Methodology Investigations for Shear Wave Splitting Analysis

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Summer 2016

Methodology investigations for shear wave splitting analysis

Fansheng Kong

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METHODOLOGY INVESTIGATIONS FOR SHEAR WAVE SPLITTING ANALYSIS

FANSHENG KONG

A DISSERTATION

Presented to the Faculty of the Graduate School of the

MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY

In Partial Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

GEOLOGY AND GEOPHYSICS

2016

Approved by:

Stephen Gao, Advisor Kelly Liu, Co-Advisor Mingzhen Wei Leslie Gertsch Jianguo Song

 2016

Fansheng Kong

PUBLICATION DISSERTATION OPTION

This dissertation consists of the following three articles that have been published as follows:

Pages 3-25 were published in the Journal of BULLETIN OF THE

SEISMOLOGICAL SOCIETY OF AMERICA.

Pages 26-49 were also published in the Journal of BULLETIN OF THE

SEISMOLOGICAL SOCIETY OF AMERICA.

Pages 50-77 were published in EARTH AND PLANETARY SCIENCE

LETTERS.

ABSTRACT

Over the past several decades, shear wave splitting analyses have been increasingly utilized to delineate mantle structure and probe mantle dynamics. However, the reported splitting parameters (fast polarization orientations and splitting times) are frequently inconsistent among different studies, partially due to the different techniques used to estimate the splitting parameters. Here the study conduct research on methodology investigations for shear wave splitting analysis, which are composed of two sub-topics, i.e., a systematic comparison of the transverse minimization (TM) and the splitting intensity

(SI) techniques and applicability of the multiple-event stacking technique (MES).

Numerical experiments are conducted using both synthetic and observed data.

In addition, crustal anisotropy beneath 71 broadband seismic stations situated at the eastern Tibetan Plateau and adjacent areas is investigated based on the sinusoidal moveout of P-to-S conversions from the Moho and an intra-crustal discontinuity with an average splitting time of 0.39 ± 0.19 s and dominantly fracture-parallel fast orientations. The crustal anisotropy measurements support the existences of mid/lower crustal flow in the southern

Songpan-Ganzi Terrane and crustal shortening deformation beneath the Longmenshan fault zone.

ACKNOWLEDGMENTS

First, I want to express my sincere gratitude to my advisors, Dr.Stephen Gao and

Dr. Kelly Liu, for guiding and teaching me over the past four years. I gained a great deal from their immense knowledge, sheer tenacity, and great perception on research. I really appreciate their continuous support and patience.

Besides my advisors, I would like to thank the rest of my dissertation committee members, Dr. Leslie Gertsch, Dr. Mingzhen Wei, and Dr. Jianguo Song, for their constructive suggestions through this process. I appreciate your discussions, reviews and feedback on my dissertation. The financial supports from US National Science Foundation and Missouri University of Science and Technology are greatly appreciated.

I am grateful to the staff of Geosciences and Geological and Petroleum Engineering department, Patti Adams, Paula Cochran, Sharon Lauck, Patti Robertson, and Amy

McMillen, Katherine Wagner in Graduate office, for all the assistances over the past several years. I want to thank the help from my friends and colleagues of the geophysics group. I would also like to thank the advisor of my Master study, Dr. Lianzhang Zhu, for his recommendation and encouragement.

Last but not least, I want to thank my loving family. I cannot accomplish my doctoral dissertation without their understanding, support, encouragement, and constant love.

TABLE OF CONTENTS

Page PUBLICATION DISSERTATION OPTION ...... iii

ABSTRACT ...... iv

ACKNOWLEDGMENTS ...... v

LIST OF ILLUSTRATIONS ...... ix

NOMENCLATURE ...... xi

SECTION

1. INTRODUCTION ...... 1

PAPER

I. A Systematic Comparison of the Transverse Energy Minimization and Splitting Intensity Techniques for Measuring Shear-Wave Splitting Parameters ...... 3

Abstract...... 3

Introduction ...... 4

Testing Using Synthetic Data ...... 7

Data Generation ...... 7

Measuring Techniques ...... 8

Noise Resistance ...... 11

Dominant Frequency Dependence ...... 12

Complex Anisotropy Recognition ...... 14

Testing Using Real Data ...... 14

Discussion and Conclusions ...... 17

Acknowledements ...... 23

vii

References ...... 23

II. Applicability of the Multiple-Event Stacking Technique for Shear-Wave Splitting Analysis ...... 26

Abstract...... 26

Introduction ...... 27

Measuring Technique ...... 29

Synthetic Tests ...... 32

Synthetic Data Generation ...... 32

Simple Homogeneous Anisotropy ...... 33

Laterally Varying Anisotropy ...... 34

Two Anisotropic Layers ...... 40

Testing Using Real Data ...... 42

Summary Remarks ...... 43

Acknowledements ...... 46

References ...... 47

III.Crustal anisotropy and ductile flow beneath the eastern Tibetan Plateau and adjacent areas ...... 50

ABSTRACT ...... 50

1. Introduction ...... 50

1.1. Formation mechanisms of crustal and mantle anisotropy ...... 52

1.2. Previous seismic anisotropy investigations in the study area ...... 54

2. Data and methods ...... 56

2.1. Data ...... 56

2.2. Detection of single layer of anisotropy ...... 58

viii

2.3. Characterization of two layers of anisotropy ...... 60

3. Results ...... 60

3.1. Kunlun-Muztagh Suture Zone and Xianshuihe-Xiaojiang Fault Zone ...... 62

3.2. Longmenshan Block and adjacent areas ...... 62

3.3. Sichuan Basin...... 63

4. Discussion ...... 63

4.1. Formation mechanisms of the observed crustal anisotropy and geodynamic implications ...... 63

4.1.1. Kunlun-Muztagh Suture Zone ...... 65

4.1.2. Xianshuihe-Xiaojiang Fault Zone ...... 67

4.1.3. Longmenshan Block and adjacent areas ...... 68

4.1.4. Sichuan Basin...... 70

4.2. Implications on mantle deformation ...... 70

5. Conclusions ...... 71

Acknowledgements ...... 72

References ...... 72

SECTION

2. CONCLUSIONS ...... 78

BIBLIOGRAPHY ...... 80

VITA ...... 89

LIST OF ILLUSTRATIONS

Figure Page PAPER I

1. Examples of synthetic seismograms with a signal-to-noise ratio (SNR) of 8.0 computed under a simple anisotropy model with a 휙 of 90° and a 훿푡 of 0.6 s……….10

2. Variations of (a, c) fast orientations and (b, d) splitting times as a function of SNR…………………………………………………………………………….…..…11

3. Same as Figure 2 but for the resulting splitting parameters with respect to the dominant period. The SNR is fixed at 10.0 ………..……………………....…...….....12

4. Azimuthal variations of the resulting splitting parameters measured by TM and SI under a two-layer anisotropy model:……………………………………..………..….13

5. Azimuthal equidistant projection maps showing earthquakes (open dots) used in the study for (left) station BGCA and (right) station USIN………….………….………..15

6. Examples of shear wave splitting measurement from an event recorded by station USIN………………………………………………………………………...………...18

7. Same as Figure 6 but for an event recorded by station BGCA………………………….19

8. Splitting parameters observed at station USIN using TM………….…………………20

9. Azimuthal variations of calculated splitting intensities at station USIN after manual checking, which includes adjustments for the water level and signal time window so as to output desired wavelets (Ricker wavelet), and stacking intensities into 10° azimuthal window bins………………………………………………….……………21

10. Azimuthal variations of observed-splitting parameters at station BGCA…….....…21

11. Same as Figure 8 but for station BGCA……………………………………………..22

12. Results without manual screening obtained using 100 events with the highest SNR on the original radial component recorded by station USIN………...……….……...22

PAPER II

1. A model of homogeneous simple anisotropy and results of synthetic tests.…….....…31

2. Same as Figure 1 but for a model of anisotropy with 훿푡 values randomly distributed in the 0.5 - 1.5 s range……………………………………..…………………………..32

3. Same as Figure 1 but for a model of anisotropy with 휙 values randomly distributed in the -30° - 30° range…………………………………………………………..……..35

4. MES measurements using events with different 훽 values………..………………...…37

5. Example misfit functions for the four highlighted events in Figure 3b ……...... ….38

6. Same as Figure 3 but for a two-layer anisotropy model shown in (a)……………..……39

7. (a) Cross Cross-section plots of example individual misfit functions under the two- layer model shown in Figure 6 along the 휙 axis. (b) Cross-section plots along the 훿푡 axis…………...…………………………………………..…………………….42

8. Results of shear wave splitting (SWS) analysis using data recorded by station ENH in Hubei, China.………………………..………………………..………….…………45

9. Same as the previous figure but for station RES on Cornwallis Island, Canada……...46

PAPER III

1. A topographic relief map of the study area showing the suture zones (dashed purple lines), major faults (solid black lines), and seismic stations (triangles) used in the study……….…………………………………………………………..……….54

2. (a) Types of amphibole fabrics as a function of differential stress and temperature. (b) Predicted seismic anisotropy formed by a horizontal flow system for a vertically propagating S-wave………………………………..…………………………..……..55

3. Crustal anisotropy measurements (red) with orientation of the bars representing the 휙, and the length proportional to the 훿푡values.…………………...……………….….57

4. Receiver functions recorded by station LTT…………………………………………59

5. Two-layer crustal anisotropy measurements using data recorded by stations MAQU (a)-(d) and MEK (e)-(h)……..…………………………...……………………...... 61

6. (a) Splitting times from all stations with measurements plotted against the distance from the Longmenshan Fault Zone (the dashed line in Figure 3).………...…..……….64

7. Comparison between results from this study (red bars) and previous crustal anisotropy measurements from Chen et al. (2013) (black bars) and Sun et al. (2015) (green bars)……………………………...... …………………………………….….66

8. Spatial distribution of the splitting times of crustal anisotropy measurements.……....67

NOMENCLATURE

Symbol Description

PAPER I

휙 Fast orientation

δt Splitting Time

휑 Back-Azimuth

훼 Decaying factor

푅(푡) Presplitting radial component

퐴0 Amplitude of the presplitting radial component

휃 Angular difference between the radial and fast orientation

푓 Frequency of the presplitting radial component

푆푓(푡) Fast component

푆푠(푡) Slow component

푁0(푡) Randomly-selected normalized noisy trace

퐶(푡) Noise-free north-south or east-west component

푟 Signal-to-noise ratio value

PAPER II

휙 Fast orientation

δt Splitting time

푆(휙, 훿푡) Stacked misfit function

퐹(휙, 훿푡) Misfit function for individual event

퐹푚 Minimum value of misfit function

xii

푚푎푥 |퐴(푎,푓)| Maximum absolute value between 푎 and 푓 (the beginning and end of the XKS window in seconds)

푅(푡) Presplitting radial component

퐴0 Amplitude of the presplitting radial component

훽 Modulo-90° angular difference between 휙 and back-azimuth

훼 Decaying factor

휃 Angular difference between the radial and fast orientation

푓 Frequency of the presplitting radial component

푆푓(푡) Fast component

푆푠(푡) Slow component

PAPER III

휙 Fast orientation

δt Splitting time

훼 Back-azimuth

푡 Arrival time of P-to-S converted phase

푡0 Arrival time of P-to-S converted phase in isotropic case

∆t Offset caused by crustal anisotropy along raypath

휔 Standard deviation of crustal anisotropy splitting parameter

휔휙 Standard deviation of fast orientation

휔훿푡 Standard deviation of splitting time

휎 Poisson’s ratio

훾 Vp/Vs ratio

SECTION

1. INTRODUCTION

As demonstrated by numerous previous studies, shear wave splitting (SWS) analyses using P-to-S converted phases at the core-mantle boundary, including PKS,

SKKS, and SKS (hereafter collectively called XKS), have been widely utilized as a powerful tool for detecting and characterizing deformational processes in the Earth's mantle (Bowman and Ando, 1987; Silver and Chan, 1991; Gao et al. 1994; Savage, 1999;

Long and Silver, 2009; Gao et al. 2010; Liu et al., 2014). However, the resulting SWS parameters, the fast polarization orientation (휙) and the splitting time (훿푡), are frequently dependent on the measuring methodologies (Vecsey et al., 2008). Significant discrepancies exist in published papers conducted by different groups, which led to heated debates concerning the reliability of the resulting splitting parameters and consequently their geodynamic implications (e.g., Liu et al., 2008).

