Mantle transition zone topography and structure ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, B10308, doi:10.1029/2008JB006229, 2010

Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt Xiaobo Tian,1 Dapeng Zhao,2 Hongshuang Zhang,1 You Tian,3 and Zhongjie Zhang1 Received 25 November 2008; revised 23 May 2010; accepted 8 June 2010; published 20 October 2010.

[1] In this study we calculated receiver functions (RFs) from teleseismic P waveforms recorded by stations of four seismic networks to determine the topography of the mantle transition zone (MTZ) beneath the central Tien Shan. We converted the RFs from the time domain to the depth domain and selected the depths of 410 and 660 km discontinuities after stacking the RFs in narrow raypath bins. To better determine the MTZ topography, we applied an updated RF method to invert the depth differences between the 410 and 660 km discontinuities in each RF for lateral depth variations of the two discontinuities. Using this approach, we detected several anomalies in the 410 and 660 km discontinuity depths beneath the central Tien Shan region. Extensive synthetic tests were carried out to confirm the main features of the result. Beneath the south and east of Lake Issyk‐Kul, the 410 km discontinuity becomes shallower while the 660 km discontinuity becomes deeper, leading to a thicker MTZ with a lower temperature, possibly caused by pieces of thickened lithosphere dropping down to at least the bottom of the MTZ. Beneath the northwest of Lake Issyk‐Kul, the 410 km discontinuity becomes deeper while the 660 km discontinuity becomes shallower, resulting in a thinner MTZ with a higher temperature, which may reflect a small‐scale hot upwelling from the lower mantle. Citation: Tian, X., D. Zhao, H. Zhang, Y. Tian, and Z. Zhang (2010), Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt, J. Geophys. Res., 115, B10308, doi:10.1029/2008JB006229.

1. Introduction [2] The Tien Shan is located over 1500 km north of the collision zone between the Indian and Eurasian plates and is the largest and most active intracontinental orogen in the world. It extends over 2500 km in the E‐W direction and about 300–500 km in the N‐S direction; its highest peak exceeds 7000 m. The Tien Shan orogenic belt is composed of several parallel ranges and intermontane basins and surrounded by several stable blocks, such as the Kazakh Shield and the Tarim Basin, which lie to the north and south of the central Tien Shan, respectively (Figure 1a). [3] The ancestral Tien Shan formed in the late Paleozoic through the convergence of a few continental blocks, e.g., the Tarim, Yili‐central Tien Shan, and Junggar plates [Windley et al., 1990; Carroll et al., 1995; Gao et al., 1998]. After erosion during the Mesozoic to the early Cenozoic eras, the ancestral Tien Shan Mountains became a peneplain [Avouac et al., 1993; Métivier and Gaudemer, 1997]. Its tectonic activity resumed in the Oligocene, presumably as a consequence of the India‐Eurasia collision, and has con-

1 State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China. 2 Department of Geophysics, Tohoku University, Sendai, Japan. 3 College of Geoexploration Science and Technology, Jilin University, Changchun, China.

Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2008JB006229

tinued to the present [Sobel and Dumitru, 1997; Yin et al., 1998; Molnar and Ghose, 2000; Fu et al., 2003; Huang et al., 2006; Ji et al., 2008; Sun et al., 2009]. [4] A number of studies have focused on the Tien Shan orogenic belt, but the dynamics of the tectonic rejuvenation are still not well understood. Some researchers suggest that the Tien Shan mountain building was caused by the shortening of the crust, accompanied by a thickening of the lithosphere [Fleitout and Froidevaux, 1982]. Such shortening may have been caused by the collision between the Indian and Eurasian plates, which transferred the stress from the collision front through an abnormally strong lithosphere in the Tarim Basin to the Tien Shan [England and Houseman, 1985]. The shortening, which amounts up to 20 mm/yr across the Tien Shan, has been demonstrated by GPS observations and geologic surveys [e.g., Abdrakhmatov et al., 1996; Thompson et al., 2002]. Using evidence from earthquake focal mechanisms and tomographic images, other researchers suggest that the Tien Shan orogenic belt was caused by the underthrusting of the Tarim Basin and the Kazakh Shield beneath the Tien Shan [e.g., Ni, 1978; Nelson et al., 1987; Roecker et al., 1993; Ghose et al., 1998; Zhao et al., 2003; Guo et al., 2006; Lei and Zhao, 2007]. Furthermore, some researchers speculate that the underthrusting could form a root that can lead to further crustal shortening because of its greater density and subsequent gravitational instability, and with time, the root will detach and be filled by the underlying asthenospheric materials. Some rootlike structures have been revealed under certain mountainous regions, such

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TIAN ET AL.: MTZ TOPOGRAPHY BENEATH THE TIEN SHAN

Figure 1. (a) Topographic map of the central Tien Shan showing the locations of 44 seismic stations from four seismic networks. XW, GHENGIS (blue triangles); KN, KNET (red inverted triangles); KZ, KZNET (red inverted triangles); and G, GEOSCOPE (red inverted triangles). The station code is shown beside each station. The bold trace denotes the Talas‐Fergana Fault and the thin lines denote the boundaries of the states. F. Basin, Fergana Basin; Lake I‐K, Lake Issyk Kul. (b) Distribution of 1537 teleseismic events (squares) used in this study, which shows a relatively uniform distribution, although more events are located in the Eastern Hemisphere. The triangle denotes the center of the study area.

