Geophysical Journal International

Transcription

1 Geophysical Journal International Geophys. J. Int. (014) 198, GJI Seismology doi: /gji/ggu13 Estimation of shear velocity contrast from transmitted P s amplitude variation with ray-parameter Prakash Kumar, 1, Mrinal K. Sen 3 and Chinmay Haldar 1, 1 CSIR - National Geophysical Research Institute, Hyderabad , India. prakashk@ngri.res.in AcSIR-National Geophysical Research Institute, Hyderabad , India 3 Institute for Geophysics, The University of Texas at Austin, Texas 78758, USA Accepted 014 June 3. Received 014 May 30; in original form 014 March 14 1 INTRODUCTION The converted wave technique (commonly termed as receiver function analysis) in passive seismology is routinely used to map the subsurface regional crustal and upper mantle structures. In order to enhance the signal-to-noise ratio in the scattered phases, the general procedure is to stack (either station-wise or conversion point-wise) many traces and then model the resulting trace, either by forward modelling or by an inversion (Ammon et al. 1990; Ligorrıa & Ammon 1999) approach to arrive at a meaningful structural model. The primary objective of this modelling is to estimate the shear velocity contrast across an interface. The amplitudes of the converted phase from an interface are expected to show a moveout with respect to slowness. The stacked trace would typically represent an average amplitude. Although the stacking process improves the signal-to-noise ratio, however, in areas with significant amplitude variation with ray parameter, the shear wave velocity derived from it may not be reliable. Julia (007) proposed a grid search approach using the amplitudes of primary and converted phases using receiver function data to estimate the velocity and density contrast across an interface. However, our approach is quite different in that we investigate the applicability of characteristic transmitted amplitude versus ray-parameter in teleseismic records, similar to amplitude versus offset analysis done in exploration seismology (e.g. Castagna & Backus 1993), to estimate elastic parameters. The Zoeppritz equation expresses the transmission coefficients as a function of slowness and independent elastic parameters. We derive a linear SUMMARY Amplitude versus offset of P to P reflection is commonly used by the exploration seismology community for hydrocarbon exploration. In this paper, we investigate the feasibility to estimate crustal velocity structure from transmitted P- to S-wave amplitude variation with ray-parameter. First the transmission coefficient for the plane P wave converting to S wave (P- to-s) is approximated and expressed as a function of slowness. The resulting linear relation involves two coefficients (intercept, X and gradient, Y), which are functions of velocities and densities. Due to the stable nature of X and the fact that P-to-Samplitudes are weakly dependent on the density contrast, we use this parameter next to estimate the shear wave velocity contrast across an interface using the forward scattered P-to-Samplitude versus slowness data. We report on the effectiveness of the approach using various synthetics data sets. The present methodology is also tested on real data sets from two broad-band seismic stations from HYB and COR. Key words: Body waves; Computational seismology; Theoretical seismology. approximation of the P s amplitude that can be used to estimate the elastic parameters from the observation of amplitude as a function of slowness for transmitted phases, particularly P- to-s. The method is first tested on synthetic data generated from a plane horizontal, isotropic medium for various types of models. The robustness is tested further on two real datasets from the broadband seismic stations HYB and COR. THEORY Exact reflection and transmission coefficients for an incident plane wave as a function of angle at an interface of two layers in welded contact are given by the Zoeppritz equations. We focus here on the analytic form for the converted wave transmission coefficient from P to S (P- to-s) at a planar boundary of two elastic media (Fig. 1). Fig. 1 demonstrate the possible combination of reflection and transmission ray geometries. The P- to-s transmission coefficient is given by (the notations and convention are after Aki & Richards 00) A Ps = Gpα 1 β 1 F, (1) where G = a d ( ) cos i1 cos j and F = b α 1 β ( cos j1 β 1 ) + c ( cos j β ), C The Authors 014. Published by Oxford University Press on behalf of The Royal Astronomical Society. 1431

2 143 P. Kumar, M. K. Sen and C. Haldar s P i 1 j 1 discontinuity α 1 β 1 ρ1 α β ρ i P s j Figure 1. Schematic ray diagram showing different possible combination of reflection and transmission ray geometries at the welded interface between two different solid interface. α, β and ρ are the model parameters that is P-wave, S-wave velocities and density, respectively, of the medium. The different angles are also shown by i 1,i,j 1 and j are the angles as shown. s P Figure 3. Dependence of the P- to-s converted amplitude on the density contrast of the medium. The abscissa and ordinate denote the percentage change in density contrast and amplitude, respectively. It is clear that the density has insignificant influence on the amplitude of the transmitted shear wave. Figure. (a) P- to-s converted amplitude curves plotted with increasing order of slowness for an isotropic velocity model (shown in boxes as insets in the upper two panels). Note that in panel (b), the model has no density contrast between the two layers. The dashed line denotes the amplitude compute using the exact equation (from Aki & Richards 00), while the grey and black solid lines are the approximated curves derived from eqs (1) and (), respectively. Bottom subplot of each panel is the A ps /p verses p plot, which is a straight line according to the eq. (), and the intercept is denoted by X. The thick grey dashed curve in (b) is the exact curve from (a) that is the grey dashed line in (b) is the dashed line from (a). Another interesting feature of the panel (a) and (b) is that for a small density contrast, both approximation tend to approach the exact curve.