The dissertation is mainly composed of three parts. The first part provide results from a systematic comparison of the transverse minimization (TM) and the splitting intensity (SI) techniques. Results from the numerical experiments using both synthetic and observed data show that under single-layer anisotropy models with a horizontal axis of symmetry, both TM and SI can provide measurements with similar reliability. The testing confirms conclusions from previous studies that, although SI cannot distinguish between simple and complex anisotropy models with horizontal axis of symmetry, TM can serve as a powerful tool in recognizing the existence of complex anisotropy, which is characterized by a systematic dependence of the splitting parameters on the back-azimuth of the events.

The second part conducted numerical experiments to confirm frequently-reported discrepancies between the two popularly used methods of Silver and Chan (1991) (SC) and

MES and to explore the causes. The results show that when the anisotropic structure can be represented by a horizontal single layer of anisotropy with constant or spatially varying splitting times, MES can accurately retrieve the splitting parameters. However, when the fast orientations or both splitting parameters vary azimuthally due to lateral heterogeneities or double-layer anisotropy, the station-averaged fast orientations from MES and SC are mostly comparable, but the splitting times obtained using MES are underestimated. For laterally varying fast orientations in the vicinity of a station, the magnitude of the underestimation is dependent on the arriving azimuth of the events participated in the stacking; for two-layer models of anisotropy, the resulting splitting parameters using MES are biased toward those of the top layer, due to the dominance of events with a back azimuth parallel or orthogonal to the fast orientation of the lower layer.

The third part provides constrains of crustal anisotropy and ductile flow beneath the eastern Tibetan Plateau and adjacent areas. The resulting fast orientations are mostly parallel to the major shear zones in the Songpan-Ganzi Terrane, and can be explained by fluid-filled fractures, favoring the model of rigid block motion with deformations concentrated on the block boundaries. In the vicinity of the Xianshuihe-Xiaojiang fault zone in the southern Songpan-Ganzi Terrane, the crustal anisotropy results, when combined with previously revealed high crustal Poisson’s ratio in the area, support the existence of mid/lower crustal flow. The Longmenshan Fault Zone and adjacent areas are dominated by strike-orthogonal fast orientations, which are consistent with alignments of cracks associated with compressional stress between the Plateau and the Sichuan Basin.

PAPER

I. A Systematic Comparison of the Transverse Energy Minimization and Splitting Intensity Techniques for Measuring Shear-Wave Splitting Parameters

by Fansheng Kong, Stephen S. Gao, and Kelly H. Liu

Abstract Over the past several decades shear wave splitting (SWS) analyses have been increasingly utilized to delineate mantle structure and probe mantle dynamics.

However, the reported splitting parameters (fast polarization orientations and splitting times) are frequently inconsistent among different studies, partially due to the different techniques used to estimate the splitting parameters. Here we report results from a systematic comparison of the transverse minimization (TM) and the splitting intensity

(SI) techniques. The study was motivated by the fact that recent comparative studies led to conflicting conclusions, which include the suggestion that TM, which is arguably the most-widely used SWS-measuring technique, performs significantly poorly relative to SI under most circumstances in terms of stability and reliability of the resulting splitting parameters. We use both synthetic and real seismograms to evaluate the performance of the techniques for noise resistance, dominant period dependence, and complex anisotropy recognition. For single-layer anisotropy models with a horizontal axis of symmetry, our results show that the two techniques can provide measurements with similar reliability.

The testing confirms conclusions from previous studies that while SI cannot distinguish between simple and complex anisotropy models with a horizontal axis of symmetry, TM can serve as a powerful tool in recognizing the existence of complex anisotropy, which is

4 characterized by a systematic dependence of the splitting parameters on the back-azimuth of the events. Therefore, when the existence of complex anisotropy beneath a study area is unknown, TM is a better choice.

Introduction

As demonstrated by numerous previous studies, shear wave splitting (SWS) analyses using P-to-S converted phases at the core-mantle boundary, including PKS,

Arguably the most popularly used SWS measuring method is the transverse minimization method (hereafter called TM) proposed by Silver and Chan (1991). It estimates splitting parameters based on a grid-search technique for the optimal fast orientation and splitting time that can best remove the energy on the corrected transverse component. TM is an event-specific measuring technique, i.e., each event with a sufficient signal to noise ratio (S/N) on both the radial and transverse components will lead to an optimal pair of parameters. For simple anisotropy, i.e., anisotropy characterized by a single layer with a horizontal axis of symmetry, the observed splitting parameters are independent

5 of the back-azimuth (BAZ) of the events. For events with a BAZ that is orthogonal or parallel to the fast orientation, or for stations below which the Earth's crust and mantle is isotropic, no energy on the transverse component will be observed, resulting in a 'NULL'

(N) measurement (Silver and Chan, 1991). When the anisotropy is complex, i.e., anisotropy that cannot be adequately characterized by simple anisotropy, the observed splitting parameters are dependent on the BAZ and thus are not true but apparent parameters.

Apparent splitting parameters are frequently used to characterize complex anisotropic structures, e.g., multiple layers based on periodicity of splitting parameters over BAZ (e.g.,

Silver and Savage, 1994; Yang et.al., 2014), spatial variation based on ray-piercing point

(e.g., Liu and Gao, 2013), and lower mantle contributed splitting based on ray paths of SKS and SKKS (e.g., Niu and Perez, 2004).

The splitting intensity method (hereafter called SI) was proposed by Chevrot (2000) and has been utilized by several studies for measuring SWS parameters and for tomographic inversion (e.g., Chevrot and van der Hilst, 2003; Monteiller and Chevrot,

2010; Monteiller and Chevrot, 2011; Romanowicz and Yuan, 2012). The splitting intensity for an event is measured by projecting the transverse energy on the derivative of the radial component (Monteiller and Chevrot, 2010). The splitting parameters can be retrieved by fitting the azimuthal variation of the splitting intensities using a sine function, in which the phase shift is related to the fast orientation, and the amplitude is proportional to the splitting time (Chevrot, 2000).

Long and van der Hilst (2006) conduct comparative studies of TM and SI using data from two stations in Japan. The splitting parameters observed at station TKA using

TM and SI agree well. In contrast, at station SGN, large discrepancies exist between the

6 results obtained using different techniques. Such discrepancies are considered to be the results of complex anisotropy (Long and van der Hilst, 2006). They test the stability of results from different measuring techniques in terms of the frequencies for band-pass filtering, and conclude that SI is more robust and stable. Monteiller and Chevrot (2010) test the noise resistance and frequency dependence of resulting splitting parameters obtained by SI and TM using both synthetic and real seismograms recorded by 4 broadband stations. They apply a Wiener filter to normalize the XKS arrivals from different events in order to enhance the effective signal on the radial and transverse components. The conclusion from the comparative study is that TM can provide reliable measurements only under ideal circumstances, including large splitting time (e.g., ≥ 1.3 s), short dominant period (e.g., ≤ 6.0 s), and very strong signal on the transverse component which is possible only when the difference between the BAZ and the fast orientation is close to 45°. For instance, when synthetic data with a low S/N of 3 and a large dominant period of 12 s are used, the SWS parameters calculated using TM are essentially unconstrained. Such a poor performance of TM is also suggested when it is applied to measure the splitting parameters at the 4 stations (Monteiller and Chevrot, 2010).

This study systematically evaluates the TM and SI techniques in terms of noise resistance, dominant period dependence, and complex anisotropy recognition using both synthetic data and real data. In contrast to previous studies, we conclude that for simple anisotropy, SI and TM are similar in terms of reliability in the resulting splitting parameters, but TM is advantageous in detecting complex anisotropy.

Testing Using Synthetic Data

Data Generation

To produce synthetic SKS seismograms under a model of simple anisotropy with a given pair of 휙 and 훿푡, we first define a pre-splitting radial component in the form of

−훼푡 푅(푡) = 퐴0 ∗ sin (2휋푓푡)푒 (1)

in which 퐴0 is the amplitude, f is the frequency, and 훼=0.1 is the decay factor. We then generate 36 synthetic events with a randomly selected BAZ ranging from 0° to 360°. The fast (푠푓) and slow (푠푠) components for an event can be computed using

푆푓(푡) = 푅(푡) ∗ cos 휃 (2) and

푆푠(푡) = −푅(푡 − 훿푡) sin 휃 (3) in which 휃 is the angle between the fast and radial directions. The resulting fast and slow components are rotated based on the BAZ to create the N-S and E-W components.

To resemble real data that contain noise of various levels, we add noise recorded by station USIN located in Indiana, USA to the N-S and E-W components. To accomplish this task, about 1500 seismograms recorded by the station are extracted, and for each seismogram, a 40-s-long noise trace 푁(푡) is selected in the time window of (a-40, a) s, in which a is the beginning of the SKS window and is 5 s before the IASP91 theoretical SKS arrival time. The noise trace is then detrended and normalized by the mean of the absolute values, that is,

푁0(푡) = 푁(푡)⁄|푁(푡)| (4)

A noisy synthetic seismogram with an SNR of r, defined as 푚푎푥|퐴(푎,푓)|⁄푚푎푥|퐴(푎−10,푎)|

(in which 푚푎푥|퐴(푎,푓)| is the maximum absolute value between 푎 and 푓 [the beginning and end of the XKS window] and 푚푎푥|퐴(푎−10,푎)| is that between 푎 − 10 and 푎), is then created using 푟 ∗ 퐶(푡) + 푁0(푡). 퐶(푡) is the noise-free north-south or east-west component, and

푁0(푡) is a randomly selected normalized noise trace. Finally, the north-south and east-west traces are rotated to radial and transverse components for splitting analysis. Examples of radial and transverse waveforms with an SNR of 8.0 are shown in Figure 1.

For a two-layer model of anisotropy, the fast and slow components after passing through the lower layer are generated using Equations (2) and (3), and are consequently used as waves incident to the upper layer to compute the final fast and slow components.

The two pairs of fast and slow waves after traveling through the upper layer are summed in the time domain and rotated to the radial and transverse directions to produce the synthetic seismograms using the same procedure as that used for the one-layer model.