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as the Transverse Ranges in western United States [Humphreys and Clayton, 1990] and the Karakorum in Pakistan [Pandey et al., 1991]. However, in other regions, a rootlike structure is not visible or its appearance is inconsistent, such as under the Alps [Babushka et al., 1984] and the Sierra Nevada [Jones et al., 1994]. So far, seismological studies have not found such a root beneath the Tien Shan [e.g., Roecker et al., 1993; Vinnik et al., 2004; Lei and Zhao, 2007]. [5] Many RF and tomography studies have been conducted on the Tien Shan region [e.g., Roecker et al., 1993; Kosarev et al., 1993; Chen et al., 1997; Bump and Sheehan, 1998; Xu et al., 2002; Vinnik et al., 2004; Kumar et al., 2005; Lei and Zhao, 2007]. The crustal thickness varies from 45–70 km in the Tien Shan to approximately 42 km in the southern Kazakh Shield [Bump and Sheehan, 1998; Vinnik et al., 2004]. The thickness of the lithosphere is about 90 km underneath the Tien Shan, but it increases to 120 and 160 km beneath the Kazakh Shield and the Tarim Basin, respectively [Oreshin et al., 2002; Kumar et al., 2005]. Cool lithospheric materials residing near the 410 km depth beneath the Tien Shan have been revealed in the analysis of converted seismic phases from the 410 km discontinuity [Chen et al., 1997]. Recent tomographic studies revealed a high‐velocity (high‐V) anomaly at 150–200 km depths that extends down to the MTZ under the Tien Shan [Yang et al., 2003; Lei and Zhao, 2007]. In addition, some low‐velocity (low‐V) anomalies are revealed beneath the Tien Shan at 50–60 km depths, which also extend downward beneath the Tarim Basin and the Kazakh Shield [Roecker et al., 1993; Xu et al., 2002, 2007; Vinnik et al., 2004; Lei and Zhao, 2007]. Some researchers suggest the existence of a small‐ scale convection [e.g., Roecker et al., 1993; Wolfe and Vernon, 1998], while others propose the presence of a small mantle plume under the Tien Shan [e.g., Sobel and Arnaud, 2000; Xu et al., 2002; Friederich, 2003; Vinnik et al., 2004; Kumar et al., 2005; Lei and Zhao, 2007]. The origin of the low‐V zones observed beneath the Tien Shan and its surrounding regions has important implications with respect to the dynamics of the tectonic rejuvenation. To clarify these problems, we need to determine precisely the structure in and around the MTZ under the Tien Shan. [6] The MTZ is bounded by two sharp seismic discontinuities at depths of approximately 410 and 660 km. According to the commonly accepted view, the 410 and 660 km discontinuities caused by phase transformations in olivine in an olivine‐dominated mantle. For a typical mantle adiabat, the olivine‐wadsleyite transition (a → b) occurs at a pressure corresponding to a depth of 410 km, which causes a jump in the elastic properties of the mantle rock. The breakdown of the spinel phase (ringwoodite) into perovskite and magnesiowüstite (sp → pv + mw) occurs near 660 km in the mantle, which is commonly believed to be the cause of the 660 km seismic discontinuity [Ringwood, 1969]. An important characteristic of a phase transformation is its Clapeyron slope, the temperature derivative of the pressure at which the transformation occurs. In the Earth, pressure increases with depth, and lateral variations in temperature can create topography on the seismic disconti-

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nuity. The Clapeyron slope of the a → b transformation is positive [e.g., Katsura and Ito, 1989; Bina and Helffrich, 1994], so a low‐temperature anomaly can cause a local elevation of the 410 km discontinuity, whereas a high‐ temperature anomaly can cause a local depression of the 410 km discontinuity. In contrast, the slope of the sp → pv + mw transformation is negative [e.g., Ito and Takahashi, 1989; Bina and Helffrich, 1994], which implies a depression of the 660 km discontinuity in a low‐temperature environment and its elevation at high‐temperature. Thus, lateral variations in the discontinuity depths provide information on lateral temperature variations in MTZ, which can be diagnostic of the depth of origin of mantle plumes [Shen et al., 1998; Fee and Dueker, 2004] and the deep structure of subducting slabs [Li et al., 2000; Chen and Ai, 2009]. [7] With the rapidly growing number of permanent and temporary seismic stations deployed during the last decade in Tien Shan, much information on the crust and upper‐ mantle structure has been obtained [e.g., Yang et al., 2003; Vinnik et al., 2004; Kumar et al., 2005; Lei and Zhao, 2007]. However, the detailed deep structure and dynamic processes remain unclear. Understanding the dynamics driving this enigmatic mountain belt is very important, and studying the MTZ topography can extract important and independent information on the thermal structure and dynamic process beneath the Tien Shan. [8] The RF method has become an important tool in the imaging of the MTZ topography. In many previous studies, the MTZ topography has been obtained from the P‐to‐S converted phases at the discontinuities (P410s and P660s) by migrating or stacking RFs. However, the topography of the 410 and 660 km discontinuities that is obtained using such a conventional approach suffers from the lateral velocity variations in the crust and upper mantle. Consequently, the topography results depend on the velocity model adopted [Niu et al., 2004]. To remove the effect of the velocity heterogeneity in the crust and upper mantle, in this work we have developed an updated RF method that determines the MTZ topography from the differential travel time TP660s – TP410s (or the differential depth D660−410), and we have applied the new method to investigate the MTZ structure beneath the central Tien Shan.

