Chapter 3 Minimum 1-D Velocity Model: Using joint determination of hypocenters and velocity 3.1 Introduction

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1 Chapter 3 Minimum 1-D Velocity Model: Using joint determination of hypocenters and velocity 3.1 Introduction This chapter deals with the estimation of a new 1-D velocity model in the Kumaon- Garhwal Himalaya region, based on travel times using the Joint hypocenter and velocity determination (JHD) method. A one-dimensional P- and S- wave velocity structures of the upper crust beneath the Kumaon-Garhwal Himalaya region is determined by simultaneously inverting the hypocentral locations as well as the velocity structure of the study region. Seismic velocity structure of a region not only provides a window to its deeper geological setting but constitutes basic information required for analyzing seismograms generated at its various sites. In particular, it is indispensable to accurate mapping of hypocentral locations of earthquakes that, in turn, illuminate ambient strain concentrations as well as distribution of interactive fault systems, to model earthquake hazard and design mitigation works such as the formulation of building codes and design of advanced warning systems. Also, with the use of known hypocentral parameters, we can estimate the seismic velocities beneath the area under investigation. One, therefore, tries to determine the hypocenters and the velocity structure simultaneously. Results of local earthquake tomography highly depend on the initial reference model (Kissling et al., 1994). Kissling (1988); Kissling et al. (1994) introduced the concept of the minimum 1-D model in local earthquake tomography that can be use as a initial reference model. The minimum 1-D model itself is a result of a series of simultaneous inversions of hypocentral parameters, 1-D velocity models (V P & V S ), and station corrections. Besides serving as an initial reference model, the minimum 1-D model will provide high precision hypocenter locations for use in 3-D local earthquake tomography. Initial earthquake locations with computer code HYPOCENTER using an earlier known velocity model is presented in the first section of this chapter. This is followed by joint inversion of P- and S- wave velocity model and the earthquake hypocenter. For the purpose we use well documented software VELEST. Finally, model errors are estimated by means of different reliability tests for the derived model. 67

2 3.2 Initial Hypocenter locations A total 1250 local earthquake records, which had registered a minimum of 5 P- and 3 S- arrivals, were selected for inversion of their hypocenters by using HYPOCENTER program. With the availability of the GPS timing system, reliability of the internal clock system was always better than a few microseconds. We assigned a time uncertainty to each interval; for events inside the network time uncertainties of P- wave arrivals ranges from 0.05 to 0.50 s and for S- wave arrivals 0.1 to 1.5 s. For locating earthquakes we used Nepal Himalayan velocity model (Monsalve et al., 2006) shown in Table 3.1, and an average V P /V S ratio (1.73) abstracted from the P- and S- wave arrival time data from our network using the Wadati diagram (Fig. 3.1). Our choice of the Nepal Himalaya velocity model for this first step inversion of hypocenters was guided by the consideration that it was apparently the best constrained model available which was likely to be fair representative of the Himalayan arc generally and of the adjoining central Himalaya in particular. For initial locations the average error in latitude, longitude is 4 km and for depth 5 km (Fig. 3.2). These events are well distributed all over the region covered by the network and scanned epicenter distances with in 450 km. All of these events have their local magnitude between 1 and 5.3. The distribution of located epicenters is shown in Figure 3.3. Table 3.1: Initial 1-D Velocity model used for location Depth (km V P (km/s) V s (km/s) >

3 Figure 3.1: Wadati diagram. Linear fit of S-P time versus P- time. The root mean square error (RMS) is 0.09 and the computed V P /V S ratio is Figure 3.2: Histograms showing error statistics for hypocenter (km) (a, b) and time residuals (c). 69

4 Figure 3.3: Epicenter distribution of initially located earthquakes from Moderate size earthquakes in the region are shown with different stars (Blue star: 2005 Chamoli, M 5.3; Red star: 2007 Kharsali, M 5.0). Whereas the seismicity of the recording period is widely dispersed in the Kumaon Garhwal Himalaya, we observed a well defined band of seismicity following the surface trace of the MCT zone. However, we also find another parallel band of earthquakes; about 70 km to its southwest in the Lesser Himalaya, and a significant number both in the Tethys Himalaya and Ganga basin. We have also located 100 earthquakes in the NCR region. As shown in Figure 3.3, during the observation period, 6 earthquakes of magnitude range 4<M<5 and two moderate earthquakes of M 5 occurred in the Kumaon-Garhwal Himalaya region. The two moderate M 5 earthquakes are: The chamoli earthquake (2005 December 14, 30.48ºN 79.25ºE, M L = 5.3, blue star) and The Kharsali earthquake (2007 July 23, 30.91ºN 78.31ºE, M L =4.9 and M W =5.0, red star). The histogram in Figure 3.4 shows the depth distribution of earthquakes. The concentration of the seismicity in the upper part of the crust will 70

