Phase Array L-band SAR of the Japan Aerospace Exploration Agency) Stripmap image cannot cover the whole area (See Table 2-1 in Chapter 2). Multi-frame works 48

62 were conducted to cover the whole faults system (Ge et al., 2008) and invert the slip distributions (Chini et al., 2010, De Michele et al., 2010). The epicentre of the 2009 L Aquila Earthquake was located at a depth of about 9 km, near a complex fault system that constitutes the Mt. Stabiata fault, Monticchio-Fossa fault, and Mt. Bazzano and Paganica faults (Group, 2010). Advanced SAR of the European Space Agency (ENVISAT ASAR) datasets have been utilised by many researchers (Atzori et al., 2009, Walters et al., 2009, Wang et al., 2010) as well as this work to analyse the C-band ability for measurement. To capture the co-seismic deformation generated by an earthquake, a pair of SAR images, one acquired before and another after the quake, are the basic images used to produce the interferogram on the area. As Chapter 2 described, the topographic phase can be eliminated by using external DEM. Here the twopass DInSAR technique using SRTM DEM is applied for interferogram generation (Massonnet et al., 1993). In this study, the ALOS PALSAR L-band datasets are utilised for mapping the 2008 Sichuan earthquake, whereas ENVISAT ASAR C-band datasets are applied for the 2009 L Aquila earthquake measurement. The L-band and C-band DInSAR results are analysed for each earthquake, and the ability of DInSAR for co-seismic research is demonstrated. In these two case studies, DInSAR measurements of both earthquake events are presented with modelling results inverted from the surface deformation Okada dislocation elastic model (Okada, 1985). The ability of two-pass DInSAR deformation measurement from phase information for coseismic mapping and monitoring is verified. More discussions with details are in the following sections. 49

63 4.2 DInSAR data analysis To map the deformation of a co-seismic area with selected images taken before and after the event, the data perpendicular baseline, time baseline, and coherence are taken into account. The first row of Table 4-1 lists the pairs of ALOS images for the 2008 Sichuan Earthquake, which covers the Beichuan- Yinxiu fault (YB fault). The next two rows show the 2009 L Aquila data details of ENVISAT ASAR with both ascending and descending orbits. Table 4-1 Images for Interferometric Pairs Used Earthquake Satellite Orbit Interferometric Pair Date (dd/mm/yyyy) Sichuan ALOS Ascending (Track 473 R /02/ /05/2008 Track 474 R /03/ /06/2008 Track 475 R613) 20/06/ /06/2008 L Aquila ENVISAT Ascending (Track 401) 23/02/ /05/ L Aquila ENVISAT Descending (Track 79) 18/03/ /04/ Perpendicular Baseline (m) 245/ / Both ALOS and ENVISAT datasets were processed using SARscape 5.2, whereas model results inverted from SARscape and Matlab combined inversion. The 3D modelled results were then projected using equation 3.5. Considering the measurement error, the equation turns to the following: sin θ cos α [U E U N U Z ] [ sin θ sin α ] + δ los = d los (4.1) cos θ Here α is the heading angle of the satellite, θ is the incidence angle of beam at the scatterer point, and δ los is the measurement error due to atmosphere caused signal delays, low coherence of phase, coarse DEM, and imprecise satellite orbit (Fialko et al., 2001). A comprehensive illustration for the geometry is shown in figure 3.3. As discussed in Chapter 2, the key information is the deformation measured by phase, that is φ Defo. The processing strategy here for the 2008 Sichuan 50

64 earthquake is firstly to mosaic the image from the same path. The fundamental step is to measure the relative displacement from the mosaicked SLC data from the same scale, as DInSAR measures the relative displacement. Another issue is to enhance the Signal Noise Ratio (SNR) of the interferogram using the multilook procedure. Depending on different image modes, the azimuth vs range number 4 to 2 or 2 to 1 for ALOS PALSAR FBD (Fine Beam Dual polarization) or FBS (Fine Beam Single polarization) is utilised respectively, whereas the multilook number for ENVISAT ASAR dataset is 5 to 1. The DEM used is 90 m SRTM as an external DEM to subtract the topography phase. Orbit phase is removed from the interferogram. While ALOS PALSAR contains accurate orbit records, ENVISAT dataset utilises the precise orbit files which are distributed by the Delft Institute for Earth-Oriented Space Research (DEOS). A further step to eliminate the phase ramp from orbit contribution is orbit refinement, which utilises Ground Control Points (GCPs) either in the radar coordinate system or in the geographic coordinate system, where there is no deformation or evident residual fringes. To measure the displacement, the minimum cost flow (MCF) algorithm (Costantini, 1998) for phase unwrapping has been utilised to convert the deformation phase into displacement. In the case of the 2008 Sichuan earthquake, the seismic event ruptured a wide zone. Multi-frame pairs of ALOS images are used to cover the whole area. From the ADPS (Automatic DInSAR Process System) developed by GEOS (Geoscience and Earth Observing Systems Group), the pair of images taken on 20 June 2007 and 22 June 2008 from ascending track 475, frame 613, generated clear fringes with a shorter baseline. However, this pair only covers the epicentre of the M w 7.9 earthquake, with a looking angle around 34.3º. To 51