Measuring Techniques

The splitting parameters based on TM are calculated by following the procedure for making SWS measurements of Liu and Gao (2013). The procedure initially sets the

XKS window as 5 s before and 20 s after the predicted XKS arrival calculated by using the

IASP91 Earth model. It applies a band-pass filter in the initial range of 0.04 - 0.5 Hz to the original radial and transverse components to enhance the S/N and automatically rejects events with a S/N lower than 3.0 on the radial component. The resulting SWS measurements are automatically ranked into 4 groups: A (excellent), B (good), C (bad),

9 and N (null) based on the S/N on the original radial, original transverse and corrected transverse components (Liu et al. 2008; Liu and Gao, 2013). Only Quality A and B measurements are kept. The last step of the procedure is to manually screen the waveforms to verify and adjust if necessary the beginning and end times of the XKS Window, the band-pass filtering parameters, and the ranking results. In this study manual screening is applied to real data, but not to synthetic data, for the following reasons:

1). The main purpose for manual screening is to adjust the XKS window to exclude non-XKS arrivals. Such arrivals are absent in the synthetic data, and

2). The frequency composition of the synthetic XKS waveform is known and thus adjusting the filtering parameters is not necessary. The corresponding standard deviation

(SD) for the parameters (simple SD for 훿푡 and circular SD for 휙) are computed based on the resulting individual measurements. For complex anisotropy models, which are characterized by systematic azimuthal variations of the splitting parameters, the resulting parameters are displayed against the BAZ.

To measure splitting parameters based on SI, we use the same band-pass filtering criteria to pre-process the data, and apply a Wiener filter to standardize the waveforms from all events. We use the suggested value of 0.001 for the water level when applying the

Wiener filter (Monteiller and Chevrot, 2010), and define the signal time window the same as that for TM. The calculated splitting intensities are then stacked into 10° BAZ bins to enhance the reliability of measurements. The splitting parameters are found by fitting the azimuthal variation of the splitting intensities using a sine function. The amplitude of the fitting function is related to the splitting time, and the phase shift is associated with the fast orientation (Chevrot, 2000). We apply a bootstrap method to calculate the splitting

10 parameters 10 times (Press et al., 1992; Efron and Tibshirani, 1986) to estimate the SD of the resulting 휙 and 훿푡 from SI.

Figure 1. Examples of synthetic seismograms with a signal-to-noise ratio (SNR) of 8.0 computed under a simple anisotropy model with a 휙 of 90° and a 훿푡 of 0.6 s. The back azimuth (BAZ) of the events is randomly selected. (a) Original radial components plotted against BAZ. (b) Original transverse components plotted against BAZ.

Noise Resistance

We construct a simple anisotropy model with a 휙 of 90° and a 훿푡 of 0.6 s to test the reliability of the resulting splitting parameters from TM and SI, using noisy synthetic data with S/N ranging from 1.0 to 10.0 with an increment of 1.0. The dominant period is set as

8.0 s. The resulting 휙 and 훿푡 with respect to S/N (Figure 2) show that with S/N ≥ 3.0, both methods can lead to reliable results.

Figure 2. Variations of (a, c) fast orientations and (b, d) splitting times as a function of SNR. The dominant period of the seismograms is 8.0 s. (a) and (b) show results obtained using transverse minimization (TM), whereas (c) and (d) show results from splitting intensity (SI). The horizontal lines show the parameters of the simple model of anisotropy used to generate the synthetic seismograms.

Dominant Frequency Dependence

To test the frequency dependence of the resulting parameters, we generate a set of synthetic data with different dominant periods for the pre-splitting radial component under a simple anisotropy model with 휙 = 90° and 훿푡 = 0.6 s. The dominant period ranges from

1 s to 20 s with an increment of 1 s, while the S/N is set as 10.0.

The resulting splitting parameters (Figure 3) show that overall both TM and SI can provide reliable measurements with different dominant frequencies. The splitting parameters obtained using SI are less dependent on the dominant periods, because the

Wiener filter is a shaping filter which alters the dominant frequency of the seismogram to that of the desired wavelet. The conclusion from the above tests suggests that the two methods produce comparable results in the main XKS frequency bands with moderate S/N.

Figure 3. Same as Figure 2 but for the resulting splitting parameters with respect to the dominant period. The SNR is fixed at 10.0.

Figure 4. Azimuthal variations of the resulting splitting parameters measured by TM and SI under a two-layer anisotropy model: (a) fast orientations from TM, (b) splitting times from TM, and (c) splitting intensities from SI. The input parameters are 0°, 0.6 s for the lower layer and 60°, 0.5 s for the upper layer with an SNR of 10.0 and dominant period of 8 s. Solid lines in (a) and (b) are theoretical two-layer splitting parameters computed based on Silver and Savage (1994). The solid line in (c) is the best-fitting sine curve, which reveals a fast orientation of 26.3° and a splitting time of 0.57 s.

Complex Anisotropy Recognition

In order to investigate the capability of TM and SI in complex-anisotropy recognition, we construct a two-layer anisotropy model with splitting parameters of 0°, 0.6 s for the lower layer and 60°, 0.5 s for the upper layer. We generate a data set of 36 events with a S/N of 10.0 and a dominant period of 8.0 s. Figures 4a and 4b show the apparent splitting parameters calculated by using TM, which demonstrate a clear 90° periodicity over BAZ, suggesting a complex anisotropy model (Silver and Savage, 1994; Bonnin et.al.,

2012).

The splitting intensities (Figure 4c) computed using SI are well-defined and follow a sine function well, with a resulting pair of splitting parameters of 휙=26.3° and 훿푡 = 0.57 s which are related with the splitting parameters of the 2 layers by 훿푡 sin2(휙 − 휑) =

훿푡1 sin 2(휙1 − 휑) + 훿푡2 sin 2(휙2 − 휑) (Montagner et.al., 2000), where 휙 and 훿푡 are equivalent one layer splitting parameters, 휑 is the BAZ, and (휙1, 훿푡1) and (휙2, 훿푡2) are splitting parameters of layers 1 and 2, respectively. Obviously, since SI observations from single and two-layer anisotropy models are indistinguishably sinusoidal, if only SI is used to obtain the splitting parameters, one could incorrectly conclude that the mantle beneath the station is characterized by a simple anisotropy model with a well-defined single pair of splitting parameters.

Testing Using Real Data

We next compare the two techniques by using real seismograms recorded by two broadband stations, BGCA (Bogion, Central African Republic, with a period of operation of 1994 - 2002) and USIN (Evausville, Indiana, USA, 2002 - 2013). At USIN, no systematic azimuthal variations of the splitting parameters are revealed (Liu and Gao,

2013). On the other hand, the anisotropy structure beneath BGCA is controversial between results obtained by using various methods (Monteiller and Chevrot, 2010; Niu and Perez,

2004). The XKS data were requested from the IRIS Data Management Center for events with an epicentral distance of 84° - 180° for SKS, 90° - 180° for SKKS, and 120° - 180° for PKS. The cutoff magnitude is 5.6 for events with a focal depth less than 100 km, and

5.5 for events with a focal depth 100 km or greater to make use of sharp waveforms for all the three phases. The distribution of the teleseismic events used in the SWS analyses is shown in Figure 5, and example waveforms and Wiener filtered traces are shown in Figures

6 and 7.

Figure 5. Azimuthal equidistant projection maps showing earthquakes (open dots) used in the study for (left) station BGCA and (right) station USIN. The dashed circles are centered at the stations and represent the epicentral distances in degrees.

Following the procedure of Liu and Gao (2013), a total of 63 and 94 well-defined

(Rank A or B) measurements are obtained from USIN and BGCA, respectively. The mean fast orientation obtained at USIN is 59.2 ± 7.0°, and the mean splitting time is 1.0 ± 0.3 s

(Figure 8), which are consistent with results from previous studies (Liu and Gao, 2013).

Station-averaged results using SI are 64.8 ± 5.0°, and 0.77 ± 0.1 s (Figure 9), which are statistically consistent with those from TM. This conclusion is consistent with that from using synthetic data.

The resulting splitting parameters using TM for station BGCA demonstrate a systematic azimuthal dependence with a period of 90° (Figure 10), which is characteristic of a two-layer anisotropy structure (Silver and Savage, 1994). We apply a grid-search method to find the two optimal pairs of splitting parameters that can best fit the apparent splitting parameters (Silver and Savage, 1994). The resulting parameters are -30° and 0.55 s for the lower layer, and 31° and 0.9 s for the upper layer. The station-averaged splitting parameters are 27.8 ± 24.0° and 0.9 ± 0.3 s.

By fitting the azimuthal variation of the splitting intensities using a sine function, a

휙 of 11.5 ± 3° and a 훿푡 of 0.71 ± 0.1 s are obtained (Figure 11). The results are close to the values of 휙 = 12 ± 2° and 훿푡 = 0.65 ± 0.1 s reported by Monteiller and Chevrot (2010).

These values are inconsistent with the station-averaged splitting parameters obtained from

TM, or the parameters for the upper or lower layers. In addition, the goodness of the fitting of the intensities at BGCA, which is characterized by a double-layered model, is similar to that at USIN, which possesses simple anisotropy

Discussion and Conclusions

As discussed in Liu and Gao (2013), the XKS signal in the automatically- determined (based on theoretical travel-time predictions using a 1-D Earth model) XKS window can be contaminated by noise and non-XKS arrivals in both the time and spectral domains. Consequently, unless under the ideal condition of outstanding XKS signals on both the radial and transverse components, erroneous splitting parameters can be obtained unless careful manual screening is applied. Such a condition requires strong XKS signals on the radial component, large splitting times, sharp waveforms, a significant deviation between the fast orientation and the BAZ, and a paucity of contamination by non-XKS arrivals. Under less than ideal conditions, manual verification of the automatically determined results and careful adjustments to the data processing parameters are necessary to make reliable measurements. The omission of this critical step in the comparative study of Monteiller and Chevrot (2010) is mostly responsible for the conclusion that TM only works well under the rare ideal conditions.

To illustrate this point, we choose 100 events recorded by USIN with the highest

S/N on the radial component, and apply both the TM and SI procedures to the events, without any manual screening and adjustments to the data processing parameters. The results from TM (Figure 12) are inconsistent from each other, even for events from the same BAZ, suggesting that many of the measurements are not reliable. Similarly, results using SI are significantly different from those obtained using manually-screened waveforms (Figure 9).

Figure 6. Examples of shear wave splitting measurement from an event recorded by station USIN. (a) Original radial, original transverse, corrected radial, and corrected transverse components using TM. The verticals bars define the beginning and end of the signal time window. (b) Resulting fast (dashed) and slow (solid) components (left) before and (right) after shifting the slow components in advance by the optimal splitting time. (c) Particle- motion patterns (left) before and (right) after the corrections. (d) Contour map showing the energy on the corrected transverse component with respect to fast orientation and splitting time. The star represents the optimal pair of splitting parameters that can best remove the energy on the transverse component. (e) The (left) radial and (right) transverse components before (dashed) and after (solid) Wiener filtering.

Figure 7. Same as Figure 6 but for an event recorded by station BGCA.

Figure 8. Splitting parameters observed at station USIN using TM: (a) fast orientations plotted against BAZ, (b) fast orientations plotted against modulo-90° BAZ, (c) splitting times plotted against BAZ, (d) splitting times plotted against modulo-90° BAZ, (e) rose diagram showing distribution of fast orientations, and (f) splitting parameters plotted above ray-piercing points at 200 km deep. The orientation of bars represents the fast orientation, whereas the length represents the size of the splitting time.