2. Data and Method 2.1. Data [9] We used 44 seismic stations belonging to four seismic networks of GHENGIS (28 stations), GEOSCOPE (1 station, WUS), KZNET (2 stations, PDG and TLG), and KNET (13 stations) (Figure 1a). The GHENGIS network was in operation for about 18 months, while the stations of the other three networks had operated for at least a few years. [10] Figure 1b shows the epicentral distribution of 1537 earthquakes used in this study. The magnitude of these events is M > 5.3. All of the events are located at epicentral distances of 30°–90° from the center of the study area. The distribution of the selected events is not uniform. Most of them are located in the subduction zones in the northern and western Pacific as well as Indonesia, and only a few events are located in the Western Hemisphere. We used the

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Figure 2. Map showing the locations of the ray‐piercing points at 410 (blue crosses) and 660 (red crosses) km depths. Black lines denote the national boundaries.

P waveforms from these events and isolated the P‐to‐S conversions from the seismic discontinuities to compute RFs in the frequency domain using a band‐pass filter of 0.03∼0.2 Hz [Ammon, 1991]. After removing poorly deconvolved RFs, we obtained 8855 high‐quality RFs and calculated the raypaths of the RFs using the IASP91 Earth model [Kennett and Engdahl, 1991]. The piercing points of the RFs at 410 and 660 km depths cover the study area densely and uniformly (Figure 2). 2.2. Measuring D660−410 in Common Raypath Stacking [11] To study the MTZ topography and structure, we measure the depths of the 410 and 660 km discontinuities (D410 and D660). In the first step, we convert all the RFs from the time domain to the depth domain [Chevrot et al., 1999]. The IASP91 Earth model is used as the reference model of seismic velocities (Vp and Vs) to calculate the raypaths and the delay times between the converted phases and the direct P wave. The elevations of seismic stations are taken into account in the calculation. After converting all the RFs to the depth domain, the effects of the epicentral distance on travel time are corrected automatically. The second step is to stack RFs. Some bins are designed for stacking RFs to improve the signal‐to‐noise ratio, for example, the common conversion point (CCP) bins [Dueker and Sheehan, 1998; Kind et al., 2002; Ozacar et al., 2008]. To measure the D410 and D660 with a high spatial resolution, we stack RFs in a narrow cylindrical bin (with a radius of 25 km) along the raypath of each RF between 410 and 660 km depths. We call this process common raypath (CRP) stacking. The third step is to measure the D410 and D660. For identifying the P410s and P660s correctly, we perform CRP stacking with different radii (e.g., 150, 100, 75, and 50 km), and identify the converted phases in CRP stacking by comparing the results with different radii. The depths for the peak value of phases

in stacking RFs are measured. To further quantify the D410 and D660, we use the bootstrap resampling method [Efron and Tibshirani, 1986] that estimates the standard deviations (STDs) of the discontinuity depths for each CRP stacking. The STDs of D410 and D660 are generally smaller than 5 km. In Appendix A, we describe the CRP stacking in detail and show some examples and statistics of our measurements. 2.3. Construction of the Grid Model [12] To map the MTZ topography, we used 2 two‐ dimensional grid meshes to express the depth variations of the 410 and 660 km discontinuities. Figure 3 shows the configurations of the grid meshes in the horizontal and depth directions. The lateral grid spacing is 0.5° (∼50 km) for each discontinuity. Taking the discontinuity depth anomaly at each grid node as the unknown parameter, we calculated the discontinuity depth anomaly at any point in the study area by using the following linear interpolation function: DD410 ð x; yÞ ¼

2 X 2 X

DD410 xi ; yj

i¼1 j¼1

x xi y yj 1 1 y2 y1 x2 x1 2 X 2 X ¼ DD410 xi ; yj Yij ;

ð1aÞ

i¼1 j¼1

where Yij = (1 − |x − xi/x2 − x1|)(1 − |y − yj/y2 − y1|) represents the weight coefficients for the linear interpolation at the 410 km discontinuity, x is the longitude, and y is the latitude; xi and yj are the coordinates of the four grid nodes surrounding a point (x, y). DD410(xi, yj) denotes the depth anomaly at a

