Receiver Function (RF) Estimation Using Short Period Seismological Data

Transcription

1 Receiver Function (RF) Estimation Using Short Period Seismological Data Shantanu Pandey Department of Earth Sciences, Kurukshetra University, Kurukshetra Abstract The advent of the receiver function (RF) technique has dramatically altered the traditional concept of the composition and structure of the crust and its evolution through geologic times. The combined power of P-to-S converted signals (Ps phase) from any interface with adequate velocity contrast, and their multiply reflected and converted waves between the surface and the interface, known as multiples recorded in the RFs are used to simultaneously determine the depth to the interface and constrain the average V P (related to Poisson s ratio s) of the intervening region. This case study is an attempt to explore the power and limitations of short period (data) RFs and strategise effective ways and means to make better use of the short-period data. It is demonstrated that short-period data after restitution and application of appropriate low pass filters can indeed become useful for H- V P studies. The efficacy of this simple approach is tested and demonstrated on data from the Japanese island arc setting. After restitution (de-convolving instrument effect from the data), the range of band-pass period best suited for the Japanese data varied from a minimum of 1.5 to 3s up to a maximum of 15 to 20s. The resultant filtered RFs have come out with sharper Ps and multiple arrivals. The choice of optimal filters after restitution is found region sensitive. In conclusion, we find that: a) restituted short period RFs can be used to estimate the crustal thickness (H) and Poisson ratio (s) due to improved quality in observation of the multiple phases (Pps, Pss), b) the restituted short-period data is broadband enough to pick signals related to the first P- and S- multiples even in a complex setting such as the Japanese islands, and c) appropriate choice of the low pass filters and the band-pass range need to be tailored after careful study of the data. Introduction Knowledge about the structure of the earth s interior used to narrow down the competing hypotheses for continental evolution has mainly emerged from seismological studies as it reveal presence of a stratified earth, based on changes in its physical and chemical properties with depth manifested as seismic velocity discontinuities. These acts as building blocks to trace the evolutionary path of the earth, since they carry in their bowels the imprints of both past and present convective regimes of the mantle, which are governed by the motion of tectonics plates, resulting in the observed diverse surface geologic expressions. Teleseismic P waveforms recorded at a threecomponent seismic section contains immense information about the earthquake sources, the earth s structure in the vicinity of both source and receiver, and mantle propagation effects. If the source and mantle propagation effects are eliminated then we are able to obtained the local crustal and upper mantle structure underneath the station. Source equalized receiver function analysis is such a technique to explore crustal and upper mantle structure at the receiver site. A seismic signal that essentially contains the effects of local structure beneath a station devoid of effects due to source complexities and path effects is termed as Receiver function (Ammon, 1997). The teleseismic record is the output of convolution of seismic source, underlying structure response and the instrument effect besides some noise. Owing to the large velocity contrast at any interface (e.g. crust-mantle boundary), the incoming incident teleseismic P energy partly gets converted into P-to-S waves that transmit across the boundary besides the direct arrivals and reflections. These transmitted P and P-to-S conversions (Ps) in turn can get multiply reflected between the free surface and the interface (converter) resulting in multiples of varied nature. From these Ps conversions and Pps, Pss multiples, we get a first-order information about the crustal structure beneath a station (Zhu and Kanamori 2000). Most of the available RF images focus on use of broadband data from various networks to map the underlying crust-mantle structure. The main apprehension to use short-period data for H-V P /V s determination is based on the apparent belief that multiple (Pps, Ps s ) may be poorly registered by short period (1 Hz) sensors. This case study is intended to study the power and limitations of short period data RF s and strategies effective ways and means to make better use of the large amount of short-period data accrued in the past and remains unutilized. (St-40)