5 influence the model parameterization that will be discussed in the next section. In addition, the depth distribution provides important information about the rheological behavior of the crust. Figure 3.4: Depth distribution of earthquakes 3.3 Significance of S-arrival time Theoretically, P- and S- arrival time are interchangeable with given V P /V S ratio. However, S-wave phases provide important additional constraints on hypocenter locations. Also, the additions of S- wave data in earthquake locations have several advantages: increase in the number of observations, better constrain on the hypocenter depth and determination of independent S-wave velocity structure that provides important information about the rheology of the earth s crust. Though widely believed that P and S travel times are inter- related, Frank (Ph.D, thesis ) showed that the path used by both the rays are quiet different and hence the information provided by S- wave is complimentary to the P- wave. Also, the depth and lateral resolvability are different. Figure 3.5 show the path of P- and S- wave for a velocity model. Gomberg et al. (1990) demonstrated that partial derivatives of S-wave travel times are always larger than those of P- waves by a factor equivalent to V P /Vs and that they act as a unique constraint within an epicentral distance of 1.4 focal depths. Therefore, the use of S- wave will in general result in a more accurate hypocenter location, especially in determination of the focal depth. On the other hand, error in S- arrival-time at a station close to the epicenter can result in a 71

6 stable solution with a small Root Mean Square (RMS), but actually denoting a significantly miss located hypocenter even for cases with excellent azimuthal station coverage (Maurer, 1992). Since the onset of S- phases are often masked or distorted by P- wave coda, error in arrival time is expected and hence quality control is needed. Figure 3.5: Ray paths for P and S waves through the one dimensional velocity model for the ANZA network (After Frank L. Vernon). Seismic sources were placed at 2.5, 5, 10, and 20 km depth in the model. At each depth the same take-off angles from the source were used for P and S waves. 3.4 Minimum 1-D velocity model using VELEST We used the program VELEST (Kissling et al., 1994) for simultaneous determination of hypocenters, 1-D P, S velocity structures and station corrections. The model geometry (layer thicknesses) is held fixed during inversion. The travel times are calculated by ray tracing using the shooting method (Thurber, 1981), and directly solves the normal equation with Cholesky decomposition (Press et al., 1988). 72

7 3.4.1 Data Selection To estimate a minimum 1-D model we used a set of well located earthquakes because uncertainties in hypocenter locations will introduce instabilities in the inversion process due to hypocenter-velocity coupling. Apart from the velocity model, there are three main factors that control the quality of a location: Number of readings used: The over-determinacy of the inverse problem depends on the number of recording stations used and the magnitude of an event. We selected only 385 events for inversion with minimum of 7 P- and 5 S- readings (Fig. 3.6 and Table 3.2). Thus, a total of 5327 P- phases and 4927 S- phases were used for inversion. Final solution has 1598 variables (1540 hypocenters, 8 P- and S- velocities and 50 station corrections), against data elements, the inverse problem with a fixed velocity was over-determined by a factor of 6.4, when using P- and S- observations and by a factor 3.3, when only P readings are used. Geometry of the station distribution: To obtain a well-constrained solution, the epicenter should be surrounded by recording stations. Thus, well locatable events must occur within a network. The relative position of an epicenter to network is described by the GAP. This is the largest azimuthal angle (seen from epicenter), within which no readings are available. Events that occurred inside a network always have a GAP <180. We have 385 events with at least 7 P- and 5 S- readings and with GAP <180. Figure 3.7 shows the GAP distribution of earthquakes used for inversion. Assuming small and Gaussian reading errors, the GAP and the number of observations roughly describe the expected quality of an epicenter location. Phase reading errors: It is always better to filter out mis-picked arrival times. However, the use of an in correct velocity model introduces systematic errors that can hide miss-picked readings. Therefore, the detection of gross errors requires an advanced knowledge of the velocity structure. To filter out mis-picked arrival times, we have chosen the earthquakes with RMS residual <1.0 sec. (Table 3.2). 73

8 Figure 3.6: Constraints on the data used for inversion. Histograms show the number of events with (a) P- readings and (b) S- readings. Figure 3.7: Distribution of the GAP parameter. 74