65 cover the whole YB fault, another two tracks, namely track 473 and track 474 (Table 4-1) are used. With the L-band s ability of vegetation penetration, using ALOS images to compute the deformation can achieve a better coherence result in the Wenchuan area. Figure 4.1 (a) shows the differential interferogram of track 475, from which we can see the fringes along YB fault and use the information to visually define the fault area. Nevertheless, MCF underestimates the unwrapped phase value close to the fault due to large displacement gradient caused by the rupture. A mask of the low coherent areas is suggested and 0.2 was selected as the threshold in the study. (a) (b) (c) Figure 4.1 (a) Interferogram of ALOS PALSAR for Sichuan earthquake (Track 475) (b) Interferogram from ENVISAT ASAR for 2009 L Aquila (Track 79) (c) Interferogram from ENVISAT ASAR for 2009 L Aquila (Track 401) Figure 4.1 (b) and (c) are interferograms of the 2009 L Aquila Earthquake in descending and ascending viewing geometry. The images are shown in UTM projection and each cycle of the fringe stands for about 2.8 cm. 4.3 Modelling method The surface deformation was then obtained from the unwrapped interferograms, which can be used for a finite dislocation model in an elastic and homogeneous 52

66 half-space (Okada, 1985) to model underground slip distribution and focal mechanism. The interferogram provides millions of observations and to enhance the computational capability and efficiency, the uniform sampling method is utilised for the images. The 2008 Sichuan earthquake, due to the mosaicked images, is sampled every 500 m 500 m near the fault and then 1000 m 1000 m at the remaining area, which yields 43,234 points in total. The 2009 L Aquila area is captured in single track and frame and subsampled to 9,985 points and 7,634 points for descending and ascending track, respectively. The subsampled data then were appropriate for inversion and estimation of the parameters to describe the earthquake fault. Geoscientists are looking at the parameters which constitute the length, width, and depth of the fault, the strike angle, dip angle, and rake angle of the hanging wall, the East and North coordinate of the source points and the slip vector with respect to the fault plane. All these parameters were inverted by comparing the forward modelling displacement using these parameters and the observed displacement from DInSAR. The inversion procedure is a nonlinear procedure, with the general equation (4.2) as: [ d east d north d up ] = d LOS = G m (4.2) Where G is Green s function, m is the parameters mentioned above for fault geometry, and d represents the simulated dislocation from East, North and vertical, then projected into LOS. The nonlinear inversion utilised Levenberg- Marquardt algorithm (Marquardt, 1963) to invert the parameters on the fault plane to minimise the d model d Obs 2. The GCMT (Global Central Moment 53

67 Tensor) is initialised as the start value and to set the inversion boundary correspondingly. After that the parameters are put into linear inversion, and fixed rake with a trial and error process to find the best damping value ε. [ d Obs 0 ] = ( Gg ε 2) U (4.3) Where G g is the generalised Green s function, d Obs is the observed displacement, ε 2 is the smooth factor, and U is the slip vector on the fault plane in patches. 4.4 Discussion The unwrapped interferogram shows the seismic hazard area caused by the main shock and aftershocks during the period of images collected. Displacement maps of both earthquake events are illustrated in Figure 4.2, and the modelling displacement maps with misfit along profiles are shown. (a) 2008 Sichuan earthquake DInSAR and Modelling comparison (b) 2009 L Aquila earthquake DInSAR and Modelling comparison (track 79) 54

68 (c) 2009 L Aquila earthquake DInSAR and modelling comparison (track 401) Figure 4.2 DInSAR measurement and Modelling result comparison Figure 4.2 (a) shows that the YB fault in the 2008 Sichuan earthquake strikes NE-SW, with the deformation ranging from 0.9 m to m in the LOS direction. This result is different from that reported in Chini et al. (2010). This could be due to using the single YB fault model instead of using the 3 faults (Guanxian- Anxian fault). Moreover, DInSAR measures relative displacement, the image pair in track 475 in this research is different, where a longer time baseline is used but clearer fringes are generated. For the 2009 L Aquila earthquake, the measured deformations from the ascending and descending track interferograms show ranges from m to 0.28 and m to 0.38 m, respectively (Figure 4.2 (b) and (c)). The difference is due to different viewing geometry contributing slightly different components for east and North projection. The ramp value can be calculated on the basis of equation (4.4) through linear inversion, where X and Y are the coordinates of each observed point whereas the coefficients a and b for the points. Ramp = offset + X a + Y b (4.4) A profile across the co-seismic area was presented for comparison between the DInSAR result and the modelling interferogram correspondingly (Figure 4.2). 55

69 In the L Aquila case, the descending track 79 shows a more complicated modelling result, and different looking geometry of sensitivity could be due to the earthquake striking NW-SE. However, with the DInSAR results we can determine the most probable strike angle for initialization and check against the modelling results. The co-seismic parameters are modelled by minimising the misfit between the modelling consequence and the DInSAR result. Compared to the Sichuan earthquake, the L Aquila earthquake impacted a much smaller area so that one ENVISAT ASAR image could cover the entire seismic area. The modelling results for the two seismic events are presented in Table 4-2. Table 4-2 Nonlinear Results for 2008 Sichuan earthquake and 2009 L Aquila Event Width (km) Length (km) earthquake Top Depth (km) Strike (deg) Dip (deg) Rake (deg) Slip (m) Sichuan (YB fault) CMT * L Aquila (Track 79) L Aquila (Track 401) CMT * Open (m) *Stands for global Centroid Moment Tensor results (Ekström et al., 2012) and the depth is epicentre For the Sichuan earthquake we selected the interferogram covering the 12 th May 2008 main shock, and a single fault model along the YB fault was utilised for the inversion. From GCMT results, we know there were 27 aftershocks with a magnitude higher than M w 5.0 that occurred during the last image acquired for the last pair to generate the mosaicked DInSAR map. Different temporal baseline DInSAR pairs were mosaicked with the aim of choosing the capture time as close as possible. Taking track 475 as an example, from Figure 4.2 (a), 56