Figure 9. Azimuthal variations of calculated splitting intensities at station USIN after manual checking, which includes adjustments for the water level and signal time window so as to output desired wavelets (Ricker wavelet), and stacking intensities into 10° azimuthal window bins.

Figure 10. Azimuthal variations of observed-splitting parameters at station BGCA. Solid lines are the theoretical splitting parameters computed using a uniform frequency of 0.23 Hz and the two-layer parameters for this station.

Figure 11. Same as Figure 8 but for station BGCA.

Figure 12. Results without manual screening obtained using 100 events with the highest SNR on the original radial component recorded by station USIN. (a) Fast orientations using TM, (b) splitting times using TM, and (c) splitting intensities using SI. The scatter in these results demonstrates the importance of manually screening the data.

In summary, testing using both synthetic and real data demonstrates that under the simple anisotropy model, both TM and SI can obtain reliable splitting parameters, even when the splitting times are small (e.g., 0.6 s). The testing shows that the dominant frequencies of the XKS waves have insignificant effect on the resulting measurements obtained by using TM or SI. However, a good azimuthal coverage is necessary for SI to obtain reliable results. In terms of detecting and characterizing complex anisotropy, TM is a powerful tool in recognizing complex anisotropy which is characterized by systematic azimuthal variations of the splitting parameters. Thus when the existence of complex anisotropy beneath a station is unknown, TM is a better choice than SI for measuring SWS parameters, although for some applications such as anisotropy tomography, the latter is a more suitable choice.

Acknowledements

We thank S. Chevrot for assistance in the implementation of the Wiener filter, and three anonymous reviewers and Associate Editor Eric Chael for constructive suggestions.

This study was partially supported by the U.S. National Science Foundation under Grant

EAR-1009946 and Statoil.

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II. Applicability of the Multiple-Event Stacking Technique for Shear-Wave Splitting Analysis

by Fansheng Kong, Stephen S. Gao, and Kelly H. Liu

Abstract For several decades, shear wave splitting (SWS) parameters (fast polarization orientations and splitting times) have been widely measured to reveal the orientation and strength of mantle anisotropy. One of the most popularly used techniques for obtaining station averaged SWS parameters is the multiple-event stacking technique

(MES). Results from previous studies suggest that the splitting times obtained using MES are frequently smaller than those derived from simple averaging of splitting times obtained using the event-specific technique of Silver and Chan (1991). To confirm such apparent discrepancies between the two popularly used methods and to explore the causes, we conduct numerical experiments using both synthetic and observed data. The results show that when the anisotropic structure can be represented by a horizontal single layer of anisotropy with constant or spatially varying splitting times, MES can accurately retrieve the splitting parameters. However, when the fast orientations or both splitting parameters vary azimuthally due to lateral heterogeneities or double-layer anisotropy, the station averaged fast orientations from MES and Silver and Chan (1991) are mostly comparable, but the splitting times obtained using MES are underestimated. For laterally varying fast orientations in the vicinity of a station, the magnitude of the underestimation is dependent on the arriving azimuth of the events participated in the stacking; for two- layer models of anisotropy, the resulting splitting parameters using MES are biased

27 towards those of the top layer, due to the dominance of events with a back azimuth parallel or orthogonal to the fast orientation of the lower layer.

Introduction

Shear wave splitting (SWS) analyses have been increasingly used by geoscientists as an important tool in studying seismic anisotropy, which is directly related to the deformation and dynamics of the Earth's interior (Fuchs, 1977; Ando et al., 1983; Silver and Chan, 1991; Silver, 1996; Silver and Holt, 2002; Becker, 2008; Gao and Liu, 2009;

Gao et al., 2010; Long and Becker, 2010; Yang et al., 2014). The splitting parameters, fast polarization orientation (휙) and splitting time (훿푡), convey information about the direction and strength, respectively, of finite strain. A number of techniques aimed at accurately retrieving the splitting parameters using P-to-S converted phases at the core-mantle boundary (XKS, including SKS, SKKS, and PKS) have been developed to quantify seismic anisotropy beneath the recording stations (Ando et al., 1983; Vinnik et al., 1989; Silver and

Chan, 1991; Wolfe and Silver, 1998; Levin et al., 1999; Restivo and Helffrich, 1999;

Chevrot, 2000).

Among these techniques, arguably the most popularly used one is the transverse energy minimization method (Silver and Chan, 1991; hereafter called SC). For each event recorded by a station, SC grid-searches for the optimal pair of splitting parameters corresponding to the minimum value on the contour map for the energy of the corrected transverse component. In most previous studies, the splitting parameters from individual events are then averaged to obtain a mean pair of splitting parameters for the station.

Another widely-used approach to obtain station averaged splitting parameters is the multiple-event stacking technique (hereafter called MES) proposed by Vinnik et al. (1989)

28 and modified by Wolfe and Silver (1998). It was initially designed to obtain splitting parameters using noisy teleseismic data such as those recorded by ocean island stations, at which SC could not lead to reliable measurements due to the high noise level. MES is also effective for situations when the splitting time is significantly smaller than the global average of 1.0 s, or when the fast or slow orientation is close to the back-azimuth of the event. Restivo and Helffrich (1999) proposed a revised version of the approach of Wolfe and Silver (1998) by introducing two weighting factors to place emphasis on high-quality signals and to partially correct for uneven distributions in the back azimuth of the XKS events recorded by the station.

While splitting parameters estimated by MES usually have a smaller 95% confidence interval than those obtained using SC (Wolfe and Silver, 1998; Restivo and

Helffrich, 1999), numerous measurements using both techniques at the same stations suggest that the splitting times estimated by MES are systematically lower than those from averaging the event-specific measurements using SC. For instance, at station QIZ (Hainan

Island, China), Bai et al. (2009) reported a station averaged 훿푡 of 0.88 s using MES, but

1.28 s using SC. Similarly, the same study revealed a 훿푡 of 1.08 s at station SPVO

(Vietnam) using MES, and 1.66 s using SC. This discrepancy was highlighted in two recent

SWS studies using hundreds of broadband seismic stations in the western United States.

The study of Liu et al. (2014) used SC and reported a mean 훿푡 of 1.33 s for the western

U.S. orogenic zone, while that of Walpole et al. (2014), which used MES and the covariance matrix eigenvalue minimization method of Silver and Chan (1991), reported a value of 1.08 s. Several dramatic examples include USArray TA station 433A (Art, Texas,

USA) at which Walpole et al. (2014) obtained a 훿푡 of 0.3 s and Liu et al. (2014) reported

29 a value of 1.3 s; at 435B (Jarrell, Texas, USA), the corresponding values are 0.47 s and 1.1 s, while at ANMO (Albuquerque, New Mexico, USA), the values are 0.72 s and 1.6 s.

Globally, the Walpole et al. (2014) study reported a mean 훿푡 of 0.8 s which is smaller than the global average of 1.0 s obtained by Silver (1996) and the 1.1 s from a global compilation of SWS measurements by Becker et al. (2012). Such differences may lead to conflicting implications of mantle deformation and dynamics, especially when the splitting parameters are used in geodynamic modeling (e.g., Becker, 2008) and as constraints for seismic tomography (Yuan and Romanowicz, 2010).

In this study we use both synthetic and observed seismograms to test if the discrepancies were the results of normal fluctuations among different studies, or were caused by a systematic underestimation of 훿푡 by MES (or alternatively, a systematic overestimation by SC). We use several anisotropy models including a single homogeneous anisotropy layer, spatially varying single-layer anisotropy in the vicinity of a station, and a model with two anisotropic layers for the synthetic tests. We also measured splitting parameters using both techniques for two broadband stations, one with spatially varying 휙 values in the vicinity of the station and the other being characterized by systematic azimuthal variations of individual splitting parameters.

Measuring Technique

For each of the events recorded by a station, MES first computes the XKS energy on the corrected transverse component as a function of the candidate 휙 and 훿푡, using SC.

Following Restivo and Helffrich (1999), in this study we refer to the resulting function as a misfit function. Each misfit function is then normalized by its minimum value, and a stacked misfit function for the station is obtained using

푁 푆(휙푖, 훿푡푗) = ∑푚=1 퐹푚(휙푖, 훿푡푗)⁄min (퐹푚) (1)

(Wolfe and Silver, 1998), in which 푆(휙푖, 훿푡푗) is the stacked misfit function at the candidate pair of splitting parameters (휙푖, 훿푡푗), N is the number of events recorded by the station, and

퐹푚(휙푖, 훿푡푗)/푚𝑖푛(퐹푚) is the normalized misfit function of the 푚푡ℎ event at the candidate pair of splitting parameters.

To give higher quality events a higher weighting factor in the stacking, Restivo and

Helffrich (1999) modified this technique to multiply the individual misfit functions by the

SNR on the radial component before stacking. In addition, to avoid dominance of many events from narrow BAZ ranges, a misfit function is also divided by the number of events in the BAZ range that the event belongs, before being used for stacking. In the following, we apply the modified version of MES proposed by Restivo and Helffrich (1999). We define the SNR as 푚푎푥|퐴(푎,푓)|⁄푚푎푥|퐴(푎−10,푎)|, in which 푚푎푥|퐴(푎,푓)| is the maximum absolute value between 푎 and 푓 (the beginning and end of the XKS window in seconds) on the radial component and 푚푎푥|퐴(푎−10,푎)| is that between 푎 − 10 and 푎 seconds. Because the back azimuths of the hypothetical events used for the synthetic tests is evenly distributed and the SNR on the radial component are the same for all the events, the two weighting factors have no effects on the synthetic tests in the study. They are applied in the tests using real data. Also, to obtain reliable event-specific splitting measurements, manual checking and necessary adjustments of the measuring parameters (such as the a and f values and results of auto-ranking) are required. Details of the procedure for measuring event-specific splitting parameters using SC can be found in Liu and Gao

(2013).

Figure 1. A model of homogeneous simple anisotropy and results of synthetic tests. (a) The model. (b) Fast orientations obtained using Silver and Chan (1991, hereafter referred to as SC). (c) Splitting times using SC. (d) Contour map of the stacked misfit function and resulting splitting parameters calculated by multiple-event stacking technique (MES). The star indicates the optimal pair of splitting parameters corresponding to minimum transverse energy.

Figure 2. Same as Figure 1 but for a model of anisotropy with 훿푡 values randomly distributed in the 0.5-1.5 s range.

Synthetic Tests

Synthetic Data Generation

To construct a simple anisotropy model composed of a single layer of anisotropy with a horizontal axis of symmetry, we first define a pre-splitting radial component as

−훼푡 푅(푡) = 퐴0 ∗ sin(2휋푓푡) 푒 , (2)

in which 퐴0 = 1.0 is the amplitude, 푓 = 0.15 Hz is the frequency, and 훼 = 0.2 is the decaying factor. The fast (푆푓) and slow (푆푠) components with an incidence angle of 0° traveling through an anisotropic layer with splitting parameters of 휙 and 훿푡 can be expressed as

푆푓(푡) = 푅(푡) ∗ cos 휃 (3) and

푆푠(푡) = −푅(푡 − 훿푡) ∗ sin 휃, (4) in which 휃 is the angular difference between the radial and the fast orientations. Synthetic seismograms are then produced by rotating 푆푓(푡) and 푆푠(푡) to the N-S and E-W directions based on the back azimuth of the event. For a two-layer anisotropy model, the fast and slow shear waves after passing the lower layer act as independent incident shear waves and travel through the upper layer. The fast and slow waves after traveling through both layers are summed in the time domain and then rotated to create the N-S and E-W components.