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Figure 3. Distribution of the grid nodes used to map the 410 and 660 km discontinuities in (a) map view, (b) north‐south, and (c) east‐west vertical crosssections. The grid spacing is 0.5° in both the latitudinal and longitudinal directions. The shaded lines in Figure 3a denote the national boundaries. grid node for the 410 km discontinuity. For the 660 km discontinuity, we have the following expression: DD660 ð x; yÞ ¼

2 X 2 X

MTZ, the measurement of D660−410 can be expressed as follows: D660 ð x6k ; y6k Þ D410 ð x4k ; y4k Þ ¼ D660410 ðk Þ

DD660 xi ; yj

i¼1 j¼1

x xi y yj 1 1 x2 x1 y2 y1 2 X 2 X DD660 xi ; yj Fij ; ¼

or DD660 ð x6k ; y6k Þ DD410 ð x4k ; y4k Þ ¼ DD660410 ðk Þ; ð1bÞ

i¼1 j¼1

where Fij = (1 − |x − xi/x2 − x1|)(1 − |y − yj/y2 − y1|) represents the weight coefficients for the linear interpolation at the 660 km discontinuity. DD660(xi, yj) denotes the depth anomaly at a grid node for the 660 km discontinuity. 2.4. Inversion for the MTZ Topography [13] For better imaging of the MTZ topography, we incorporated the D660−410 data in our new RF method in each CRP bin with a radius of 25 km, instead of using the individual measurements of D410 and D660. This is because the D660−410 data are not sensitive to velocity heterogeneities above the 410 km discontinuity, since the paths of P410s and P660s are nearly identical above that depth [Shen et al., 1998]. Note that the value of D660−410 in a RF is not a true measurement of the MTZ thickness, because the piercing points at the two discontinuities have a horizontal offset of 60–120 km. By considering the raypaths in and around the

ð2Þ

where D660−410(k) is the D660−410 measured from the kth RF stacking bin and D660(x6k, y6k) and D410(x4k, y4k) are the measurements for the 660 and 410 km discontinuity depths at the ray‐piercing points (x6k, y6k) and (x4k, y4k), respectively. In addition, DD410, DD660, and DD660−410 are equivalent to D410 – 410 km, D660 – 660 km, and D660−410 – 250 km, respectively. The measurements of DD660−410 form a data column vector d with dimension N (N = 4738). [14] As in the seismic tomography method [Zhao et al., 1992, 1994], we can express the depth variations of the 410 and 660 km discontinuities with two‐dimensional grids (Figure 3). Taking the depth anomaly at each grid node to be the unknown parameter, we calculate the discontinuity depth anomaly at any point using a linear interpolation function as in equations (1a, 1b). Thus equation (2) can be rewritten as 2 X 2 X

DD660 x6ki ; y6kj Fkij

i¼1 j¼1

2 X 2 X i¼1 j¼1

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DD410 x4ki ; y4kj Ykij ¼ DD660410 ðk Þ:

ð3Þ

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Figure 4. Distribution of RF raypaths used in this study in (a) map view, (b) north‐south, and (c) east‐ west vertical cross‐sections. White triangles denote the seismic stations used in this study. The shaded lines in Figure 4a denote the national boundaries. The shaded dashed lines in Figures 4b and 4c denote the 410 and 660 km discontinuities. The depth anomaly parameters can be expressed as a column vector m as follows:

1982], which yields a solution equivalent to that obtained by resolving equation (5) [Carroll and Beresford, 1997].

mT ¼ DD410 x1; y1 ; DD410 ðx1 ; y2 Þ; . . . ; DD410 ðxK ; yL Þ DD660 ðx1 ; y1 Þ; DD660 ðx1 ; y2 Þ; . . . ; DD660 ðxK ; yL Þ:

3. Results and Resolution Tests

Note that the total number of depth anomaly parameters in this study is 2 × K × L (K = 25, L = 13). [15] The column vectors specifying the data set and the unknown parameters are related through the following observation equation: d ¼ Gm þ e;

ð4Þ

where e is an error vector and G is an N × (2 × K × L) matrix whose elements consist of the coefficients of the depth anomaly in equation (3). Figure 4 shows the distribution of the raypaths used in the inversion. [16] The damped leastsquares method was adopted by Aki and Lee [1976] to solve equation (4) in the early tomographic studies. They used

GT G þ Q m ¼ GT d;

ð5Þ

which can be obtained by minimizing |d − Gm|2 + mT Qm, where Q = "2I and " is the damping parameter. The drawback of this inversion method is that the matrix GTG needs large memory storage and its inversion is time consuming, though G is a relatively sparse matrix [Zhao et al., 1992]. To avoid such a problem, we follow Zhao [2001, 2004] and adopt a conjugate‐gradient algorithm [Paige and Saunders,