2 6 th International Conference & Exposition on Petroleum Geophysics Kolkata 2006 In this study the basic aim of receiver functions is to estimate the crustal thickness values (depth to the Mohorovicic discontinuity) and the average crustal composition that can be inferred from the Vp/Vs values (related to Poisson s ratio σ). Using teleseismic receiver functions we determine this depth of Moho that revels the internal structure of earth illuminating the basic geology and tectonic evolution of the region. Methodology P-to-S converted phases from distant earthquake sources can be used to study the underlying discontinuities with adequate velocity contrast. Teleseismic P waves in the epicentral distance range , steeply incident (15-30 ) on any boundary with sufficient velocity contrast generates P-to-S converted as well as multiple reverberations between the surface and the discontinuity beneath the seismic station. There are many multiple reflection and conversion that occur between the surface and the interface like Ps, Pps, Pss, PsPs, etc. The P waveforms dominate the vertical component of ground motion whereas the P-to-S converted wave and their corresponding multiples- essentially radially (SV) polarized- are largely registered on the radial component. The amplitudes of conversions and multiples depend on the contrast of P- and S-wave velocity and the density. It also depends on the incidence angle of the P-wave. The incidence angle is determined by the epicenter distance and focal depth of the earthquake. Figure 1 clearly suggests polarized Ps and its multiple phases; a process of isolating them from P-arrivals becomes necessary. This is usually accomplished by applying a co-ordinate transformation that involves appropriate component rotation of the original (Z, N-S and E-W) records using the back-azimuth and/or angle of incidence information. The rotated seismograms though separately contain (ideally) P, SV and SH energy, are contaminated by common effects related to source, mantle path and instrument. By de-convolving the incident P waveform from the radial component, the effect of source time function, source site reverberation and wave propagation through mantle can be removed. The deconvolved radial component now primarily contains information about the underlying receiver side structure in the form of SV energy. In order to decompose the wave field in to P, SV and SH components, we rotate the coordinate axes from Z, N, E in to a radial and transverse coordinate system. This rotation can indeed be performed in two different ways, (1) only horizontal axes are rotated from ZNE in to ZRT (Radial, Transverse) system based on the back azimuth of the event with respect to the station, Z- and R-components contain most of the energy of the direct P and P-to-S conversions, and (2) isolate SV (SH) converted phases from P coda involves rotation of all the three axes into the ray coordinate system, LQT. Here, L points in the direction of P wave incident to the surface and Q is in the ray plane and perpendicular to L, the positive direction of Q axis is defined away from the earthquake. T is perpendicular to both L and Q, and forming the third axis of the right-hand LQT-system (Figure 2) Fig.1: Variation of P-to-S conversion coefficients vs. incidence angle. The conversion interface is assumed to be at a depth of 60km. (after Yuan, 1999) that the Ps waves, and hence the multiples, are inherently weak phases due to their small conversion coefficients. Therefore, on the original recordings, they often are obscured by the P-coda. Hence, to enable us better observe these SV Fig. 2 : Rotation of the three component (ZNE) into ZRT and LQT (St-41)

3 If the rotation is properly done, there will be higher concentration of P and SV wave energy left on the L and Q (SV) respectively. The advantage of using the Q component instead of the radial component is the disappearance of projected P energy at the P arrival time. The first onset on the Q component is usually the P-to-S conversion from a discontinuity at very shallow depth below the surface and therefore delayed with respect to the P onset (Figure 3). From Figure 3 it is evident that only those conversions (Ps) and multiples (Ppps Pps) that are taking place at interface have positive polarity and those multiples (Ppss Pss) that are getting converted at free surface having negative polarity. component. This L-component is used to generate an inverse wavelet (filter) in a specified time window by the process of spiking, that essentially involves computation of the autocorrelation function of the specified time window. The time response function of this filter is nothing but a time series which when convolved with the observed L results the desired delta like spike function. The designed inverse filter when convolved with the observed Q and T component would minimize source related effects in the least square sense. As this process involves the operation of inverse filtering it is generally termed as deconvolution in time domain. To put in simple terms, in time domain we generate inverse filter by minimizing the least square difference between the observed seismogram and desired delta-like spike function of normalized amplitude. After deconvolution, all components are normalized to the maximum amplitude of the spike on the L component (Figure 4) to preserve the absolute amplitude of conversion ratio. Fig. 3: Comparison of the receiver function arrivals in ZRT and LQT frames of rotation The P-to-S converted phases recorded on the rotated seismograms, SV (Q, R) and SH (T) components, are often obscured by effects/signals related to different sources of varied magnitudes, common path propagation and instrument related effects. Recognizing that the L (Z) component is dominant with source related (P-signal) signatures and also realizing that the other two effects are common to all the three components, we use the process of deconvolution to eliminate these effects. We deconvolve the L(Z)-component from the Q(R)- and T-components. Now the deconvolved Q and T components have information about the shear structure directly beneath the receiver. These Q and T-components are called the SV and SH receiver functions. The above process of deconvolution also makes receiver functions of different sources of varied magnitudes comparable in amplitudes and waveforms besides eliminating instrument related and mantle propagation effects. Time Domain deconvolution The P waveform contains the signatures of the source function and is prominently registered on the L Fig.4: Restituted (Instrument deconvolved), rotated and deconvolved seismograms (after Yuan, 1999) Simultaneous estimation of V P and H After isolating the desired P-to-S converted waves (SV polarized energy) from P-coda adopting appropriate component rotation (ZRT, or LQT rotation) the process of source equalization, minimization of common path and instrument related effects from raw teleseismic records through the process of deconvolution results in obtaining the receiver function which essentially contains the response of the underlying structure directly beneath a seismic station. The differential travel time between the incident P-wave and the P-to-S converted wave (delay time) is used for the computation of discontinuity depths. The delay time of P-to-S converted wave can be calculated by- (1) (St-42)