70 the strike angle can be initialised with the boundary limitation from 200º to 260º with respect to the initial strike angle from global CMT result of 231º. Interferograms from ALOS PALSAR covered the YB fault area. HH polarization SLC data was selected for its better backscatter and coherence. The lame constant λ and shear modulus μ were both set as 30 GPa, assuming a uniform layer under deep Earth. The modelling result shows the fault has a right-lateral strike slip and a gentler dip angle (15º) with reverse thrust. Though the length is shorter as the interferogram covers a smaller area compared to the whole Sichuan fault, the moment magnitude was estimated to Mw 7.8, which is close to the global CMT result. These results show that multi-frame interferograms can produce closer results to the CMT result. However, the LOS deformation of the 2008 Sichuan earthquake measured is much less than the result of a field survey (Li et al., 2008). This can be explained by the L-band signal coherence loss and phase saturation when the surface dislocation is too high (i.e. in the near fault area). In other words, the radar phase reaches its saturation point to measure changes when the displacement gradient is greater than half of the radar wavelength per pixel. These areas are the case in the near fault field area. These phenomena lead to error propagation and underestimating of the actual deformation measured. The moment magnitude of this earthquake N m (Mw 7.8) is achieved, which is a little less than the USGS Moment Tensor result of N m (Mw 7.9). The possible reason is that the fault length does not include the Beichuan-Qiangchuan (BQ fault). Nevertheless, cases for the 2009 L Aquila earthquake are different. The fringes in the seismic zone are clear with less area losing coherence than the Sichuan 57

71 earthquake. Furthermore, the single frame captures the whole seismic area. Figure 4.2 (b) shows the area observed by track 79 and track 401, and the relevant wrapped fringes are depicted. In this case, the ENVISAT ASAR captured the whole seismic event with a short temporal baseline. Nonlinear inversion results in Figure 4.2 (b) and (c) show similar patterns from the ascending and descending looking direction for this earthquake. Rake at 100 indicates it is a normal fault with slightly right-lateral movement. The geodetic moments for track 79 and track 401 modelling are N m (Mw 6.2) and N m (Mw 6.3), respectively, a little smaller than the USGS result of N m (Mw 6.3). The rigidity moduli are assumed to be 30 GPa. A in-depth study of the inversion results with damping value by Atzori and Antonioli (2011) is recommended. Track 401 and track 79 achieved different results because the temporal baseline is different and the viewing geometry is different. The deformation shown in the two 2009 L Aquila earthquake displacement maps depicts reasonable surface change. The modelling results are close to previous studies (Walters et al., 2009, Atzori et al., 2009). Figure 4.3 Slip distribution of the Sichuan YB fault 58

72 Figure 4.3 shows modelling slip distributions of the Sichuan earthquake, which is based on the YB faults. Peak slip distribution is less as the central seismic area in the mosaicked displacement map has low coherence. These areas need to be taken into consideration because this fault does not fully cover the additional Beichuan to Qingchuan fault. Slip distributions of the L Aquila earthquake are shown in Figure 4.4. The fault has a strike angle of about 137 and is a normal fault moved slightly right-lateral. (a) (b) Figure 4.4: (a) Slip distribution estimated for L Aquila earthquake in 2009 of track 79. (b) Slip distribution estimated from track 401. However, compared to the 2008 Sichuan earthquake with L-band interferograms, it appears that the case of the 2009 L Aquila earthquake with C- band interferogram gives much clearer fringes. The reasons are: 1. The C-band has a shorter wavelength and is more sensitive to deformation variation. 59

73 2. Secondly, in the case of the Sichuan earthquake, due to the rugged terrain of the region, dense vegetation and rainfall, C-band could be more susceptible to being uncorrelated than L-band. 3. Thirdly, the 2009 L Aquila earthquake is comparatively small and the fault is shorter in respect to the 2008 Sichuan earthquake, even the C-band has a shorter wavelength but it is not saturated at the seismic central area. This is the reason why the L-band interferograms were chosen for studying the Sichuan earthquake, while C-band datasets were used for the 2009 L Aquila event. 4.5 Concluding remarks In this Chapter, by using the DInSAR technique to measure the surface deformation, we have studied both the 12 th May 2008 Sichuan earthquake and 6 th April 2009 L Aquila earthquake. The ability of L-band and C-band SAR data to measure deformation was shown and analysed. The saturation of radar waves for phase measurement should be taken into consideration to constrain the error propagation. An elastic model in half-space for dislocation was used and the modelling results agreed well with DInSAR observations. Fault geometry was also matched with global CMT results and USGS CMT results. Both interferometry and seismology results demonstrated the 2008 Sichuan earthquake struck along the South-West and North-East, with inversed thrust and right-lateral strike slip. It is also found that the 2009 L Aquila earthquake struck along South-East with SW-dipping and with right-lateral strike slip. 60

74 As a further analysis, we subsampled the interferograms into tens of thousands of points. It is almost impossible for other conventional methods to achieve the same observations in such a short period. Furthermore, phase variation is very sensitive to surface change in LOS direction. With centimetric accuracy, these advantages make elastic half-space dislocation modelling based on DInSAR observations more reliable. DInSAR results and modelling results were utilised with different bands (L-band and C-band) for the two seismic events respectively. It showed the capability of DInSAR to map earthquakes and delivered comprehensive geospatial information to assess regional seismic hazards. This study has depicted both single frame and the mosaicked interferograms inversion for earthquake study and capabilities of single fault modelling. 61