9 Table 3.2: Data selection thresholds for the combined P- and S- inversion Number of Observations per event 12 Number of P arrivals per event 7 Number of S arrivals per event 5 GAP < 180 degrees Root Mean Square (RMS) < 1 seconds Based on the above restrictions, data selection for our data set has been adopted. Then, a combined inversion for both a P- and S-wave velocity model is done, using the proposed selection scheme P- and S-wave Velocity Inversion We used three different existing velocity models (Figs. 3.8 a, b) corresponding to the Nepal Himalaya (Monsalve et al., 2006), Western Himalaya (Rai et al., 2006), and the Delhi region (Julià et al., 2009), to jointly invert for the earthquake hypocenter and 1-D velocity model. The initial S-wave velocity models are constructed from P- wave velocity using V P /V S ratio The velocity of the first layer strongly depends on the calculation of the station corrections. In order to calculate these corrections a boundary condition must be applied. A possible constraint is the average of all station corrections must be zero. However, because of heterogeneities of the near surface lithology below the different stations for the inversion, this constraint leads to a first layer velocity, which is only a mathematical average without any relation to the actual geology. Therefore, an alternative approach is chosen: the station correction of one reference station is fixed to zero. So, the first layer velocity reflects the velocity beneath this reference station. The station GTH was chosen as reference station, due to following criteria: (a) located close to the center of the network, (b) not located at the boundary of two units with strongly different geology, (c) had long recording period comprising of at least 50% of the total possible readings, and (d) had data of high S/N ratio. 75

10 Figure 3.8: Initial and final velocity models for (a) P- wave, and (b) S- wave The three input velocity models were initially parameterized as stack of 2 km thick layers. The optimum model calculation requires number of iterations to select and test control parameters, which are suitable to data set and problem. The damping parameter provides the balance between the solution and the initial model. We started with damping coefficient of 0.01, 0.1 and 1.0 for the hypocentral parameters, the station corrections and velocity parameters, respectively. In subsequent runs we changed the damping parameters of velocity parameters and station corrections, in order to get data misfit reduction and the good parameter resolution. The inverted velocity models were then iteratively simplified by fusing layers with similar velocities to form the next initial model (Kissling, 1994). The RMS residual obtained for the three velocity models are shown in Table 3.3. The resolving power of the data is defined by the ray distribution in the modeling volume. The inverted models (Figs. 3.8 a, b) are seen to resolve layers only up to a depth of ~20 km, this is caused due to inadequate data and criss-cross incidence at deeper levels. The ray hit count is shown in Figure 3.9. Therefore the velocity of the layers below this depth is fixed. We kept changing the starting model in subsequent runs as we 76

11 get solutions with smaller misfits. Random variations of this starting model can also be used as starting model in order to get better solutions. The following criterion is made to judge the quality of different solutions. There should not be large oscillations of model parameter during the inversion. Convergence of the solution should be fast and stable. The model should adjust the shifted hypocenters properly. The station corrections of the neighboring stations should be similar. Figure 3.9: Ray Distribution in depth. Table 3.3: Initial and final RMS residual for different models Model Name Initial RMS (s) Final RMS (s) NCR Western Himalaya Nepal Himalaya Optimum 1D (This study) The final P and S velocities obtained from combined inversion along with depth distribution of earthquakes shown in Figure The final velocity model resulting from travel 77

12 time inversion is well resolved only down to a depth of 20 km, because of very few hypocenters (Fig. 3.10) and rays below 20 km (Fig. 3.9). The resolution of different velocity layers obtained from inversion is shown in Table 3.4. The optimum 1-D velocity model obtained from simultaneous inversion of arrival times of P- and S- phases is shown in Table 3.5. This shows that the upper crust to a depth of 20 km into a three-layer structure. At a depth of 4 km first discontinuity appears and the P- wave velocity becomes 5.90 km/s and S- wave velocity is 3.40 km/s. Below 4 km the velocity is constant and it reaches 6.0 km/s, 3.51 km/s for P- and S- waves at a depth of 16 km. Another discontinuity is mapped at a depth of 20 km where the velocity increases to 6.40 km/s, 3.72 km/s for P- and S- waves respectively. The total RMS residual reduced from s before inversion to s after inversion (Table 3.3). The epicenter and depth distribution of 385 earthquakes, used for joint hypocenter location and optimum 1- D velocity model estimation is shown in Figure Velocity (km/s) NEQ = Depth (km) Vs Vp 50 Not resolved 60 Figure 3.10: Final 1-D velocity models from combined and hypocentral parameters. 70 inversion for P- and S- wave velocities 78

13 Figure 3.11: (a) Distribution of 385 earthquakes used in joint inversion for hypocenter and velocity parameters using VELEST. (b) Earthquake depth distribution is projected along the BB' cross-section. Topography along the cross-section is also plotted. Table 3.4: Resolution parameters of various velocity layers obtained from Travel-Time inversion of P- and S- phases Depth (km) P Resolution S Resolution