Simple Homogeneous Anisotropy

We first consider a model with a single homogeneous layer of anisotropy with a horizontal axis of symmetry (Figure 1a). A total of 71 synthetic records with a SNR of 100 were generated using the same 휙 of 0° and 훿푡 of 1.0 s. The back azimuths of the events range from 5° to 355° with an interval of 5°. Uncorrelated noise with a pre-filtering maximum amplitude of 10% of the incident wave amplitude was created by a random number generator (Press et al., 1992) and was added to the N-S and E-W components after being low-pass filtered (0.3 Hz), and the individual splitting measurements and

34 corresponding misfit functions were obtained by following the SC-based procedure of Liu and Gao (2013).

The resulting station averages obtained using SC for both 휙 and 훿푡 (Figures 1b and

1c) are identical to the splitting parameters used for generating the synthetic seismograms.

Similarly, when MES is used, the optimal pair of splitting parameters corresponding to the minimum value on the stacked misfit function (Figure 1d) are also consistent with the true parameters. The high accuracy of the results from MES is easily understandable because all the individual misfit functions have the same minimum point (0°, 1.0 s). The above tests suggest that both SC and MES can accurately retrieve the splitting parameters when homogeneous simple anisotropy is present.

Laterally Varying Anisotropy

The XKS ray paths arriving at a station sample an approximately cone-shaped volume centered at the station. The diameter of the cone increases with depth and can reach a few hundred kilometers in the upper mantle, depending on the angle of incidence as well as the frequency (which determines the size of the Fresnel zone) (Alsina and Snieder,

1995). In such a large area, significant heterogeneities in the orientation and strength of seismic anisotropy are likely to exist. The heterogeneities can lead to inconsistent splitting parameters obtained from different events recorded by the same station, even when the anisotropy can locally be represented by a single layer with a horizontal axis of symmetry

(e.g., station ENH in Hubei, China, described in Liu and Gao, 2013). In such a situation the splitting parameters are dependent on the location of the ray-piercing points and the back azimuth.

Figure 3. Same as Figure 1 but for a model of anisotropy with 휙 values randomly distributed in the -30° - 30° range. (b) The tilted lines indicate the situation of 휙 = 푏푎푐푘 푎푧𝑖푚푢푡ℎ ± 푛 ∗ 90 (표푟 훽 = 0°), in which n is an integer. The misfit functions of the four events highlighted by black circles are shown in Figure 5.

The model shown in Figure 2a has a uniform 휙 of 0° but randomly distributed 훿푡 in the range of 0.5 - 1.5 s, with a simple mean of 0.98 ± 0.03 s. The application of the SC- based procedure of Liu and Gao (2013) resulted in an average 휙 of -0.06 ± 0.1° and 훿푡 of

0.99 ± 0.03 s (Figures 2b and 2c), both of which are consistent with the parameters used to

36 generate the synthetic seismograms. Similarly, the resulting optimal 휙 and 훿푡 from MES are 1.0 ± 0.0° and 1.0 ± 0.0 s (Figure 2d) which are also consistent with the expected values.

Therefore, both SC and MES can lead to accurate results for the situation of constant 휙 and spatially varying 훿푡.

We next explore the performance of MES for a model with a constant 훿푡 of 1.0 s but randomly distributed 휙 in the range of -30 - 30° (Figure 3a). The mean of the individual

휙 values used to generate the synthetic seismograms is 1.24 ± 2.05°. The SC approach resulted in a station average of 1.82 ± 2.15° for 휙, and 1.0 ± 0.00 for 훿푡 (Figures 3b and

3c), both of which are consistent with the splitting parameters used to generate the seismograms. Note that 5 of the 71 events produced null results because the fast orientation is nearly parallel or orthogonal to the back azimuth. The resulting 휙 from MES is 1.00 ±

0.00° which is also close to the expected value. However, the resulting 훿푡 is 0.8 ± 0.00 s

(Figure 3d), in spite of the fact that the model has a uniform 훿푡 of 1.0 s for all the events.

This discrepancy seems counter-intuitive and consequently needs additional exploration. To facilitate this task, we first define 훽, which is the modulo-90° absolute angular difference between the fast orientation and the back azimuth of an event. When 훽 is greater than 45°, it is taken as 90° − 훽, so that 훽 is limited to the range of 0 - 45°. For instance, for the first event shown in Figure 3b, 훽 = 2° because the event has a back azimuth of 5° and a local 휙 of 7°; for the fifth event, 훽 = 41° because back azimuth=25° and 휙 = −24°. Note that 훽 = 0° for events along the tilted lines in Figure 3b.

Figure 4. MES measurements using events with different 훽 values. (a) Number of events in each group for groups 1-9. (b) Observed 훿푡 of each group obtained by applying MES. (c) Contour map of stacked misfit function and resulting splitting parameters from MES using events in group 1. (d) Same as (c) but for group 3. (e) Same as (c) but for group 5. (f) Same as (c) but for group 9.

Figure 5. Example misfit functions for the four highlighted events in Figure 3b. The star indicates optimal splitting parameters for each of the events, and the diamond represents the point of minimum transverse energy when 휙 = 1°, which is the global 휙 from MES. The back azimuth of the event and resulting event-specific parameters are shown at the top of each plot.

To identify possible relationships between the global 훿푡 (i.e., the 훿푡 from MES) and the 훽 values of the participating events, we divide the 71 events into 9 groups based on the 훽 values. The 훽 value for events in the 𝑖푡ℎ group ranges from 5 ∗ (𝑖 − 1) to 5 ∗ 𝑖°.

The number of events for each of the groups is shown in Figure 4a. We then perform MES separately using events from each of the groups. The resulting global 훿푡 values increase significantly with increasing β, from as small as 0.05 s for group 1, to 1.0-1.1 s for groups

7-9 (Figure 4b). Misfit functions for 4 of the groups are shown in Figures 4c - 4f.

Figure 6. Same as Figure 3 but for a two-layer anisotropy model shown in (a).

Such a strong dependence of the global 훿푡 on 훽 can be explained using the example misfit functions shown in Figure 5. While the resulting 훿푡 for the individual events (i.e., local 훿푡) is 1.0 s (which was used to generate the synthetics), the 훿푡 associated with the minimum energy when 휙 = 1° (which is the global 휙 from MES) is mostly smaller than the local 훿푡. Thus when the individual misfit functions are stacked, the point with the minimum energy shifts towards a 훿푡 value that is smaller than the local 훿푡. The magnitude of the shift increases with decreasing 훽 (Figure 5).

We also performed similar tests using a model in which both 휙 and 훿푡 vary with the back azimuth, and significant underestimation of 훿푡 was also observed. The main conclusion from these tests is that when the fast orientations in the vicinity of a station vary spatially, the resulting 훿푡 from MES could be significantly underestimated, and the magnitude of the underestimation is dependent on the 훽 values of the events participated in the stacking.

Two Anisotropic Layers

The most commonly discussed complex anisotropy model in previous studies consists of two layers of simple anisotropy with non-parallel and non-orthogonal fast orientations. For a two-layer model, the apparent splitting parameters obtained using SC under the assumption of simple anisotropy vary systematically with the back azimuth with a 90° periodicity (Silver and Savage, 1994). As discussed in Liu and Gao (2013) using synthetic data, under such a model, the XKS energy on the transverse component cannot be completely removed using SC, except for the special cases when the back azimuth is parallel or orthogonal to the fast orientation of the lower layer. This is because the XKS

41 phase from an event with such a back azimuth does not split when traveling through the lower layer, i.e., it only splits once instead of twice. Such anisotropy cannot be satisfactorily represented by station averaged splitting parameters. Unfortunately, due to reasons such as limited back azimuth coverage and the associated incapability to recognize the existence of complex anisotropy, many previous studies reported station averages

(obtained by MES or SC) for areas with complex anisotropy. In the following we discuss the consequences of such a practice using a two-layer model with 휙1 = 55°, 훿1 = 1.0 s for the lower layer, and 휙2 = 55°, 훿2 = 1.0 s for the upper layer (Figure 6a).

As expected, the application of the SC-based procedure of Liu and Gao (2013) resulted in a set of apparent splitting parameters that vary periodically with the back azimuth (Figures 6b and 6c). The optimal splitting parameters from MES (Figure 6d), 23° and 1.15 s, are apparently well-defined and interestingly, they are similar to the splitting parameters of the upper layer (10° and 1.0 s). We conducted similar tests using different combinations of the splitting parameters for the two layers, and the resulting optimal splitting parameters using MES are almost always close to those of the upper layer. This similarity can be explained by the fact that the individual misfit functions with the quickest convergence towards the minimum energy point are those with a back azimuth parallel or orthogonal to the fast orientation of the lower layer, as shown in Figure 7. The stacked misfit function is thus dominated by such events, which have splitting parameters similar to those of the top layer (because the XKS waves from these events only split when traveling through the top layer). The incomplete removal of energy on the corrected transverse component for events with non-parallel and non-orthogonal back azimuth values is responsible for the relatively slow convergence towards the minimum (Figure 7).

Testing Using Real Data

We next compare results from SC and MES using data recorded by 2 stations, one with laterally varying splitting parameters, and one with periodic azimuthal variations of the splitting parameters that are indicative of multi-layer anisotropy.

Figure 7. (a) Cross Cross-section plots of example individual misfit functions under the two-layer model shown in Figure 6 along the 휙 axis. (b) Cross-section plots along the 훿푡 axis. For both (a) and (b), the cross sections traverse the point with the minimum value in the individual misfit function. Labels near the curves indicate the back azimuth of the XKS event. The thickest curves are for the events with a back azimuth parallel to the fast orientation of the lower layer. Note that in the lower plot, the misfits for some of the events are relatively too small to be visually observed.

Apparent fast orientations obtained using SC from station ENH (Hubei, China) demonstrate strong azimuthal variations but such variations are not periodic with either 90° or 180° periodicity (Figure 8). They were interpreted as evidence for spatially varying simple anisotropy (Liu and Gao, 2013). The resulting 훿푡 from MES (0.5 s) is smaller than that from SC (0.71 s), a result that is consistent with the conclusions from synthetic tests using a model of spatially varying fast orientations (Figure 3).

Station RES (Cornwallis Island, Canada) shows 90° periodic variations in the event-specific splitting parameters with respect to the back azimuth (Figure 9). Under the assumption that the variations are associated with a two layer model, we apply the technique of Silver and Savage (1994) to grid-search for the optimal pairs of parameters for each of the two layers. Given the uneven back azimuth distribution of the events, individual measurements are inversely weighted by the number of events in the back azimuth range that they belong before the grid-searching. The results are 112°, 0.7 s for the upper layer, and 76°, 0.35 s for the lower layer. Application of MES on data from the station led to a pair of optimal parameters (104°, 0.7 s) that are comparable with those of upper layer, an observation that is consistent with the conclusion from synthetic tests that the resulting splitting parameters from MES are similar to those of the upper layer (Figure

6).