75 Chapter 5 Deformation detection by InSAR of 2010 Darfield earthquake With the ability of the C-band and L-band microwave sensor in Stripmap mode to measure surface deformation, a case study using both datasets was deducted for the same earthquake event. In Section 5.1 the information of Christchurch area is discussed, and the DInSAR analysis is discussed in Section 5.2. Section 5.3 gives the modelling result. 5.1 Introduction for Christchurch area The Canterbury sequence consisted of several calamitous quakes, which started with the Mw 7.1 earthquake on 3 rd September 2010 (UTC), and continued with large aftershocks widely spread across the city of Christchurch with dramatic consequences, particularly the Mw 6.3 event which occurred on 21 st Feb 2011 (UTC) (Figure 5.1). A liquefaction study was carried out with the coherence map generated from the InSAR technique (Beavan et al., 2011, Salvi et al., 2012). 62

76 Figure 5.1 New Zealand seismic sequence: focal mechanisms of main earthquakes from GCMT. Aftershocks from USGS until 10 th Mar This earthquake sequence was located in an area that lies about 90 km east of the Alpine Fault, which is a strike-slip fault. These events took place beneath the Canterbury Plains, where the gravel-dominated alluvial plains have a thickness of 200 to 600 m, and in the east the Banks Peninsula has a maximum elevation of 910 m (Forsyth et al., 2008). The pre- and post-event ENVISAT and ALOS images were used to detect the ground movement. All the images were provided as single look complex (SLC) data. The phase information extracted was the information used to measure the deformation. This research focuses on the C-band and L-band sensor ability to map the surface deformation and validates the finite modelling results for both inversions. 5.2 DInSAR results analysis The two major earthquakes were captured by L-band ALOS satellite and C- band ENVISAT satellite (Table 5-1). 63

77 Table 5-1 Darfield Earthquake Data Sets Sensor Path/Frame Pairs Orbit Look angle ALOS 337/ /08/2010 Ascending 38.9 ( ) 28/09/2010 ENVISAT 51/ /07/2010 Ascending 23.3 ( ) 17/09/2010 The selected data pairs measured the same area, with part of the observed area overlapping (Figure 5.2). Figure 5.2 Overlapping area for ENVISAT and ALOS sensor InSAR data processing The pair of ALOS datasets (Table 5-1) was selected due to their minimum temporal baseline (46 days). This pair of images generated an interferogram with clear fringes of the seismic area (Figure 5.3). It is obvious that ENVISAT data offered dense observations since more fringes were observed, but ALOS data provided clear fringes for each cycle, especially the bottom left part showing the deformation generated where more fringes were detected. The red rectangular area shows the same observed area for both satellite sensors, where the white circle depicts the different sensitivity for generating fringes. 64

78 Each fringe in ENVISAT data stands for ~2.8 cm deformation on LOS (Line of Sight), while in ALOS datasets each fringe represents ~11.6 cm deformation on LOS. Figure 5.3 ENVISAT interferogram (Left) and ALOS interferogram (Right) comparison in radar coordinate system The results were retrieved by two-pass InSAR technique (Massonnet et al., 1993), adopting the 1 arc SRTM DEM to remove the topographic contribution. For ENVISAT datasets, the orbital file from DEOS (Delft Institute for Earth- Oriented Space Research) was utilised to remove the orbit phase ramp, while for ALOS datasets the auxiliary orbit files were accurate to apply orbit refinement InSAR deformation detection The Mw 7.1 Darfield earthquake occurred on a previously unknown fault (Atzori et al., 2012). The rupture generated by the fault plane was thought to have started on a steeply dipping reverse fault, which then propagated on the main 65

79 Greendale fault (Elliott et al., 2012). The interferogram obtained from ENVISAT and ALOS showed the earthquake has a ruptured length of about 60 km, with NW-SE alignment in the west while almost West to East components exist in the epicentre area (Figure 5.4). The red area in Figure 5.4 ENVISAT image above the seismic area indicates the atmosphere impact and phase ramp influence, due to the C-band wavelength is shorter. Figure 5.4 LOS displacement measured by ENVISAT and ALOS for 2010 Darfield earthquake ENVISAT ASAR data has a peak value of 1.4 m in LOS while ALOS observed 2.1 m, which matches with Atzori et al. (2012) and Liu et al. (2013). The difference could be caused by the different looking angle and saturation of the wavelengths. Both observations showed that the Southern part was experiencing a lift-up movement, where the positive sign represents the decrease of the sensor-to-target slant range distance. 5.3 Modelling procedure and result analysis To improve the computational efficiency, the interferograms have been subsampled to a 300 m regular grid in the deformed area and to 2000 m for the 66

80 far range area. From the DInSAR interferograms, it is possible to define that the fault plane consists of several segments. Beavan et al. (2010) utilised two fault planes obtaining the fault geometry showing it was the right-lateral strike-slip on the fault to its southwest. Elliott et al. (2012) and Atzori et al. (2012) adopted a two-fault solution, but have five continuous segments along the Greendale fault line. This research applied similar fault solutions, but segmented the Greendale fault plane (Table 5-2) into two rather than five. Table 5-2 Source parameters of Darfield earthquake Fault Segment Strike (deg) Dip (deg) Rake (deg) Length (km) Width (km) Patch Numbers Hororata Fault (HF) Greendale 1 (G1) Greendale 2 (G2) Charing Cross North (CCN) Charing Cross South (CCS) The fault planes were divided into patches along strike and dip directions respectively to retrieve the slip distribution on the fault plane. The results inverted from ENVISAT (Figure 5.5) matched with the result from ALOS (Figure 5.6). 67