[17] We performed many inversions with different values of the damping parameter. Figure 5 shows the trade‐off curve for the norm of the solution versus the final RMS depth residual. We found the optimal value of the damping parameter to be 0.5, because it best balances the reduction of the RMS residual and the smoothness of the model for the 410 and 660 km discontinuities. The results obtained are shown in Figure 6. The MTZ thickness (TMTZ) is defined by subtracting the depth of 410 km discontinuity from the depth of 660 km discontinuity at the same horizontal location. The anomaly of the MTZ thickness, DTMTZ, is obtained by subtracting 250 km from TMTZ. [18] To the northwest of Lake Issyk‐Kul, the 410 km discontinuity is depressed while the 660 km discontinuity is elevated (Figures 6a and 6b). Beneath the south and east of Lake Issyk‐Kul, the 410 km discontinuity is elevated while the 660 km discontinuity is depressed. As a result, the MTZ becomes thin to the northwest of Lake Issyk‐Kul and becomes thick to the east and south of the lake (Figure 6c). [19] In order to confirm the main features of our MTZ topographic image (Figure 6), we performed several synthetic tests following the approach of Zhao [2001]. In the input models (Figure 7), we assumed a few topographic anomalies with an amplitude of 20 km relative to the IASP91 model. We computed the synthetic data for the input models and added

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Figure 5. Trade‐off curve for the RMS residual of the data versus the norm of the solutions determined by the inversions conducted with different values of the damping parameter (values beside the open circles). The optimal damping parameter is found to be 0.5. random noises with zero mean and a standard deviation of 5 km to the synthetic data to account for the measurement errors that are usually present in the measurements [Ozacar et al., 2008]. Then we inverted the synthetic data using the same seismic stations, events, and raypaths as those in the real data set. [20] We conducted three synthetic tests (Figure 7). In the first test, the input model contained a 20 km depression for the 410 km discontinuity and a 20 km elevation for the 660 km discontinuity beneath the northwest of Lake Issyk‐ Kul, and a 20 km elevation for the 410 km discontinuity and two 20 km depressions for the 660 km discontinuity beneath the south and east of Lake Issyk‐Kul (Figures 7a–7c). In the second test, the input model contained a 20 km depression and a 20 km elevation for the 410 km discontinuity (Figures 7g–7i). In the third test, the input model contained a 20 km elevation and two 20 km depressions for the 660 km discontinuity (Figures 7m–7o). The test results show that the input anomalies are generally recovered (Figures 7d–7f, 7i–7k, 7p–7r), despite some differences in the amplitude, and there is some smearing in the output models, particularly in Figures 7k and 7p. [21] These synthetic tests show that the main features of our results are reliable (Figure 6). It is difficult to determine the MTZ topography with high resolution by using the conventional RF method which suffers from the lateral velocity heterogeneity in the crust and upper mantle. This problem can be resolved by using our new RF method.

4. Discussion 4.1. Comparison of Different Methods [22] In the previous RF studies for the Tien Shan region, there was no local 3‐D velocity model to correct for the

effect of lateral heterogeneity in the crust and upper mantle, and the depths of the 410 and 660 km discontinuities were determined by using the measurements based on the IASP91 model. In this work, we also measured the depths of 410 and 660 km discontinuities by using CCP with a radius of 25 km based on the IASP91 model. Using equation (1), the measurements of the D410 and D660 are inverted to obtain the DD410 and DD660 at the grid nodes (Figure 3). The results are shown in Figures 8a–8c. The CCP stacking with the IASP91 model results in a deeper 410 km discontinuity under the southern Kazakh Shield and a normal 410 km discontinuity under the northern central Tien Shan (Figure 8a). This stacking result is consistent with that of Chen et al. [1997], who obtained a later arrival (about 2.0 s) of P410s under the southern Kazakh Shield and a normal arrival of P410s under the northern central Tien Shan. [23] In some regions, local 3‐D seismic velocity models are determined. On the basis of these models, the effect of lateral heterogeneity in the crust and upper mantle can be removed from RFs before stacking and measurement. Vinnik et al. [2004] conducted a joint inversion of both P and S wave RFs and determined Vp and Vs models in the crust and upper mantle down to 150 km depth beneath the central Tien Shan. Using teleseismic tomography, Lei and Zhao [2007] determined a 3‐D P‐wave velocity model of the upper mantle under Tien Shan. In this work, we used these local 3‐D velocity models [Vinnik et al., 2004; Lei and Zhao, 2007] to remove the effect of the crust and upper mantle heterogeneity. We carried out the CCP stacking to measure the D410 and D660 with different reference models. After fitting the measurements at the grid nodes (Figure 3) using equation (1), the topography of 410 and 660 km discontinuities and the MTZ thickness are determined (Figure 8).