Summary Remarks

MES has been used by numerous SWS studies to obtain a single pair of splitting parameters by stacking misfit functions from individual events. It is especially useful for stations with a limited amount of high quality data. Synthetic tests and tests using observed data presented above suggest that this technique should be applied with caution.

Specifically, it should only be used when seismic anisotropy beneath a recording station can be represented by a single layer of anisotropy with a horizontal axis of symmetry and is characterized by azimuthally invariant fast orientations. Otherwise, conflicting implications might be obtained especially when 훿푡 is used to constrain the anisotropy strength in studies involving geodynamical modeling or tomographic inversion (Becker,

2008; Yuan and Romanowicz, 2010).

In order to explore the existence of azimuthal variations of the individual fast orientations, high-quality XKS events in a wide back azimuth band are needed. When such events are available at a station, SC can be used to obtain the splitting parameters from each of the events. If the individual fast orientations from SC are found to be azimuthally invariant, the individual measurements can safely be used to compute station averaged splitting parameters without the need for MES. On the other hand, if systematic azimuthal variations are observed, complex anisotropy can be identified and possibly be characterized by grid-searching or other approaches (e.g. Silver and Savage, 1994). Obviously, MES can still be used in areas with complex or spatially varying anisotropy to obtain reliable results by stacking events from narrow back-azimuthal windows (Bastow et al., 2011), especially when limited amounts of high-quality data are present.

In summary, the study indicates that while MES is a powerful tool for retrieving reliable splitting parameters of simple anisotropy with constant fast orientations, applying

MES for areas with laterally varying fast orientations may lead to significantly underestimated splitting times. In addition, applying it for areas with two-layer anisotropy could result in a pair of splitting parameters resembling those of the top layer and not the actual anisotropic structure.

Figure 8. Results of shear wave splitting (SWS) analysis using data recorded by station ENH in Hubei, China. (a) Fast orientations plotted against back azimuth. (b) Splitting times plotted against back azimuth. (c) Splitting parameters plotted above the ray-piercing points at 200 km depth. (d) Stacked misfit function and resulting optimal parameters using MES.

Figure 9. Same as the previous figure but for station RES on Cornwallis Island, Canada. The solid lines in (a) and (b) are theoretical splitting parameters calculated using the splitting parameters from the two layers.

Acknowledements

We thank two anonymous reviewers for constructive suggestions. The study was partially funded by the U.S. National Science Foundation under Award EAR-1009946 and by Statoil of Norway..

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III. Crustal anisotropy and ductile flow beneath the eastern Tibetan Plateau and adjacent areas

Fansheng Kong, Jing Wu, Kelly H. Liu, Stephen S. Gao

ABSTRACT

Crustal anisotropy beneath 71 broadband seismic stations situated at the eastern

Tibetan Plateau and the Sichuan Basin is investigated based on the sinusoidal moveout of

P-to-S conversions from the Moho and an intra-crustal discontinuity. Significant crustal anisotropy is pervasively detected beneath the study area with an average splitting time of

0.39 ± 0.18 s. The resulting fast orientations are mostly parallel to the major shear zones in the Songpan-Ganzi Terrane, and can be explained by fluid-filled fractures, favoring the model of rigid block motion with deformations concentrated on the block boundaries. In the vicinity of the Xianshuihe-Xiaojiang Fault Zone in the southern Songpan-Ganzi

Terrane, our results, when combined with previously revealed high crustal Poisson's ratio in the area, support the existence of mid/lower crustal flow. The Longmenshan Fault Zone and adjacent areas are dominated by strike-orthogonal fast orientations, which are consistent with alignments of cracks associated with compressional stress between the

Plateau and the Sichuan Basin. The observations suggest that crustal thickening is the main cause of the high topographic relief across the Longmenshan Fault Zone.

1. Introduction

The growth of the Tibetan Plateau, which has an average elevation of ~5000 m, is widely considered to be the result of progressive collision between the Indian and Eurasian plates, starting approximately 70 Ma (e.g., Yin and Harrison, 2000). N-S lithospheric

51 shortening associated with the collision has resulted in eastward extrusion of the Plateau since about 15 - 20 Ma (Royden et al., 2008). Global Positioning System (GPS) velocity measurements (Gan et al., 2007) show eastward extrusion of central Tibet at a rate of about

15 - 20 mm/yr relative to the Sichuan Basin (Fig. 1). The bulk of the eastern Tibetan Plateau is the Songpan-Ganzi Terrane located between the Kunlun-Muztagh Suture to the north, the Jinsha River Suture to the south, and the Longmenshan Fault Zone to the east (Fig. 1).

Blocks of the Songpan-Ganzi Terrane, including Aba, Litang, and Longmenshan, move relatively from each other along the sinistral Xianshuihe-Xiaojiang and dextral Longriba faults (Fig. 1), partially due to the blockage by the relatively rigid Sichuan Basin.

A recent study (Ji et al., 2015) suggests that the southeastward movement of the

Litang Block resulted in the transformation of the E-W oriented, highly-foliated structures originally located at the Eastern Himalayan Syntaxis into NW-SE oriented tectonic fabrics.

The present-day surface motion of the northern Songpan-Ganzi Terrane is characterized by a northward decreasing rate and a slight spatial variation of direction, indicating the presence of both compression and strike-slip shear deformations, which are also indicated by the pervasive thrust and strike-slip faults (Fig. 1). The eastern margin of the Tibetan

Plateau, the Longmenshan Fault Zone, is characterized by a significant topographic relief relative to the plateau interior and the Sichuan Basin, with a low strike-orthogonal shortening rate of less than 3 mm/yr, but a high compressional stress rate (Gan et al., 2007).

As discussed below, the fault zones contribute significantly to the observed crustal anisotropy, together with lower crustal flow and the aforementioned tectonic fabrics developed from foliated structures.

Mechanisms responsible for the expansion and uplifting of the eastern Tibetan

Plateau remain enigmatic, in spite of numerous studies (e.g., Molnar and Tapponnier, 1975;

England and Houseman, 1986; Royden et al., 1997; Gan et al., 2007; Bai et al., 2010; Liu et al., 2014a). Proposed geodynamic models applicable to eastern Tibet can be loosely divided into three groups. Those in the first group suggest a dominant role of a channeled ductile flow system in the mid/lower crust in the uplifting and lateral expansion of the

Plateau (e.g., Bird, 1991; Royden et al., 1997; Clark and Royden, 2000; Burchfiel et al.,

2008; Zhao et al., 2012). Those models are consistent with the general absence of upper- crustal thrust faults in the area. The second group of models advocate broadly distributed deformation of crustal shortening and thickening as a predominant mechanism (England and Houseman, 1986; Wang et al., 2008; Hubbard and Shaw, 2009). Those in the third group attribute the uplifting to successive developments of crustal thrust-wedges associated with the oblique subduction of the lithospheric mantle along major fault zones (Tapponnier et al., 1982; 2001; Replumaz and Tapponnier, 2003). One of the key constraints on the various models is a high-resolution quantification of crustal deformation, which can be characterized by seismic anisotropy measurements.

1.1. Formation mechanisms of crustal and mantle anisotropy

Numerous studies demonstrate that seismic azimuthal anisotropy, as quantified by the polarization orientation of the fast shear wave (휙) and the splitting delay time (훿푡) between the fast and slow shear waves, is a nearly ubiquitous property of the Earth's crust and mantle (Silver, 1996; Savage, 1999). It is generally believed that azimuthal anisotropy in the continental upper crust is mostly the result of shape preferred orientation of fluid- saturated vertical cracks (Crampin, 1981), which are sub-parallel to the maximum

53 horizontal compression direction. The resulting 훿푡 is normally smaller than 0.2 s (Crampin,

1994), but can reach 0.5 s or greater for stations located in or close to a fault zone (e.g.,

Savage et al., 1990; Liu and Niu, 2012). Highly-deformed fabrics with a vertical foliation plane formed by compressional folding are also found to produce observable azimuthal anisotropy originating from anisotropic minerals in the crust such as mica and amphibole

(Ji et al., 2015).

In the mid/lower crust, due to the closure of cracks, azimuthal anisotropy is mostly produced by the lattice preferred orientation (LPO) of anisotropic crystals, primarily amphibole (Tatham et al., 2008; Ko and Jung, 2015). A recent study of amphibole (Ko and

Jung, 2015) suggests that channelized plastic flow in the mid/lower crust can result in azimuthal anisotropy. The relationship between the resulting 휙 and flow direction is dependent on the differential stress level and temperature (Fig. 2). Under the condition of high differential stress and high temperature, which is possible for the Tibetan Plateau due to significant crustal shortening and thickening (Yin and Harrison, 2000), type I and ІІІ fabrics, for which 휙 is sub-parallel to the flow direction, will dominate (Fig. 2).

Seismic anisotropy in the mantle is generally regarded as the consequence of LPO of anisotropic minerals, primarily olivine (Zhang and Karato, 1995). Mantle flow results in a fast orientation that is sub-parallel to the flow direction, and for areas experienced lithospheric shortening, the resulting 휙 is frequently observed in accordance with the strike of the mountain belt (e.g., McNamara et al., 1994; Silver, 1996; Bokelmann et al., 2013).

1.2. Previous seismic anisotropy investigations in the study area

Fig. 1. A topographic relief map of the study area showing the suture zones (dashed purple lines), major faults (solid black lines), and seismic stations (triangles) used in the study. Different colors are assigned based on the sub-area that the station belongs to. Red: Kunlun-Muztagh Suture Zone; Green: Longmenshan Block and adjacent areas; Blue: Xianshuihe-Xiaojiang Fault Zone; Orange: Sichuan Basin. Light blue arrows show GPS velocities (Gan et al., 2007) relative to the solid blue circle in the Sichuan Basin. The Longriba Fault is digitized based on Ren et al. (2013), and the other faults are based on Styron et al. (2010). Dashed line in the inset map shows the location of the study area within Eurasia.

Fig. 2. (a) Types of amphibole fabrics as a function of differential stress and temperature. (b) Predicted seismic anisotropy formed by a horizontal flow system for a vertically propagating S-wave (Ko and Jung, 2015). On the top plane, the fast orientation is shown in red, and the flow direction is parallel to the gray bar.

Crustal and mantle azimuthal anisotropy beneath the eastern Tibetan Plateau has been investigated by a number of studies (e.g., Sol et al., 2007; Wang et al., 2008; Sun et al., 2012; Chen et al., 2013; Sun et al., 2015). Studies using the splitting of XKS phases

(including SKS, SKKS, and PKS), which measure the integrated anisotropy of the crust and mantle, reveal an average splitting time of about 1.0 s. The fast orientations from XKS are mostly parallel to the strike of surface geological features (Fig. 3).

Crustal anisotropy studies(e.g., Sun et al., 2012; Sun et al., 2015) suggest that the crust at some sites can produce large splitting times comparable to the global average of

1.0 s from XKS studies, suggesting a significant crustal contribution to the observed XKS splitting. A crustal anisotropy investigation (Sun et al., 2015) in the vicinity of the

Longmenshan Fault Zone at 21 stations using the P-to-S converted phases from the Moho reports significant crustal anisotropy, with 훿푡 values ranging from 0.22 to 0.94 s. The

56 observed anisotropy is attributed to the LPO of mica or amphibole deformed by lower crustal flow. The same formation mechanism of crustal anisotropy has been suggested beneath the Xianshuihe-Xiaojiang Fault Zone (e.g., Sun et al., 2012; Chen et al., 2013). In contrast, Ji et al. (2015) proposes that sub-vertical foliation planes, which lead to transverse isotropy with a horizontal axis of symmetry, are responsible for the observed crustal anisotropy beneath the study area.