81 Figure 5.5 Slip distributions from ENVISAT for the 3 rd September 2010 (UTC) Darfield earthquake Figure 5.6 Slip distributions from ALOS for the 3 rd September 2010 (UTC) Darfield earthquake 68

82 The fault geometries from ALOS data are slightly different from geometries from ENVISAT data. Segment CCN in ALOS inversion results were located further west than ENVISAT results. This could be explained by the different sensitivity and saturation for the phase measurement in different wavelengths. From the DInSAR results and the modelling results, ALOS datasets showed better coherence and offered more detailed information for deformation. The modelling result obtained the oblique slip on the fault above, plus right-lateral strike-slip on a near vertical fault (Greendale fault). The trend was towards the East, which indicated the risk for the eastern part of the Darfield area. 5.4 Concluding remarks The Darfield earthquake involved complex fault geometries, raising important issues for estimating the risks or the possibility of triggering the second major event on 21 st February 2011 in Christchurch, which is located east of the Darfield area. C-band and L-band radar data were utilised to map the deformation for this event. The longer wavelength ALOS data were coherent in parts of central and eastern Darfield, but with smaller coverage. The ENVISAT data lost coherence because of severe ground damage, but with larger coverage for the area. However, because there are several segments in the construction of the fault geometry, further geodetic modelling should take into account other data sources such as GPS to constrain the elastic model. More sophisticated modelling with different segments could lead to slightly different fault geometry, but this research has good agreement with previous publications. The ability of seismic research using radar interferometry for C-band and L-band data was presented. 69

83 Chapter 6 The 2015 Nepal earthquake sequence modelling by ScanSAR results The 2015 Nepal earthquake sequence caused enormous loss and damage to the area, which started with a main shock of M w 7.8 on 25 th April 2015 at 06:11:26 (UTC). It continued with several large aftershocks, particularly the M w 7.3 event striking on 12 th May 2015 at 07:05:19 (UTC). Both earthquake events were captured by ALOS-2 ScanSAR images. The displacement maps are generated while the respective modelling results are discussed in this chapter. A single fault model best fits the main shock event striking 290, dipping gently north with a 7 shallow thrust fault. Moreover, a single fault for the second event model and a two faults system utilising an interferogram pair capturing both events on 22 nd Feb 2015 and 17 th May 2015 respectively are compared. The result shows the slip vectors struck to the South generally, which depicts the risks since the main shock occurred. 6.1 Background introduction Nepal is generally divided into five major tectonic zones with an east-west trend, namely, the Terai Tectonic Zone, the Churia Zone, the Lesser Himalayan Zone, the Higher Himalayan Zone and the Tibetan Tethys. The dominant tectonic architecture of the Himalaya can be divided into three major thrusts from North to South: the Main Central Thrust (MCT), the Main Boundary Thrust (MBT) and the Main Frontal Thrust (MFT) (DeCelles et al., 2001). In the central Himalayan thrust belt, the isolated Kathmandu klippe results in a shallow dip with a transport orientation between N-S and NE-SW (Khanal et al., 2015). A 70

84 seismicity study in Himalaya shows that the collision of the India and Eurasia plates converges at a relative rate of mm/yr ((USGS, 2015b)). On 25 th April 2015, intense ground shakings struck Nepal, with a M w 7.8 devastating main shock firstly striking Gorkha at 11:56 am (local time). The epicentre of this calamitous event was located 77 km northwest of Kathmandu, Nepal with a depth of approximately 15 km (USGS, 2015b). Following a M w 6.6 aftershock event, 36 sequencing aftershocks larger than M w 3.0 occurred in the 24 hours after the main shock (Figure 6.1). Figure 6.1 Seismic events occurred in the first 24 hours After the Gorkha earthquake a second major aftershock, with M w 7.3 occurred on 12 th May 2015, with 87 aftershock sequences which were larger than M w 3.0. The epicentre was located 19 km southeast of Kodari, Nepal, with a depth of about 15 km (USGS, 2015a). Figure 6.2 illustrates the magnitude of aftershocks with respect to time, from the moment the main shock occurred to the first 24 hours of the 12 th May event. 71

85 Figure 6.2 Seismic events happened from Main shock to the first 24 hours of 12 th May Event Both earthquake events can be regarded as thrust fault slip on the Main Himalayan Thrust, though the second earthquake occurred slightly further north with respect to the conventional Main Frontal Thrust. It is important to recognise that the Main Himalayan Thrust has an intricate geometry, varying from east to west (Whipp, 2015). In this work the two major shocks are analysed. The different fault models corresponding to the events are analysed, and the relative slip distributions are given. This research is based on ground deformation mapped by ScanSAR interferometry providing the analysis of the two harmful earthquakes. 6.2 InSAR data analysis The Gorkha seismic sequence was observed by a variety of satellite missions from the occurrence of the main shock. Japan Aerospace Exploration Agency (JAXA) received the emergency observing request from Sentinel Asia and the 72