14 Table 3.5: 1-D Velocity model obtained from Travel-Time Inversion and Corresponding V P /V S ratio Depth (km) V P (km/s) V S (km/s) V P /V S In order to obtain stable results, no low-velocity layers have been allowed in the inversion. However, Kumar et al. (2009) reported existence of low velocity layer at a depth of 15 to 18 km to the north western part of our network. Based on this, combined inversion for P- and S-wave velocity models is attempted which allows layers with low velocities. In order to resolve the low velocity layer, it is necessary to resolve at least one layer below the low velocity layer. Accordingly the stack of layer is subdivided. Even though we have good number of earthquakes in the depth range of 15 to 18 km and the layer is well resolved, we could not find the low velocity Stability Tests For Velocity model To test the stability of our optimum 1-D velocity model we carried out the following tests. (i) Joint inversion of the phase data was repeated using a relaxed average initial velocity model with bounds as shown in Figure All solutions were found to converge to the optimum 1-D model obtained earlier, up to a depth of 20 km. (ii) To test if the earthquake locations were well constrained and not conditioned by the initial hypocentral parameters, we repeated the inversions using a perturbed model of hypocentral locations: the latitude, longitude and depth parameters of alternate individual earthquakes being randomly shifted by ± 12 km (Figs a, b, c). Again, the results show excellent convergence to the earlier solutions with horizontal and vertical locations suffering a maximum divergence of 700 and 1087 m, respectively. 80

15 (iii) Figure 3.14 compares the RMS travel time residuals, epicenter and focal depth error for earthquakes located using the Nepal Himalaya velocity model (Monsalve et al., 2006), used for initial locations, and the 1-D optimum velocity model obtained from our joint inversion. Most of the earthquakes (more than 80%) located using our optimum 1-D model show RMS value of s as compared to s using the Nepal Himalaya model. This is also reflected in error in epicenter and focal depth skewed to lower values. Figure 3.12: Stability test for the optimum 1-D velocity model. Thin lines show the upper and lower bounds of the optimum 1-D velocity model, used as input. Output velocity models and Optimum 1-D are shown as dashed and thick solid lines, respectively. 81

16 Figure 3.13: Hypocenter stability test with respect to latitude (a), longitude (b), and depth (c). Black closed circles: coordinate difference between randomized input and minimum 1-D locations. Grey open circles: difference after inverting with the randomized input data. The average remaining shifts between the minimum 1-D locations and the output of this test and the variance is given on the right. Figure 3.14: Histograms showing error statistics for time residual (s) and hypocenter (km) for (a) the initial (Monsalve et al., 2006), and (b) optimum 1-D velocity model (this study). 82

17 3.4.4 Station Corrections Station corrections represents deviations of the 1-D velocity model and depends strongly upon the topography and lateral velocity variations associated with heterogeneous near-surface structure which is otherwise not resolved in 1-D model (Kissling, 1995). In the study region the topography varies from 800 meters in south to 3000 meters in the north. Station corrections for individual seismograph locations, excluding MNA and DBN having inadequate phase data, were calculated with respect to the reference station GTH. The station corrections for individual seismograph locations show variations between -0.4 to 1.0 s for P- wave and to 1.5 s for S- wave (Table 3.6 and Figs a, b). The positive and negative distributions of station corrections reflect to some part of the overall three dimensionality of the velocity field. Negative station correction means where the true velocities are higher than the predicted fields at the recording station with respect to the reference station GTH and positive correction means where the true velocities are lower than the predicted fields. As expected, stations in the same geological unit have similar corrections. Relative positive station corrections of both P- and S- waves are observed for the stations to the south of MBT, which overlay by the low-velocity Siwalik formation and the sediment filled Indo- Gangetic plain. The stations to the north of the MBT, in the Higher Himalayan crystalline shows relatively negative station corrections of both P- and S- waves (Fig. 3.15). The stations near to the reference station are showing almost zero corrections. 83

18 Table 3.6: P- and S- wave corrections obtained from travel time inversion Station Code P-wave Correction (s) S-wave Correction (s) LTA HLG NAL SRP KSL BNK MRG DKL PKH JLM GHT OKM ALM NTI KSP TMN BGR BHT NND DRS NTL MNY PTG DCL DDR NTR HSL SYT PPL KTD LGS TNP ALI ABI CKA DDN GKD GTU KSI KHI NHN TPN GTH

19 Figure 3.15: Station corrections (in seconds) for (a) P- waves and (b) S- waves with respect to reference station GTH (marked as star). Variations in sizes of triangle and circle correspond to magnitude of positive and negative station correction values, respectively. 85

20