In this study, crustal azimuthal anisotropy beneath the eastern Tibetan Plateau and adjacent areas is explored based on the sinusoidal moveout of the P-to-S converted phases from the Moho and (at a few stations) an intra-crustal discontinuity (Rumpker et al., 2014).

The measurements have an average 훿푡 of 0.39 ± 0.18 s, and show dominantly fracture- parallel fast orientations.

2. Data and methods

2.1. Data

The broadband seismic data used in the study were recorded by 71 stations (Fig. 1), of which 53 were provided by the Data Management Centre of China National Seismic

Network at Institute of Geophysics, China Earthquake Administration for the recording period of 2007 – 2011 (Zheng et al., 2010). Data from the other 18 stations were obtained from the Incorporated Research Institutions for Seismology (IRIS) Data Management

Center (DMC) for the period of 2003-2014. All the tele-seismic events with magnitude ≥

4.0 and epicentral distance in the range of 30° - 180° are band-pass filtered in the frequency band of 0.08 - 0.8 Hz, and those with visible first P-arrivals on the vertical component are converted to radial receiver functions (Ammon, 1991), which are visually inspected to select the ones with clear P-arrivals and without anomalously large arrivals in the P-wave

coda. The two phases utilized in this study include 푃푚푠, which is the P-to-S converted phase from the Moho for measuring the bulk crustal anisotropy, and 푃푖푠, which is the P-to-

S converted phase from an intra-crustal interface for detecting upper crustal anisotropy at a few stations where 푃푖푠 is clearly observed.

Fig. 3. Crustal anisotropy measurements (red) with orientation of the bars representing the 휙, and the length proportional to the 훿푡 values. At stations MEK and CD2, the blue bar shows anisotropy of the upper layer, and the purple bar shows that of the lower layer. The gray bars are the station-averaged XKS splitting results obtained from http://splitting.gm.univ-montp2.fr/DB/public/searchdatabase.html. The area southwest of the green line is dominated by high Vp/Vs ratio (≥1.78) from Wang et al. (2010). The orange dashed arrows show the location of proposed flow channel from Bai et al. (2010). The dashed line traversing the Longmenshan Fault Zone separates areas with large and small splitting times.

2.2. Detection of single layer of anisotropy For a single layer of anisotropy with a horizontal axis of symmetry, the arrival times of the P-to-S converted phase (푃푚푠 or 푃푖푠) vary systematically with the back-azimuth

(BAZ) of the events (Liu and Niu, 2012; Rumpker et al., 2014), i.e.,

훿푡 푡 = 푡 + ∆푡 = 푡 − cos[2(훼 − 휙)] (1) 0 0 2

where 푡0 represents the arrival time in the isotropic case, ∆푡 is the offset caused by crustal anisotropy along the ray path, 훿푡 is the delay time which reflects the strength of crustal anisotropy, 휙 is the fast orientation of crustal anisotropy measured clockwise from the north, and α is the BAZ of the events. In this study, two pre-processing steps are applied to enhance the reliability of the measurements. First, in order to eliminate the moveout caused by epicentral distances, all the receiver function traces are adjusted to a uniform epicentral distance of 60°. Second, traces belonging to the same BAZ window of 10° wide are stacked together to enhance the signal-to-noise ratio. The splitting parameters, 휙 and 훿푡, can be obtained by fitting the 푃푚푠 (or 푃푖푠) arrival times relative to the direct P-wave using

Equation (1) based on a non-linear least-squares fitting procedure. An example can be found in Fig. 4.

To quantify the uncertainties of the resulting crustal anisotropy measurements, we apply the bootstrap resampling procedure (Efron and Tibshirani, 1986; Press et al., 1992) to estimate the splitting parameters 10 times. The standard deviation (SD), 휔, for the station is quantified by a unit-less value computed using

휔 = 휔휙⁄90.0 + 휔훿푡⁄1.0 (2)

where 휔휙 and 휔훿푡 are the SD of 휙 and 훿푡, respectively, estimated using the bootstrap procedure. Only results from stations with a 휔 ≤ 0.4 are presented and discussed below.

Fig. 4. Receiver functions recorded by station LTT. The black dots show the peak locations of the 푃푚푠 and the red line is the theoretical 푃푚푠 moveout calculated based on Equation (1) using the optimal pair of splitting parameters.

2.3. Characterization of two layers of anisotropy

Two layers of crustal anisotropy are detected and characterized at 3 of the stations where a 푃푖푠 phase is clearly identified in addition to the 푃푚푠 (Fig. 5), following the layer- stripping technique of Rumpker et al. (2014). For a given station with both 푃푚푠 and 푃푖푠 arrivals, the 푃푖푠 phases are used first to constrain the anisotropy in the layer above the interface ("upper crust"). The 푃푚푠 arrival times, which reflect the integrated effects of anisotropy in both the upper and lower crust, are then corrected using the resulting anisotropy parameters of the upper crust to remove the contributions of upper crustal anisotropy. The anisotropy of the lower layer can then be quantified by applying Equation

(1) to the corrected 푃푚푠 travel-times (Fig. 5).

In order to derive robust two layer crustal anisotropy measurements, some preconditions need to be satisfied: (1) the existence of an intra-crustal discontinuity, (2) clear and azimuthally varying 푃푖푠 and 푃푚푠 arrivals, and (3) good back-azimuthal coverage of high-quality radial receiver functions. Only three of the stations, CD2, MAQU, and

MEK, which are all located in the vicinity of known fault zones (Fig. 3), lead to reliable characterization of two-layer crustal anisotropy structure.

3. Results

Well-defined crustal anisotropy is measured at a total of 71 stations (Fig. 3). While the resulting 휙 measurements are dominantly parallel to the strike of major surface features, a sharp contrast of the 훿푡 values, which have an average value 0.39 ± 0.18 s, is observed between the Tibetan Plateau and the Sichuan Basin separated by the

Longmenshan Fault Zone, with an mean value of 0.44 ± 0.18 s for the west, and 0.27 ±

0.13 s for the east (Fig. 6).

Fig. 5. Two-layer crustal anisotropy measurements using data recorded by stations MAQU (a)-(d) and MEK (e)-(h). (a) and (e) are the original receiver functions showing both the 푃푚푠 and 푃푖푠 phases; (b) and (f) show the 푃푖푠 arrivals and the fitting curve; (c) and (g) are the original 푃푚푠 arrivals, and (d) and (h) are 푃푚푠 arrivals after correcting for upper crustal anisotropy.

Comparison between our results and those by Chen et al. (2013) and Sun et al.

(2015) are shown in Fig. 7. Chen et al. (2013) provided 33 crustal anisotropy measurements in our study area, and Sun et al. (2015) reported 21 measurements along the Longmenshan

Fault Zone. While some differences exist at some stations (Fig. 7), the measurements from the 3 studies are generally consistent, in spite of the significantly larger spatial coverage that this study provides. As detailed in the Discussion section, the increased spatial

62 coverage is essential for constraining anisotropy-forming mechanisms, as well as for providing valuable constraints for crustal deformation models.

Based on the major geologic features, we divide the study area into four regions, including the Kunlun-Muztagh Suture Zone, Xianshuihe-Xiaojiang Fault Zone,

Longmenshan Block and adjacent areas, and the Sichuan Basin (Fig. 1).

3.1. Kunlun-Muztagh Suture Zone and Xianshuihe-Xiaojiang Fault Zone

Crustal anisotropy measurements from the 28 stations situated in the Kunlun-

Muztagh Suture Zone (Fig. 1) result in an average 훿푡 of 0.47 ± 0.18 s. The 휙 measurements are dominantly ESE-WNW, consistent with the strike of the major faults. Fault-parallel fast orientations are also obtained at several stations in the same area by a recent crustal anisotropy study (Wang et al., 2016). Station MAQU demonstrates the existence of two layers of anisotropy (Fig. 5), with comparable 휙 and 훿푡 values between the 2 layers. The similarity of anisotropy between the upper and lower crust may suggest that beneath the station, the entire crust deforms coherently.

Similarly, the Xianshuihe-Xiaojiang Fault Zone in southern Songpan-Ganzi

Terrane also exhibits large 훿푡 measurements (0.53 ± 0.16 s) and strike-parallel fast orientations. The Kunlun-Muztagh Suture Zone and Xianshuihe-Xiaojiang Fault Zone possess the largest 훿푡 values in the study area (Fig. 8).

3.2. Longmenshan Block and adjacent areas

The Longmenshan Block and adjacent areas between the Kunlun-Muztagh Suture

Zone and the Xianshuihe-Xiaojiang Fault Zone are sampled by 20 stations. The 휙 measurements are dominantly NW-SE and the rest are mostly consistent with the NE-SW

63 strike of faults (Fig. 3). The measurements from the 3 stations located at the Longriba Fault

Zone are characterized by small 훿푡 with a mean value of 0.17 ± 0.03 s, and the fast orientations are either parallel or orthogonal to the strike of the faults. Measurements at station MEK (Fig. 5) suggest the presence of two anisotropic layers with orthogonal 휙 and comparable 훿푡 measurements. The 휙 of the lower layer is normal to the strike direction of the fault zone, while it is strike-parallel for the upper layer.

The 휙 measurements from the 3 stations situated in the Longmenshan Fault Zone are parallel to the NE-SW strike of the faults, while the 8 stations situated in the adjacent areas of the faults are strike-orthogonal. The 휙 of the upper layer anisotropy beneath station

CD2 is parallel to the strike of the Longmenshan Fault Zone, and that of the lower layer is orthogonal to it. Generally, the 훿푡 values along the Longmenshan Fault Zone are smaller than those obtained in the Kunlun-Muztagh Suture Zone and Xianshuihe-Xiaojiang Fault

Zone, and the average 훿푡 is 0.35 ± 0.13 s (Fig. 8).

3.3. Sichuan Basin

The 15 stations located in the Sichuan Basin lead to a mean 훿푡 value of 0.25 ± 0.13 s, with smaller 훿푡 (≤ 0.1 s) at stations in the interior of the basin. The 휙 measurements are mostly parallel to the surface fabric. The results are similar to those obtained by Sun et al.

(2015) at 3 stations in the Sichuan Basin.

4. Discussion

4.1. Formation mechanisms of the observed crustal anisotropy and geodynamic implications

Fig. 6. (a) Splitting times from all stations with measurements plotted against the distance from the Longmenshan Fault Zone (the dashed line in Figure 3). Thick horizontal bars represent mean values, and thin bars represent mean ± SD. (b) Splitting times from stations situated in the Kunlun-Muztagh Suture Zone plotted against the distance of stations to the nearest fault. Red dots show the moving averages in 10 km windows.