86 International Charter to observe Kathmandu area (EORC, 2015). Several pairs of Stripmap and ScanSAR observations from ALOS-2 PALSAR-2 sensor were captured (Figure 6.3). Figure 6.3 Time line of image captured in the first month of Gorkha Earthquake occurred 6.3 Modelling strategy and processing The ScanSAR datasets are processed to infer the seismic source of both major events. Table 6-1 shows the datasets utilised that captured the two events. Table Nepal Earthquake Data Sets Satellite Path Mode Image date Look Angle (deg) Orbit ALOS-2 48 WD1 22/02/ Descending ALOS-2 48 WD1 03/05/ Descending ALOS-2 48 WD1 17/05/ Descending To meet the computational capability and efficiency, the displacement maps are subsampled by uniform sampling spanning the data space (Lohman and Simons, 2005). The modelling process was carried out first by a simple uniform slip model termed as nonlinear inversion procedure. Ten parameters were utilised to describe the fault geometry, namely, strike (φ), dip (δ), rake (λ), strike-slip (U 1 ), dip-slip (U 2 ), fault width (W), fault length (L), dilation (dia), East coordinate of the source point (E) and North coordinate of the source point (N). 73

87 Because the dilation in the 2015 Nepal earthquake sequence is zero, the parameters can be reduced to 9. Furthermore, the Levenberg-Marquardt algorithm (Marquardt, 1963) was applied for the nonlinear inversion process to retrieve these parameters through InSAR observations, which provided excellent results in short processing time (Atzori and Salvi, 2014). Global Central Moment Tensor (GCMT) was utilised as start value for nonlinear inversion, however. The obtained fault geometry was then held fixed to estimate the slip vector U, while fixed rake angle with non-negative inversion method was utilised. This process inverts the slip distribution results linearly related to the surface deformation (Massonnet and Feigl, 1998). The fault plane was then discretised into patches along the strike and dip directions respectively. This linear function model was set up as following: [ d Obs 0 ] = ( G κ 2 2) U (6.1) Where d Obs is a vector containing the observed displacement, G is the matrix of Green s function derived from a rectangular dislocation model in a homogeneous and elastic half-space (Okada, 1985), and κ 2 2 is the smooth vector constraining the slip value U. The Lagrange multiplier κ 2, which is the damping value, determines the weight of Laplacian operator 2. The higher the damping value, the smoother is the slip solution. 6.4 Discussion of the main shock on 25 th April, 2015 The M w 7.8 Gorkha earthquake occurred on the Main Himalayan Fault (MHF) system. The fault is thought to have started on a shallow dipping reverse fault at about 10. The seismic area was captured by ALOS-2 ScanSAR datasets from 74

88 path 48 and frame 3050 with descending track. Uniform sampling method for InSAR datasets were utilised to reduce the observations from millions to points. The Centroid Moment Tensor result was selected as the start value for nonlinear inversion. However, different focal mechanisms gave slightly different moment tensor solutions (Table 6-2) for Gorkha Earthquake. Table 6-2 Focal mechanism solutions for Gorkha Main Shock (USGS, 2015b) Type of Measurement Global Centroid Moment Tensor Centroid Moment Tensor (US) W-phase Moment Tensor Magnitude Strike ( ) Dip ( ) Rake ( ) Mw Mwc Mww The focal mechanism solutions suggested that the fault striking about 293, dipping a shallow angle near 10 with a reverse thrust. GPS data from JPL were utilised with a unit diagonal matrix (Jonsson, 2002). Seven GPS points were selected in the UTM zone 45 (Figure 6.4). 75

89 Figure 6.4 GPS locations and Nepal earthquakes sequence sketch The interferogram also illustrated a seismic area with length about 120 km and width of at least 60 km. After several trials, the fault geometry for nonlinear inversion which best fitted the DInSAR result was striking 292.4, dipping 7 with rake angle 101. The dipping angle of 11 was tested too but the RMS of both InSAR dataset and GPS are slightly higher than inversion result with dipping angle at 7. The nonlinear results are listed in table 6-3, which is close to W- phase moment tensor result. Table Gorkha Earthquake Nonlinear Inversion Length Width Depth Strike Dip Rake Slip Lat Lon Dilation (km) (km) (km) ( ) ( ) ( ) (m) ( ) ( ) (m) A shallower fault was tested, but the modelled interferogram showed error propagation near the seismic area. The fault depth was then increased during 76

90 nonlinear inversion procedure to achieve a better result. Fault depth from 8 km to 19 km can achieve a smaller RMS value. The linear inversion process was conducted following the nonlinear result. The InSAR result suggested a narrow fault geometry while according to the seismometer modelling result (USGS, 2015b), an expanded fault with 130 km length was recommended (Cheloni et al., 2015). The linear inversion in this research expanded the fault length to 140 km with a width of 100 km. The fault trace along the MFT is consistent with what was presented by Lindsey et al. (2015). The forward modelled results (Figure 6.5) were projected into LOS (Line of Sight) as a modelled displacement map, and this displacement map was wrapped into a phase which could be compared with the DInSAR interferogram observed (Figure 6.6). The pattern and trends were close. Figure 6.5 Forward modelled 3D components (U E is East component, U N is North movement, and U Z is vertical deformation) The positive signs in figure 6.5 indicate the movement towards the direction at East, North and Up, respectively. The negative signs show the movement in opposite direction correspondingly. 77

91 Figure 6.6 Modelled interferogram and Observed LOS interferogram The trends of the modelled interferogram matched with the observations, and showed more clear fringes. With the peak LOS values ranging from m to 1.16 m in observed (Figure 6.7 (b)), and m to 1.08 m modelled (Figure 6.7 (a)), a profile was taken in both results to compare the modelled result with the observed map from DInSAR (Figure 6.7 (d)). This profile illustrated that the modelling result had good consistency with observed information. 78