3 Estimation of shear velocity 1433 Figure 4. Application of the present method to a synthetic data. (a) Synthetic P-receiver functions generated at various slowness values for a simple model shown in (b), where the contrast in β from crust to subcrust is 1. km s 1. The top phase around 5 6 s is the P- to-s conversion from the interface at 40 km depth. The amplitudes from (a) are picked automatically within the time window of 8 s and plotted in (c) as open circle. Now, using the velocity model of (c) the amplitude curves are generated analytically and shown in (c) as, dashed curves: exact, grey: approximation -I and black solid curve is for approximation -II as shown in eqs (1) and (), respectively. A ps /p verses p plot in (d), which is a straight line according to the eq. (). The intercept (X) has been estimated by fitting a regression line to the data. Once we know X, the shear wave velocity contrast can be estimated as δβ = X/ = 1. km s 1 (according to eq. 5), which is in good agreement with the real value. p = rayparameter = sin i 1 α 1 = sin i α = sin j 1 β 1 = sin j β, ( a = ρ 1 β p) ( ρ 1 1 β 1 p) ; ( b = ρ 1 β p) + ρ 1 β 1 p, ( c = ρ 1 1 β 1 p) + ρ β p ; d = ( ρ β ρ ) 1β 1. Angles i s and j s are defined in the Fig. 1. In the following we will derive two different approximations of eq. (1). Assuming that i 1, i, j 1 and j are small, we can express eq. (1) in the following form A ps p = X + Yp, () which is a straight line for (A ps /p) versusp with intercept, X and slope Y. The intercept and slope are given by X = ( ρ β ρ ) ( ) 1β1 α1 β ρ ρ 1, (3a) ρ 1 β 1 + ρ β and Y = ( ρ β ρ ) 1β1 α1 β X ( )( β β 1 ρ1 β1 ρ ) β. (3b) ρ 1 β 1 + ρ β ρ 1 β 1 + ρ β Further, as a special case if we assume that β/β 1and ρ 1 /ρ 1 1 then relations (3) reduce to the following form ( ( ρ β X = ρ ) ) 1β1, (4a) ρ 1 β 1 + ρ β Figure 5. This is same as Fig. 4, but for a different velocity model, where the contrast from crust to subcrustal shear wave velocity has been kept low (0.4 km s 1 ). Here, the value of X has been found to be 0.8 and thus δβ = 0.4.