As discussed previously, a number of processes can lead to observable crustal anisotropy, including fluid-filled fracture zones, vertical foliation planes containing anisotropic minerals, and mid/lower crustal flow that aligns anisotropic minerals. For a

65 given area, the relative importance of the processes is dependent on the tectonic setting and crustal properties such as thickness and Vp/Vs ratio (훾) which is uniquely related to the better-known Poisson's ratio (휎) by 휎 = 0.5[1 − 1⁄(훾2 − 1)]. In this section, we speculate on the formation mechanisms for each of the areas on the basis of existing surface geology and crustal property observations, as well as their relationship with the observed crustal anisotropy parameters.

4.1.1. Kunlun-Muztagh Suture Zone Significant crustal anisotropy is observed throughout the Kunlun-Muztagh Suture

Zone, with the 휙 measurements being dominantly parallel to the major faults in the suture zone. Previous receiver function studies of the crust report Vp/Vs values of about 1.73 which are lower than the global average of 1.76 for continental crust (e.g., Wang et al.,

2010; Sun et al., 2015), suggesting the absence of large-scale crustal partial melting, which would lead to much higher Vp/Vs values (e.g., Reed et al., 2014). Vertically coherent crustal-mantle deformation and a possible absence of lower crustal flow beneath this area are also suggested by a recent study of Wang et al. (2016), who observed low crustal Vp/Vs ratio and strong fault-parallel crustal and mantle anisotropy.

To explore the relationship between crustal anisotropy measurements and the faults, we plot the observed splitting times against the distance of the stations from the nearest fault. As shown in Fig. 6b, for stations within 20 km from the nearest fault, the splitting times are the largest (about 0.6 s) and are not varying with the distance, implying the existence of a broad shear zone at depth. For stations that are more than 20 km away from the fault, there seems to be a gradual decrease in the splitting times with increasing distance. This relationship, together with the fact that the fast orientations are mostly

66 parallel to the strike of the faults in the suture zone, suggests that crustal anisotropy in this area is mostly related to fractures associated with the suture zone.

Fig. 7. Comparison between results from this study (red bars) and previous crustal anisotropy measurements from Chen et al. (2013) (black bars) and Sun et al. (2015) (green bars).

4.1.2. Xianshuihe-Xiaojiang Fault Zone Similar to the Kunlun-Muztagh Suture Zone, the Xianshuihe-Xiaojiang Fault Zone is characterized by fault-strike-parallel fast orientations (Fig. 3) and large splitting times

(Fig. 8). However, unlike the former, an inverse relationship between the splitting times and the distance to the nearest fault is not robustly observed. This could indicate that unlike those in the suture zone, fractures in the Xianshuihe-Xiaojiang Fault Zone have a limited lateral extent and thus contribute insignificantly to the observed crustal anisotropy.

Fig. 8. Spatial distribution of the splitting times of crustal anisotropy measurements. To produce the data plotted here, a smooth surface was generated by fitting the observed values, with a spatial sampliting inteval of 0.1°.

Another difference between the two areas is that while the former has lower than normal crustal Vp/Vs values, the latter is dominated by high Vp/Vs ratio (≥ 1.78; Fig. 3) and thus may indicate the existence of crustal partial melting (e.g., Wang et al., 2010; Sun et al., 2015). This is independently evidenced by the high electrical conductivity observed beneath this area (Bai et al., 2010), and may reflect plastic flow in the mid/lower crust toward the southeast (Clark and Royden, 2000; Bai et al., 2010). The consistency between the fast orientations and the predicted flow direction suggests that the dominant LPO of amphibole in the area is Type II, Type III (Fig. 2), which results in a flow-parallel fast orientation for a vertically propagating S-wave (Ko and Jung, 2015).

Besides faults in the upper crust and plastic flow in the mid/lower crust, another potential contributor to the observed anisotropy in this area is shear-related mineral lineation. A recent study (Ji et al., 2015) reveals sub-vertically aligned foliation planes with nearly horizontal lineations in the southeastern Tibetan Plateau, which are being rotated through strike-slip shear around the Himalayan Syntaxis. The NW-SE oriented foliation planes contain mica- and amphibole -bearing metamorphic rocks, leading to significant transverse isotropy with a horizontal axis of symmetry. The resulting fast orientation for a vertically propagating S-wave is in the foliation plane and parallel to the lineation direction.

4.1.3. Longmenshan Block and adjacent areas Relative to other areas of the eastern Tibetan Plateau, this area has the weakest crustal anisotropy (Fig. 8), in spite of the fact that it is experiencing a high rate of NW-SE directed compressional stress (Gan et al., 2007). The consistency between the fast orientations and the direction of the maximum horizontal compression suggests that NW-

SE oriented extensional cracks in the upper crust are mostly responsible for the observed anisotropy. Such a mechanism is commonly involved to explain crustal anisotropy in areas

69 dominated by compressional tectonics (Crampin, 1981; 1994). Station LORI in the

Longriba Fault Zone and a few stations along the Longmenshan Fault show fault-parallel fast orientations and small splitting times, probably related to fluid-filled fractures in the fault zones. This mechanism can also explain the NE-SW directed fast orientation of the upper layer at stations MEK and CD2. Alternatively, the 90° difference between upper and lower crustal anisotropy can be caused by a previously revealed 90° flip as a result of pore pressure exceeding the maximum horizontal compressional stress (Crampin et al., 2003).

This mechanism implies a high pore pressure in the upper crust at the stations with two- layer anisotropy.

Crustal anisotropy studies (Shi et al., 2009; Gao et al., 2014) using shear waves from local earthquakes show mostly fault-parallel fast orientations at stations located in the north-most 100 km of the Longmenshan Fault zone, while our results are mostly fault- orthogonal in the same area. This apparent discrepancy could be caused by the fact that the former studies measure the anisotropy of the seismogenic upper crust, while our results are integrated over the whole crust. The fact that the crustal anisotropy has a fault-orthogonal fast orientation suggests that the lower crust has a NW-SE oriented anisotropy with a much larger splitting time than the upper crust.

The small splitting times may suggest the absence of strong mid/lower crustal flow beneath this area. The blockage of the Sichuan Basin might be responsible for the absence, although the study alone cannot rule out the existence of partial melting in the mid/lower crust. However, the normal Vp/Vs values observed in most of the area (Wang et al., 2010) place doubts on the existence of significant crustal partial melting (e.g., Clark and Royden,

2000; Zhao et al., 2012), but support a crustal thickening model for the dramatic

70 topographic relief and recent large earthquakes in the Longmenshan Fault Zone (e.g.,

Hubbard and Shaw, 2009; Wang et al., 2012).

4.1.4. Sichuan Basin The crust beneath the Sichuan Basin is weakly anisotropic, as indicated by the smallest average splitting time in the entire study area (Fig. 8), an observation that is consistent with the previously suggested strong lithosphere beneath the basin (Huang et al.,

2015). Most of the fast orientations in the basin are NE-SW which might reflect the strike of crustal fabrics formed by ancient tectonic events. The several stations near the SW edge of the basin show edge-parallel fast orientations and could indicate the existence and reflect the effects of major boundary faults.

4.2. Implications on mantle deformation

For all of the study area, with possible exception of the Sichuan Basin, the fast orientation of crustal anisotropy is dominantly consistent with that of the XKS measurements, which represent the integrated anisotropy of both the crust and mantle. As shown in Fig. 3, in which the 푃푚푠 and XKS splitting parameters are plotted using the same scale, although crustal anisotropy is a significant contributor to the observed XKS anisotropy for most areas, the fact that XKS splitting times are constantly greater than 푃푚푠 splitting times suggests that the mantle is also anisotropic.

The observed mantle anisotropy can be explained by two models. The first is the coherent lithospheric deformation model for which both the crustal and mantle portions of the lithosphere deform as an entity (Silver, 1996; Wang et al., 2008). For the mantle portion, this model attributes the suture- or fault-parallel mantle anisotropy to strike- orthogonal compression, which orients the olivine a-axis to the strike direction (Silver,

1996). Because the dominant faults are strike-slip, and strike-slip faults are inefficient in re-orienting mantle anisotropic minerals (e.g., K. Liu et al., 2014b for the San Andreas

Fault), it is difficult to attribute the observed mantle anisotropy to coherent lithospheric deformation.

The second and our preferred model is that mantle anisotropy is caused by simple shear in the upper-most asthenosphere due to its differential movement with the lithosphere. Such a mechanism is widely used to explain XKS anisotropy (e.g., Refayee et al., 2014 for central North America, and Lemnifi et al., 2015 for North Africa). The differential movement can be induced by lithospheric movement along the strike-slip faults over a stationary asthenosphere, or by a faster- or slower-moving asthenospheric flow in the direction of the major fault zones.

5. Conclusions

P-to-S conversion from the Moho and an intra-crustal discontinuity reveals strong and spatially varying crustal anisotropy beneath the eastern Tibetan Plateau and Sichuan

Basin, with unprecedented spatial resolution. For most of the study area, the resulting fast orientations are dominantly parallel to the strike of major strike-slip faults, and the largest splitting times are found in major shear zones. Beneath the vicinity of the Xianshuihe-

Xiaojiang Fault Zone, our results support the existence of mid/lower crustal flow. The pervasive strike-orthogonal fast orientations in the vicinity of the Longmenshan Fault Zone suggest a significant contribution of fault-normal compressional stress to the large topographic relief across the fault.

Acknowledgements

We thank the Data Management Centre of China National Seismic Network at

Institute of Geophysics, China Earthquake Administration (SEISDMC, http:

//dx.doi.org/10.7914/SN/CB) and the IRIS DMC for providing the seismic data. Youqiang

Yu helped with the format conversion of the data sets. The study was partially sup-ported by the United States National Science Foundation under grant EAR-0911346 to K.L. and

S.G., and by the Natural Science Foundation of China under awards 41374064 and

41574055 to J.W.

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SECTION

2. CONCLUSIONS

The study conduct research on methodology investigations for shear wave splitting analysis, which are composed of two sub-topics, i.e., a systematic comparison of the transverse minimization (TM) and the splitting intensity (SI) techniques and applicability of the multiple-event stacking technique (MES). The study conducts numerical experiments using both synthetic and observed data.

For single-layer anisotropy models with a horizontal axis of symmetry, the results show that both TM and SI can provide measurements with similar reliability. The testing confirms conclusions from previous studies that although SI cannot distinguish between simple and complex anisotropy models with a horizontal axis of symmetry, TM can serve as a powerful tool in recognizing the existence of complex anisotropy.

In terms of applicability of MES, the results show that when the fast orientations or both splitting parameters vary azimuthally due to lateral heterogeneities or double-layer anisotropy, the station-averaged fast orientations from MES and Silver and Chan (1991) are mostly comparable, but the splitting times obtained using MES are underestimated. For laterally varying fast orientations in the vicinity of a station, the magnitude of the underestimation is dependent on the arriving azimuth of the events participated in the stacking; for two-layer models of anisotropy, the resulting splitting parameters using MES are biased toward those of the top layer, due to the dominance of events with a back azimuth parallel or orthogonal to the fast orientation of the lower layer.

P-to-S conversion from the Moho and an intra-crustal discontinuity reveals strong and spatially varying crustal anisotropy beneath the eastern Tibetan Plateau and Sichuan

Xiaojiang Fault Zone, the results support the existence of mid/lower crustal flow. The pervasive strike-orthogonal fast orientations in the vicinity of the Longmenshan Fault Zone suggest a significant contribution of fault-normal compressional stress to the large topographic relief across the fault.

BIBLIOGRAPHY