92 Figure 6.7 Comparison between modelled and measured coseismic deformation Figure 6.7 (a) is the modelled displacement map, Figure 6.7 (b) is the DInSAR result from ScanSAR, Figure 6.7 (c) is the difference of the two results, and Figure 6.7 (d) is the profile plotting taken from modelled and observed results respectively. Though a tectonic model from USGS (2015b) showed a slip value of 4 m in peak, a set of slightly different results were obtained. The forward modelling result (Figure 6.8) in this research shows the peak slip value was 5.11 metres, and the slip under the Kathmandu area was about 3~4 m. The black arrows were the slip direction counting from the strike direction. It is clear that the slip distributions were towards the South with a rake angle of 101, while the whole trend of earthquake propagation from the epicentre was towards ESE as the 79

93 strike angle suggested. This result shows the fault was a shallow thrust with slightly right-lateral dip-slip component. Figure 6.8 Slip distribution of 2015 Gorkha Earthquake The fault geometry was illustrated in 3D (Figure 6.9) from birds eye view, South East and East, respectively. Figure 6.9 Gorkha Main Shock Fault Geometry in 3D 80

94 6.5 Discussion of the second major shock on 12 th May 2015 On 12 th May 2015, a further strong aftershock of M w 7.3 occurred 18 km Southeast of Kodari (USGS, 2015a), about 150 km East of the hypocentre of the main shock in April. The epicentre was located slightly further north with respect to the MHF, which released a seismic moment ranging from N m (USGS-Mwb) to N m (USGS-CMT). Different fault geometries were defined according to the sources (Table 6-5). To model this source, ALOS-2 PALSAR-2 ScanSAR images from path 48 and frame 3050 were analysed. The images were captured on 3 rd May 2015 and 17 th May 2015, respectively. Table 6-4 Moment tensor solutions Name Mwc (GCMT) Mwc (USGS) Mww (USGS) Mwb (USGS) Moment (N m) Magnitude Depth (km) Strike ( ) Dip ( ) Rake ( ) 8.998e e e e In the solutions the W-phase Moment Tensor (Mww) result was initially adopted showing the NW-SE striking fault. However, this approach led to several inconsistencies with high residuals. The GCMT results showed better start value and the residual in nonlinear inversion reduced from m to m. The linear inversion process was run with the fixed patch size and rake. To achieve more realistic slip distributions, the non-negative algorithm was applied. The modelled displacement map and the modelled interferogram are shown in Figure

95 Figure 6.10 Modelled Displacement Map (a) and Wrapped Phase (b) A profile was also taken across the seismic area, and the differences of the modelling results were compared (Figure 6.11). Figure 6.11 Observed (a), modelled (b), residual displacement maps (c) of ALOS-2 PALSAR-2 ScanSAR interferogram relating to the 12 th May Event. (d) is the profile plotting of (a) and (b) 82

96 The slip vector on the fault was inverted (Figure 6.12). The peak slip was about 4.5 m. The fault struck to 312, dipping 11 with slip vector generally towards the south at 119. It was thrust and consistent with the MHF thrust system. Figure 6.12 Slip distribution of the Second Major Shock on 12 th May 2015 It can be concluded that the second major shock was an extension of the main shock on 25 th April 2015, by observing the seismic area with ScanSAR image pair from 22 nd February 2015 to 17 th May 2015 (Figure 6.13). 83

97 Figure 6.13 Observed result of both events, the red stars are the epicentre 6.6 Concluding remarks The 2015 Gorkha (Nepal) seismic sequence involved two calamitous major shocks. The modelling result of the main shock was jointly inverted using GPS and InSAR datasets. This right-lateral thrust slipped generally to the south on the single fault model with a peak slip of about 5.11 m. A slightly higher moment magnitude of N m (Mw 7.78) was achieved in this model compared to the USGS-CMT result of N m (Mw 7.76). The modelling of the second major shock was conducted with only InSAR datasets. The moment magnitude was N m (Mw 7.12), which was smaller than the GCMT result. The fault was consistent with the MHF with a gentle dip of 11. Though 84

98 there was no obvious surface rupture along the fault trace, the second major shock can be regarded as an extension of the main shock due to the consecutiveness and coherence in the fault geometry. Here the ScanSAR data provided accurate information to determine the location of earthquakes in remote areas, and the models made it possible for risk assessment in the seismic area. 85

99 Chapter 7 The ScanSAR assisted Stripmap expansion for emergency response There are three usual modes for InSAR observations as discussed in Chapter 2. Due to the different properties of these three modes, the advantages and disadvantages for each mode are various. This chapter will explore the limitation and find the theory to expand the observed area of Stripmap for modelling purpose to respond for emergency. 7.1 Limitation of Stripmap Coverage The 2015 Gorkha earthquake occurred on 25 th April at 06:11:26 (UTC) in Nepal. JAXA (Japan Aerospace Exploration Agency) received the emergency observing request from Sentinel Asia and the International Charter to observe the Kathmandu area. Several pairs of Stripmap and ScanSAR observations from ALOS-2 PALSAR-2 sensor were captured. The earliest SAR image was captured on 26 th April 2015, which was discussed with damage assessment. However, the first pair of images available for radar interferometry covering the Kathmandu area was the Stripmap image captured on 2 nd May 2015 to form an interferometric pair with image taken on 21 st Feb The problem for this high resolution image pair is that the swath was not able to cover the entire fault (Figure 7.1). 86