4 6 th International Conference & Exposition on Petroleum Geophysics Kolkata 2006 where V P and V S are P-and S-wave velocity above the interface, respectively, H is the layer thickness; p is ray parameter (slowness of incident P wave). Ps travel times also vary as function of P wave slowness. With a smaller epicentral (larger slowness), Ps arrives later, and vice versa. Similarly, delay travel-time of multiples can be derived as following. t t Pps Pss Psps t Psss = H 2 2 ( VS p + VP p) 2 H( VS p) ( VS p VP p) 2 2 (for Pps ) (2) = 2 (for Pss and Psps) (3) = H 3 (for Psss) (4) Simultaneous and independent estimates of crustal thickness (H) and Vp/Vs 2 { [ ( V ) 1] } 1 P V σ = 0.51 (5) S Differential time increases when V P or V S decreases. Keeping the ratio V P fixed, differential travel times will increase more slowly when velocities decrease. As the P-to-S conversion point from the Moho is close to the station (usually 10 km laterally), Moho depth estimates are less affected by lateral velocity variations. As evident from the above equations, a trade-off between the thickness and the average crustal velocities strongly exists. As t Ps is the differential travel time of S with respect to P wave in the crust, the dependence of H on V S is stronger than on V P. Hence, more precisely, crustal thickness H highly depends on V P ratio. Therefore, transformation of t Ps times directly into Moho depth without accurate V P ratio could thus lead to very misleading crustal thickness estimates. This ambiguity can fortunately be reduced by using the Moho multiples (Pps, Pss) which provide additional constraints. This is what is exploited in the Zhu and Kanamori (2000) method to estimate H, V P using Ps, Pps and Pss amplitude stacks. Zhu and Kanamori (2000) method is very versatile, as it can be applied to single receiver function trace or to stacked receiver function trace. In real situations, it is very difficult to identify the Moho Ps and the multiples besides measuring their arrival times on a single receiver function trace. It is simply because of background noise, scatterings from crustal heterogeneities and interference by arrivals due to shallower structure. The basic property of noise is randomness. So to enhance the signal to noise ratio (SNR), one can stack the receiver functions in which the random noise gets cancelled. Such stacking is usually done in time domain for a cluster of events. Since we are mainly interested in estimating crustal thickness, a straightforward H-σ domain stacking is proposed by Zhu and Kanamori (2000) and is defined as- ( H, σ) ω r( t ) + ω r( t ) ω r( t ) s = (6) 1 1 where r(t) is the radial receiver function, t 1, t 2 and t 3 are the predicted Ps, Pps and Pss/Psps arrival times corresponding to crustal thickness H and V P ratio σ, as given in equations (1), (2) and (3). This s(h,σ) value reaches a maximum, when all the three phases stack coherently. This happens for the optimal/appropriate choice of H and σ which represent the correct values of crustal parameters. Data Anlaysis As described above, to model the crustal structure beneath a station we use teleseismic P wave and decompose the wave field into it s P, SV, and SH components through rotation (ZRT or LQT system) of the recorded three component seismograms. For further isolation we use deconvolution. For the construction of receiver functions we follow the methods described by the Vinnik (1977) and further elaborated by the Kind et al., (1995). Teleseismic earthquake data recorded at 58 three-component stations (Figure 5) that belong to the Japanese Hi-net network (Obara, 2002) equipped with ML4-3-D sensors with a natural period of 1s installed in boreholes were used. Their sensitivity is around 200 V/m/s. A total of about 260 receiver functions from 10 good quality stations with high SNR ( 3) were selected for analysis. Fig.5: Map of the locations of the stations covering the study region in the Japan Island Data from short period records are restituted and band pass filtered. The range of band pass period best suited for the data varies from a minimum of 1.5, 2 to 3s up to a (St-43)