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[25] There are some significant discrepancies in the MTZ topography by the CCP stacking caused by different velocity models. For example, for the topography of the 660 km discontinuity, the CCP stacking with the IASP91 model leads to a large area of depression (Figure 8b), and the CCP stacking with the model of Lei and Zhao [2007] results in a smaller area of depression (Figure 8e), while there is no significant depression in the CCP stacking with the model of Vinnik et al. [2004] (Figure 8h). In contrast, the results of our new method are not sensitive to the velocity models adopted. The discrepancies in the discontinuity topography caused by different velocity models in our method are much smaller than those observed in other CCP stacking methods (Figure 8). [26] Further, the CCP stacking results from the model of Vinnik et al. [2004] are more consistent with our results than those obtained by using the CCP stacking model of Lei and Zhao [2007]. However, the model of Vinnik et al. [2004] can only partially remove the effect of the crust and upper mantle heterogeneity, because this model is valid only down to about 150 km depth. The P‐wave tomography model of Lei and Zhao [2007] is not sufficient either because damping and smoothing operations are applied in their tomographic inversion, leading to underestimation of the amplitudes of velocity anomalies.

Figure 6. The topographies of (a) the 410 km discontinuity, (b) 660 km discontinuity, and (c) the MTZ thickness obtained by using the RF inversion method. The depth and thickness perturbation scales are shown on the right. [24] Figure 8 also shows the results obtained by using our new method with different reference velocity models. Although the discrepancy in the MTZ thickness between the CCP stacking and our new method is not significant, there are some differences in the 410 and 660 km discontinuity topography between the two methods. For example, the 660 km discontinuity becomes shallower to the northwest of Lake Issyk‐Kul according to our new method, but such an anomaly is not visible in the results by the CCP stacking.

4.2. Effect of MTZ Lateral Velocity Variations [27] In our method, the seismic velocity is assumed to be laterally homogeneous in MTZ, but in fact the lateral variations in MTZ thickness imply lateral variations in temperature, which may reflect lateral variations of seismic velocity in MTZ. Thus, a thick MTZ may correspond to low temperature and high seismic velocity, and vice versa. Hence, the effect of lateral velocity variations in MTZ on the topography should be investigated. [28] If the MTZ thickness is constant, then the measurements of D660−410 from RF would be anomalously small in high‐velocity areas and anomalously large in low‐velocity ones. Under the temperature dependence of −0.33 to −0.384 m/s/K as measured in the laboratory for olivine and peridotite [Sinogeikin et al., 2003; Jackson et al., 2005], the relationships between the S wave velocity anomaly and the depth anomaly of 410 and 660 km discontinuities are c410 = (DVS/VS)/DD410 ≈ −0.0008 km−1 and c660 = (DVS/VS)/ DD660 ≈ 0.0011 km−1 (see Appendix B for details). By comparing the MTZ thickness measured from RFs with S‐wave velocity, estimated from a regional tomographic model, Lebedev et al. [2003] suggested that the MTZ thickness and the seismic velocity within the MTZ correlate with a slope of 0.19 ± 0.09 km/(m/s). The result is c410 ≈ −0.0017 km−1 and c660 ≈ 0.0023 km−1 (see Appendix B for details). [29] We introduced the S‐wave velocity anomaly into equation (3) to correct the measurements of D660−410. To

Figure 7. Results of three synthetic tests. (a–c) In the first test, the topographic anomalies are set at both 410 and 660 km discontinuities in the input model. (d–f) The inversion results of the first test are shown as the output. (g–i) In the second test, anomalies are set only at the 410 km discontinuity and not at the 660 km discontinuity in the input model; the test results are shown in Figures 7j–7l. (m–o) In the third test, anomalies are set only at the 660 km discontinuity and not at the 410 km discontinuity in the input model. The third test results are shown in Figures 7p–7r. The depth and thickness perturbation scales are shown at the bottom. 8 of 20

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simplify the problem, the S velocity anomaly or the temperature anomaly is assumed to be linear between the 410 and 660 km discontinuities. According to the above discussion, when c410 and c660 are assumed to be constant, we can obtain an equation relating the unknown parameters DD410 and DD660 with the measurements DD660−410 (see Appendix C for details). [30] Figure 9 shows the results with different values of c410 and c660. In Figures 9d–9f, we assumed c410 = −0.0008 km−1 and c660 = 0.0011 km−1 which are equal to those measured in the laboratory for olivine and peridotite. In Figures 9g–9i, c410 = −0.0017 km−1 and c660 = 0.0023 km−1, which are equal to those induced from RF and surface wave studies. In Figures 9j–9l, c410 = −0.0025 km−1 and c660 = 0.0034 km−1, indicating that the temperature variation may lead to a larger velocity anomaly than those estimated by previous studies [Sinogeikin et al., 2003; Jackson et al., 2005; Lebedev et al., 2003]. In Figures 9m–9o, c410 = −0.003 km−1 and c660 = 0.003 km−1. These results show a pattern similar to those without the velocity anomaly in MTZ, but the amplitude of the 410 and 660 km discontinuity topography is somewhat diminished and enlarged, respectively, suggesting that our results are not sensitive to the lateral velocity variations in MTZ. 4.3. Geodynamic Implications [31] With the IASP91 model, our topographic image shows a depression (10–20 km) at the 410 km discontinuity and an uplift (10–20 km) at the 660 km discontinuity beneath the northwest of Lake Issyk‐Kul (Figures 6a and 6b). By assuming that the depth variations of the discontinuities are caused solely by the temperature effect and using the laboratory‐obtained depth dependence of 3.1 MPa/K and −2.0 MPa/K for the olivine‐wadsleyite transition (a → b) and the breakdown of the spinel phase (ringwoodite) into perovskite and magnesiowüstite (sp → pv + mw) [Katsura and Ito, 1989; Bina and Helffrich,1994], respectively, researchers estimate that the depression of the 410 km discontinuity corresponds to a temperature increase of 125– 250 K, and the uplift of the 660 km discontinuity corresponds to a temperature increase of 200–400 K [Revenaugh and Jordan, 1991; Bina and Helffrich, 1994]. Beneath the south and east of Lake Issyk‐Kul (Figures 6a and 6b), our result indicate an uplift (10–20 km) at the 410 km discontinuity and two depressions (10–20 km) at the 660 km discontinuity. The uplift of the 410 km discontinuity corresponds to a temperature decrease of 125–250 K, and the depressions of the 660 km discontinuity correspond to a temperature decrease of 200–400 K. [32] Figure 10 summarizes our results schematically. The lateral temperature variations at the 410 and 660 km discontinuities provide information on the mantle circulation patterns. The higher temperature at the 410 and 660 km discontinuities beneath the northwest of Lake Issyk‐Kul