4 1434 P. Kumar, M. K. Sen and C. Haldar Figure 6. This is same as Fig. 4, but for different velocity model, where there exists a gradient at the base of the lower crust. The intercept and the jump in shear velocity are in good agreement with each other as indicated. Figure 7. This is same as Fig. 4, but for a velocity model, where we have two discontinuities, one at the intracrustal and other as similar to Fig. 6. The amplitude picking windows are shown as rectangular boxes. Here, we have two intercepts for the respective interfaces and the values of Xs and δβs are in agreement with the the real values as indicated and details are in text. Figure 8. This is same as Fig. 4. Here, we added Gaussian noise of mean = 0.0 and standard deviation = 0.0 to the synthetic data (a) generated for the model shown in (b) and repeated the procedure as described in the text and also in the earlier figures. The estimated value of X =.37 and δβ = 1., which is close to the real value. and Y = ( ρ β ρ ) 1β1 α1 β. (4b) ρ 1 β 1 + ρ β Eqs (3a and b) are useful relations used in the further analysis. However, relations (4) are just special cases derived from relations (3). Now in order to compare the above three amplitude curves, namely, the exact, approximation-i and approximation-ii, we used an arbitrary velocity model and generated amplitudes at regular interval of slowness. Fig. depicts the comparison of all the three curves. As expected, the approximate amplitudes are close to the exact one at small ray parameter; however, all the three curves are well within the realistic limit of teleseismic P slowness range (Figs a and b top subplots), which is roughly 0.04 to 0.08 s km 1 and the largest deviation lies beyond this range. In the bottom subplots of each panel (Fig. ), (A ps /p) versusp plots are shown that are straight lines (eq. ). The linear regression can be fitted to derive X and Y. Note that, for panel b) of Fig., the amplitude curves are generated keeping the density contrast of the top and bottom layer the same. Under this assumption, the discrepancies among the curves are reduced and interestingly, the intercept (X) converges to a unique value. In order to compare the exact amplitude curves of P-to-S waves for a model with and without density contrast, we superimposed the exact amplitude curve of (i) (dashed line) on (ii) of Fig. as thick dashed line, and it is clear that they are very close to each other indicating that the density contrast does not significantly affect P- to-s transmitted amplitudes. This property of converted wave amplitudes is also tested in Fig. 3, whereweshowp- to-s amplitudes with varying percentage of density contrast. It is clear that the density contrast has negligible effect for practical purposes. With this view, we further reduce the intercepts of eqs (3a) and (4a) to the following form X = (β β 1 ) = δβ, (5) where both the approximation-i and approximation-ii converge. Eq. (5) is now our working formula with which we estimate the intercept, which yields the shear velocity contrast across an interface.

5 Estimation of shear velocity 1435 Figure 9. Application of the present methodology to a real field data set form a Geoscope station HYB located in the Indian shield of Precambrian terrain. (a) is the receiver function image arranged with increasing order of slowness. The colour code represents the polarities that is red: positive and blue: negative. The positive phase at around 3 5 s is shear wave conversion from Moho. The amplitudes for the Moho phase have been picked automatically selecting a window shown by a rectangular box in (a). The picked amplitudes are plotted in (b). The dashed curve in (b) represents the amplitude curve for a velocity model derived from inversion shown in subplot (e). Plot (c) shows the estimation of intercept as described in earlier figures and also in text. The error in X with ± SD has been derived from bootstrap technique. The δβ has been estimated in (d) for the approx-i and -II to be 0.8 and 0.7 km s 1, respectively. In order to show the consistency of our estimate we inverted the stack traces in (e) for the model shown in (d). In (e) black wiggle is the stack trace derived from (a) after moveout correction and the grey wiggle is the synthetics. 3 EXAMPLES 3.1 Synthetic data In order to test the validity of the relation (5), we first applied it to synthetic data sets generated for various types of models. The first example is shown in Fig. 4. The synthetic P-receiver functions (Frederiksen & Bostock 000; Fig. 4a) have been generated for a realistic velocity model (shown in Fig. 4b) at various slowness values. The velocity model is simple and isotropic with shear velocity contrast of δβ = 1. km s 1 (Fig. 4b). In the receiver functions (Fig. 4a), the positive peaks at 4 5 s are the P- to-s conversions from the interface at a depth of 40 km. The amplitudes of these phase are picked automatically by picking the maximum amplitudes within the time window of 10 s and are plotted as a function of slowness in Fig. 4(c) as open circle. For the velocity model used in Fig. 4(c), the approximated curves are also generated using the eq () using X and Y from eqs (3a and b) and (4a and b), respectively, and superimposed on Fig. 4(c). Now, we plotted the slowness weighted amplitude (A ps /p) versusp. The intercept X, has been estimated by fitting a regression line through the data as shown in Fig. 4(d). Here, the estimated value of X =.4, which is exactly double that of the δβ given in the model as inferred by the relation (5). Hence, the estimated shear wave contrast agrees well with that of the real value. We tested the algorithm with another example shown in Fig. 5, where we used a very small δβ. We repeat the procedure as explained for Fig. 4. The values of X and δβ are labelled in Fig. 5 andtheyare in good agreement. The previous examples are simple with models having sharp velocity jumps; however, in reality we find the discontinuities are not that sharp. In order to check whether the above relation still holds, we generated synthetics (Fig. 6a) for a model (Fig. 6b), where there is a gradient at the base of the crust with a net jump of β = 1.1 km s 1. We repeated the same procedure as stated earlier and estimated the X. In this case, we found that X =.1 which is again δβ with a difference of 0.1 km s 1. In order to make the method more general, we next selected a model with two interfaces that is one at intra-crustal level and another Moho with a velocity gradient. The synthetic P- receiver functions and the model are shown in Figs 7(a) and (b), respectively. Here, we have two primary conversions from the two interfaces and are picked as shown by rectangular boxes in Fig. 7(a).