100 Figure 7.1 Stripmap image covering Kathmandu area, the white dot lines are the preliminary fault To obtain the seismic slip distributions of the earthquake event, geoscientists usually invert the slip vector based on the finite element model (Okada, 1985). However, the inversion process carrying out on the area where there is no data can introduce an artificial impact due to the unconstrained area. Different imaging modes can cover different swaths (Table 2-1). By combining different resources, the expanded displacement map can be obtained. Apart from joint inversion using Stripmap and ScanSAR images, a supplementary method is to use the coarse resolution ScanSAR pair interferogram data to expand the observing area by the contour generation method with high resolution Stripmap images. The flowchart 7-1 illustrates the procedure: 87

101 Flowchart 7-1 The procedure of contour generation with ScanSAR and Stripmap The near polar orbital track for a satellite is along the longitude. Due to this operating property, though the Stripmap mode has a swath of 70 km, it is impossible for this mode to cover the seismic area along East to West about 130 km in a single track, while ScanSAR images can do the work (Figure 7.2). 88

102 Figure 7.2 Coverage of Stripmap and ScanSAR images 7.2 Contour generation for coverage expansion It is obvious in Figure 7.2 that the Stripmap covered most of the fringes with more than half cycles. Its 10 m resolution offered sufficient observations to generate accurate contour. The problem is how to preserve the correct trend when dealing with extrapolation. The ScanSAR dataset provided auxiliary information constraining the extrapolation with better resolution. Nevertheless, the Stripmap images taken were ascending track, while the ScanSAR images taken were descending track. Due to the pixel size being 10 m for Stripmap with respect to 100 m for ScanSAR, it was assumed the horizontal movements in each tie point could be ignored. Thus the descending 89

103 LOS with respect to ascending LOS can be projected with a trigonometric function. Furthermore, due to the same coverage, a polynomial relation can be found (Figure 7.3). Figure 7.3 Relationship between ascending and descending tie points After obtaining the relationship in equation (7.1), the ScanSAR datasets with descending viewing geometry were projected into ascending to match with the Stripmap results. D Asc = f(d Des ) (7.1) After the projected points from ScanSAR were supplemented, the contour for a displacement map can be generated. Because the displacement map of Stripmap was the dominant source, we sampled dense observations in it with points, and we used ScanSAR data for the West and East parts with 5175 points and 3975 points, respectively (Figure 7.4). 90

104 Figure 7.4 Sampling points The empirical Kriging algorithm was utilised to generate the displacement model. The Gaussian Kernels was selected (Figure 7.5), and its semi-variograms and covariance are shown in Figure 7.6. Figure 7.5 Gaussian Kernel based sampling histogram 91

105 Figure 7.6 Modelling semivariogram and coherence By the interpolation work the modelled displacement map was obtained, and contour can be generated (Figure 7.7). Figure 7.7 Final LOS displacement map generated from contour map 92

106 7.3 Discussion of the results The modelled LOS interferogram was compared with the Stripmap result (Figure 7.8). In Figure 7.8, (a) is the clipped modelling result, (b) is the Stripmap result, and (c) is the difference between the two results. The residual showed that the modelling result had good consistency with the Stripmap result. A profile was taken to analyse the modelling results (Figure 7.9), where the white quadrangle depicted the Stripmap coverage. Figure 7.8 Clipped area for comparison Figure 7.9 Comparison of modelled and Stripmap results 93

107 The observing area then was expanded, and the nonlinear inversion step utilised a uniform sampling method. Global Centroid Moment Tensor (GCMT) and USGS-CMT results were considered as the starting value. The nonlinear result is given in table 7-1. Table 7-1 Source parameter for 2015 Gorkha Earthquake Length (km) Width (km) Top Depth (km) Strike Dip Rake Slip (m) The fault then was divided into patches along the strike direction and dip direction respectively. These nonlinear parameters were carried out with trial and error test looking for the minimum Root Mean Square (RMS) on the patches (Equation 7-1). [ d Obs 0 ] = ( G κ 2 2) U (7-1) Here d Obs is a vector containing the observed displacement, G is the matrix of Green s function derived from a rectangular dislocation model in a homogeneous and elastic half-space (Okada, 1985), and κ 2 2 is the smooth vector constraining the slip value U. The Lagrange multiplier κ 2, which is damping value, determines the weight of the Laplacian operator 2. The higher the damping value the smoother is the slip solution. The fault was generally located along the Main Himalayan Fault, with thrust fault striking at 293, dipping at 11. The peak slip was 6.1 m towards Southeast generally (Figure 7.10). 94

108 Figure 7.10 Slip distribution of the 2015 Gorkha Earthquake from combined modelling 7.4 Concluding remarks This research combined the advantage of Stripmap mode for its high resolution, and the advantage of ScanSAR mode for its larger coverage. The displacement contour map connected the two modes, and generated a good result for a high resolution image for modelling application. A possible way of expanding the coverage of observations when multi-frame Stripmap images are not available was discussed and demonstrated. The modelling results have good agreement with USGS-CMT results as well as ScanSAR modelling results, while the modelled interferogram offers higher resolution images with large coverage. Some challenges have been overcome, such as dataset merging and projection, but there is still more work to be done to enhance the quality of the modelled observations. For example, the time spent on a manual trial and error process for Kriging modelling was too long, the number of sampling points was too large that can be handled in a computer with a memory of 32 GB, and it is possible 95