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may be indicative of a mantle plume raising from the lower mantle [Shen et al., 1998; Li et al., 2003], while the lower temperature at the 410 and 660 km discontinuities beneath the south and east of Lake Issyk‐Kul may reflect the cold lithosphere subducting or sinking to the MTZ [Li et al., 2000; Chen and Ai, 2009]. [33] If the temperature variations exist only at the 410 km discontinuity, the origin of the mantle plume and the cold lithosphere subducting or sinking may be limited to the shallow part of the MTZ. The CCP stacking result shows the high‐temperature anomaly only at the 410 km discontinuity (Figure 8), but depends on the velocity model adopted. Our new method revealed a high‐temperature anomaly existing at both 410 and 660 km discontinuities even different velocity models are adopted, suggesting that it is a reliable feature. [34] Many previous studies with different approaches support the tectonic model of the Tarim and the Kazakh lithospheres underthrusting beneath the Tien Shan [e.g., Ni, 1978; Nelson et al., 1987; Roecker et al., 1993; Ghose et al., 1998; Xu et al., 2002; Yang et al., 2003; Lei and Zhao, 2007]. For example, seismicity studies indicate that the Kazakh lithosphere underthrusts under the Tien Shan [Roecker et al., 1993]. Regional seismic tomography shows that the underthrusting of the Tarim and the Kazakh lithosphere formed an active mountain belt [Xu et al., 2002]. Yang et al. [2003] suggested that the primary cause of a high‐V anomaly beneath the Tien Shan is a delaminated lithosphere or a detached piece of the subducting Tarim lithosphere. Teleseismic tomography revealed a high‐V anomaly extending from the upper mantle to the MTZ, suggesting that the Tarim and Kazakh lithospheres underthrust beneath the Tien Shan, and pieces of the thickened lithosphere detached and descended to the deep mantle because of gravitational instability [Lei and Zhao, 2007]. The detached cold lithosphere may have penetrated through the MTZ and changed the depth of phase transformations in olivine. According to the first‐order thermal calculations [Chen and Tseng, 2007], a temperature difference of 200– 300 K between the coldest core of sinking lithosphere and the surrounding mantle may remain 20–30 Ma after the detachment. Our results reveal low‐temperature anomalies located beneath the south and east of Lake Issyk‐Kul, suggesting that the detached cold lithosphere has sunk down to at least 660 km depth (as shown by the blue arrows in Figure 10). Analyses of converted phases show the existence of some cool materials near 410 km depth beneath Tien Shan and, thus, also support the idea that the thickened lithosphere detached and descended to the deep mantle [Chen et al., 1997]. A high Pn velocity anomaly with NE strike beneath the western Tarim Basin may be associated with the cold relic lithosphere in MTZ [Liang et al., 2004]. [35] A tomographic inversion of Pn travel times revealed a low‐V anomaly in the uppermost mantle beneath the

Figure 8. The topography of the 410 and 660 km discontinuities and the MTZ thickness determined by using different methods and velocity models: (a–c) by the CCP stacking with the IASP91 model; (d–f) by the CCP stacking with the model of Lei and Zhao [2007]; (g–i) by the CCP stacking with the model of Vinnik et al. [2004]; (j–l) by our new method with the IASP91 model; (m–o) by our new method with the model of Lei and Zhao [2007]; (p–r) by our new method with the model of Vinnik et al. [2004]. The black lines denote the national boundaries. The depth and thickness perturbation scales are shown at the bottom. 11 of 20