6 1436 P. Kumar, M. K. Sen and C. Haldar Figure 10. This is same as Fig. 9, but for another station COR located in Corvallis, Oregon, USA. The estimated δβ and inverted value of δβ are in close agreement with each other. For the two respective phases we have two sets of data shown in Fig. 7(c) and there will be two intercepts whose values are 0.8 and.1 for the top layer and bottom layer, respectively. These values are exactly equals to δβ across the interface values as indicated in the figure. Fig. 8 demonstrates another synthetic example where we added Gaussian noise of mean 0.0 and standard deviation = 0.0 to the synthetic amplitude data generated for the model shown in Fig. 8(b). The noisy synthetic data are shown in Fig. 8(c). Fig. 8(d) shows the estimation procedure of X as described in the earlier figures. The real δβ is 1. km s 1, whereas the computed value is 1.19 km s Real data In this section, we examine the robustness of the method on real data application using two real field data shown in Figs 9 and 10 from HYB (lat:+17.4, lon:+78.55) and COR (lat:+44.59, lon: 13.30), respectively. These are permanent broad-band seismological observatories which have been running for a long time. HYB is one of the Geoscope stations located in Hyderabad, on the Precambrian craton of the Indian shield, while COR is on the western part of USA in Corvallis, Oregon. Here, we only mention the geographical coordinates of the stations. For both stations we used the teleseismic earthquake data to compute the P-receiver functions (Burdick & Langston 1977; Langston 1977; Vinnik 1977; Kumar & Kawakatsu 011; Kumar et al. 011). The profiles of the receiver functions are prepared and presented in Figs 9(a) and 10(a) with slowness as abscissa. For HYB, we observe a strong conversion at 4 s from the Moho, which has been previously modelled by Saul et al. (000) and for the station COR the Moho is at 5 7 s. In order to pick the Moho amplitudes at respective slowness values, we selected time windows as indicated by rectangular boxes in in the image plots. The amplitudes show very good agreement with the theoretically predicted amplitude curves shown in Figs 9(b) and 10(b); however, for the station COR the amplitude variation with slowness is steeper. Again the amplitudes are plotted according to eq.()showninfigs9(c) and 10(c) for HYB and COR, respectively, and linear regression fit has been done. The linear regression fit yields the intercept X = 1.84 ± 0.11 for HYB and.99 ± 0. for COR. The errors in X indicate the ±SD (standard deviation) derived from bootstrap (Efron & Tibshirani 1993) analysis. Hence, the shear velocity (β) contrast from crust to mantle below HYB and COR are estimated to be 0.9 ± 0.05 and 1.5 ± 0.1 km s 1, respectively. In order to compare our result with that from the traditional modelling technique, we invert the receiver function stacks for both the stations. First, a stack receiver function trace each was generated from the Figs 9(a) and 10(a), separately after applying a moveout correction with a reference slowness of 6.4 s deg 1 (Yuan et al. 1997) using IASP91 velocity model. The observed traces are shown in Figs 8(e) and 9(e) as black wiggles for HYB and COR, respectively. Secondly, the stack traces were inverted for the best fit models as shown in Figs 9(d) and 10(d). The respective synthetic