5 maximum of 12, 15 to 20s depending on the signal characteristics of a station. The resultant filtered receiver functions have come out with sharper Ps and multiple arrivals. A Ps move-out corrected slowness stack section for the station KAMH, for both, the original RF (Figure 6a) and their restituted, filtered version (Figure 6 b) is presented (Ramesh, 2005). Data and plotting options remains same for both. The stacks binned in 0.2 s/º slowness interval are presented using reasonably good data at this generally noisy station. Note that in original data stacks, the crustal P and S multiples designated Pps and Pss respectively, are not obvious to recognize in the expected time window of there arrivals in view of competing arrivals in the vicinity of the actual multiple phases. In contrast, the Ps and it s multiple appear as relatively clear and distinct phases after restitution and filtering (Figure 6 b). Fig. 7: Slowness stack sections at a few sample individual stations. Each station stack section is low-pass filtered applying 1.5 to 3 second period filters of various orders (1 to 3) Fig. 6: Move-out corrected RF slowness stack sections at station KAMH. (a) Original records (b) Restituted section Data of this kind can now be used to determined H - V P values by methods like Zhu and Kanamori (2000) to obtained better-constrained crustal parameters. In this method, H and V P are estimated by performing grid search over a large range of H and V P values. We apply this method to find the optimal value of that maximize the summation of amplitudes of the Ps, Pps and Pss. This scheme was employed over a depth range of km and V P range of , assuming a uniform average V P value of 6.3 km/s for the whole crust beneath all the station. The receiver function of each station are stacked adopting standard weights (using equation 6), of ω 1 = 7, ω 2 = 3, ω 3 = 1. For appreciation of the quality of the data used in determination of H-V P values; we present slowness stack sections (binning interval 0.3 s/º) of few selected stations spread across the Japanese Islands (Figure 7). Finally average crustal V P values and crustal thickness (H) estimates were computed at different stations (Figure 8) applying the Zhu and Kanamori (2000) technique. The H-V P plots for these stations are presented in Figure 8. The white filled circle in the plots signifies V P and H values. The nature of the closures depends on the quality of Fig. 8: Average crustal V P versus H at a few sample stations data used. The value of the Poisons ratio (related to V P ) is the determining factor of the kind of geology of that particular area. Generally, felsic rocks have lower V P (upto 1.79) values while mafic rocks are characterized by higher values (>1.8). The global average value is about Table 1 describes the crustal parameters at all the 10 stations analyzed here. Table 1: Station code with locations, number of seismograms, crustal thickness (H) and V P Stn. Latitude Longitude No. of V p H Qua- Code (ºN) (ºE) RFs (km) lity MHRH A SINH B INMH A-B WKYH A KAMH B IZSH A-B HKTH B AIOH B HINH A MIGH A-B Conclusions Restituted short period RFs can be used to estimate the crustal thickness (H) and Poisson ratio ( ) due to (St-44)

6 6 th International Conference & Exposition on Petroleum Geophysics Kolkata 2006 improved quality in observation of the multiple phases (Pps, Pss). The restituted short-period data is broadband enough to pick signals related to the first P- and S- multiples even in a complex setting such as the Japanese islands. Appropriate choice of the low pass filters and the bandpass range need to be tailored for the data at each station after careful study. This exercise, though preliminary in nature demonstrates the power of short period (data) RFs and effective strategies to make better use of the large amount of shortperiod data that has accrued in the past and remains unutilised. References : Ammon, Charles J., An overview of Receiver Function Analysis, Home Page of Ammon, 1997, Kind, R. and L. P. Vinnik, The upper-mantle discontinuities underneath the GRF array from P-to-S converted phases, J. Geophys. Res., 62, , 1988, Kind, R., G. L. Kosarev, and N. V. Petersen, Receiver functions at the stations of the German Regional Seismic Network (GRSN), Geophys. J. Int., 121, , 1995, Obara, K., Hi-net: High sensitivity seismograph network, Japan, in Methods and Applications of Signal Processing in Seismic Network Operations, edited by T. Takanami and G. Kitagava, Springer, 266pp., 79-88, 2002, Ramesh, D. S., H. Kawakatsu, S. Watada and X. Yuan, Receiver function images of the central Chugoku region in the Japanese island using Hi-net data, Earth Planet Space, 57, , 2005, Vinnik, L. P., Detection of waves converted from from P to SV in the mantle, Phys. Earth Planet. Int., 15, 39-45, 1977, Yuan, X., Teleseismic Receiver Function Study and Its Application in Tibet and the Central Andes, Ph.D Dissertation Thesis submitted to Free university, Berlin, Germany, 1999, Zhu, L. and H. Kanamori, Moho depth variation in southern California from teleseismic receiver functions, J. Geophys. Res., 105, , (St-45)