7 traces are also shown in Figs 8(e) and 9(e) as grey wiggles. In case of HYB the inversion yields δβ = 0.8 km s 1 while for COR it is 1.5 km s 1 which are close to those generated by relation (5) as 0.9 ± 0.05 km s 1 and 1.5 ± 0.1 km s 1. 4 CONCLUSIONS In this paper, we demonstrate a new method for estimating contrast in V s from teleseismic receiver functions using P s transmitted wave amplitude variation with slowness. The approximate relation for converted wave amplitudes derived here is simple and can be used to estimate the shear wave velocity contrast across any interface from amplitude verses slowness data. The method works well for the plane horizontal and isotropic models and may serve as the first guess for velocity information before proceeding to a cumbersome forward or inversion approach. The results from the real field data from two stations corroborate well with the traditional inverted values. The limitations of the present method is that it does not account for dip and anisotropy as the present formulations are derived only for isotropic layers with a flat welded contact. ACKNOWLEDGEMENTS The director NGRI has kindly permitted to publish this work. CH is a AcSIR PhD student funded by the University Grants Commission (UGC). This work has been performed under the GENIAS Project PSC0104 (PK) of CSIR-NGRI. Seismic data for HYB and COR are from IRIS, DMC. Seismic data analysis was performed in Seismic Handler (K. Stammler 1993). Plots are generated using Generic Mapping Tool (Wessel & Smith 1995). We thank Michael Ritzwoller (editor), Jay Pulliam and an anonymous reviewer for their thoughtful and constructive comments and suggestions. REFERENCES Aki, K. & Richards, P., 00. Quantitative Seismology, University Science Books. Estimation of shear velocity 1437 Ammon, C.J., Randall, G.E. & Zandt, G., On the non-uniqueness of receiver function inversions, J. geophys. Res., 95, Burdick, L.J. & Langston, C.A., Modeling crustal structure through the use of converted phases in teleseismic body-wave forms, Bull. seismol. Soc. Am., 67, Castagna, J.P. & Backus, M.M., AVO analysis-tutorial and review, in Offset-Dependent Reflectivity Theory and Practice of AVO Analysis, pp. 3 37, eds Castagna, J. & Backus, M.M., Soc. Expl. Geophys. Efron,B. &Tibshirani, R., 1993.An Introduction to the Bootstrap, Chapman and Hall/CRC. Frederiksen, A.W. & Bostock, M.G., 000. Modelling teleseismic waves in dipping anisotropic structures, Geophys. J. Int., 141, Julia, J., 007. Constraining velocity and density contrasts across the crustmantle boundary with receiever function amplitudes, Geophys. J. Int., 171, Kumar, P. & Kawakatsu, H., 011. Imaging the seismic lithosphere- asthenosphere boundary of the oceanic plate, Geochem. Geophys. Geosyst., 1, Q01006, doi:10.109/010gc Kumar, P., Kawakatsu, H., Shinohara, M., Kanazawa, T., Araki, E. & Kiyoshi, S., 011. P and S receiver function analysis of seafloor borehole broadband seismic data, J. geophys. Res., 116, B1308, doi:10.109/011jb Langston, C.A., Corvallis, Oregon, crustal and upper mantle structure from teleseismic P and S waves, Bull. seismol. Soc. Am., 67, Ligorrıa, J.P. & Ammon, C.J., Iterative deconvolution and receiver function estimation, Bull. seismol. Soc. Am., 89, Saul, J., Kumar, M.R. & Sarkar, D., 000. Lithospheric and upper mantle structure of the Indian shield from teleseismic receiver functions, Geophys. Res. Lett., 7, Stammler, K., Seismic Handler: programmable multichannel data handler for interactive and automaticprocessing of seismological analysis, Comput. Geosci., 19, Vinnik, L.P., Detection of waves converted from P- to -SV in the mantle, Phys. Earth planet. Inter., 15, Wessel, P. & Smith, W.H.F., New version of the Generic Mapping Tools released, EOS, Trans. Am. geophys. Un., 76,33,doi:10.109/95EO Yuan, X., Ni, J., Kind, R., Mechie, J. & Sandvol, E., Lithospheric and upper mantle structure of southern Tibet from a seismological passive source experiment, J. geophys. Res., 10(7),