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Figure 9. Results showing the effect of lateral velocity variation in MTZ with different ratios between the S‐velocity anomaly and the depth anomaly (c410 and c660): (a–c) c410 = 0 km−1 and c660 = 0 km−1; (d–f) c410 = −0.0008 km−1 and c660 = 0.0011 km−1; (g–i) c410 = −0.0017 km−1 and c660 = 0.0023 km−1; (j–l) c410 = −0.0025 km−1 and c660 = 0.0034 km−1; (m–o) c410 = −0.003 km−1 and c660 = 0.003 km−1. The depth and thickness perturbation scale is shown at the bottom. northwest of Lake Issyk‐Kul [Liang et al., 2004]. Local, regional, and teleseismic tomographic studies show some prominent low‐V anomalies in the upper mantle beneath the central Tien Shan [e.g., Vinnik and Saipbekova, 1984; Woodward and Masters, 1991; Roecker et al., 1993; Yang et al., 2003; Lei and Zhao, 2007], which are consistent with the existence of negative Bouguer gravity anomalies [Burov

et al., 1990]. However, several studies have suggested a variety of depth ranges for the low‐V anomalies. Roecker et al. [1993] found that the low‐V anomalies beneath the central Tien Shan extend down to 150 km depth but no deeper than 300 km depth. Xu et al. [2002] showed that the low‐V anomalies beneath the Tien Shan extend down to the Tarim asthenosphere. Friederich [2003] suggested that

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Figure 10. A schematic showing the MTZ structure and dynamics underneath the central Tien Shan. Yellow to red colors show high temperature at the 410 and 660 km discontinuities, while cyan to blue colors show low temperature. Blue arrows denote the cold detached lithosphere penetrating or residing at the bottom of the MTZ. Red arrows denote the tilted plume conduit that penetrates the MTZ and forms a hot upwelling. LVZ denotes a low S‐wave velocity zone at depths of 110 to 130 km [Vinnik et al., 2004]. The surface topography of the Tien Shan region is shown by the 3‐D color image where the yellow and red colors represent the mountains, while the green colors represent the basins. the low‐V anomalies connect with the MTZ. Lei and Zhao [2007] revealed prominent low‐V anomalies down to 150– 200 km depth beneath the Tien Shan and suggested that these anomalies may be related to two branches of hot upwellings: one rising up from the lower mantle beneath the Tarim Basin and the other rising up from the top of MTZ beneath the western Kazakh Shield. Our present results (Figure 6) indicate that the hot anomaly has penetrated through the MTZ beneath the southern Kazakh Shield. We consider a hot upwelling to be rising from the lower mantle and penetrating the 410 and 660 km discontinuities beneath the northwest of Lake Issyk‐Kul (as shown by the red arrows in Figure 10), which corresponds to the low‐V zone in the upper mantle the previous studies [e.g., Vinnik et al., 2004; Liang et al., 2004; Lei and Zhao, 2007]. [36] In this study, the main features of the MTZ topography beneath the central Tien Shan have been revealed by the updated RF method. However, it is possible that the depth anomalies of the 410 and 660 km discontinuities are

underestimated because of the damping and smoothing operations applied in the inversion for the MTZ topography, similar to the velocity anomalies imaged by seismic tomography [e.g., Zhao et al., 1992, 1994]. 4.4. Conclusions [37] In this study, we estimated the MTZ topography and structure beneath the central Tien Shan using a new RF method. The conventional CCP method is affected significantly by lateral velocity heterogeneities in the crust and upper mantle, which can lead to an inaccurate estimation of the 410 and 660 km discontinuity topography. By utilizing the difference between D660 and D410 found in the RF, our new method is less sensitive to the velocity heterogeneities above the 410 km discontinuity since the paths of P410s and P660s are nearly identical above 410 km depth. The depth distributions of the 410 and 660 km discontinuities are determined with an inversion method. We performed synthetic resolution tests and examined the effects of different

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may reflect a lower temperature caused by a thickened lithosphere that has detached and descended to at least the bottom of the MTZ. The lithospheric thickening may result from the underthrusting of the Tarim and Kazakh lithospheres under the Tien Shan due to the collision between the Indian and Eurasian plates. We also found a depression of the 410 km discontinuity and an elevation of the 660 km discontinuity beneath the northwest of Lake Issyk‐Kul, which may reflect a small‐scale hot anomaly ascending from the lower mantle and penetrating through the 410 and 660 km discontinuities into the upper mantle. The hot upwelling may have caused a low‐V anomaly in the upper mantle and played an important role in the ongoing mountain building in the central Tien Shan.

Appendix A: Common Raypath (CRP) Stacking

Figure A1. A schematic showing the CRP stacking. The triangles represent seismic stations on the surface. The bold line denotes the raypath of the host RF, while thin lines represent the raypaths of the guest RFs. The circles at the 410 and 660 km discontinuities have the same size with a given radius (e.g., 25 km), and the centers of the circles are the piercing points of the host RF. RFs with raypaths passing through both the circles at the 410 and 660 km discontinuities are used to conduct the CRP stacking with the host RF.

velocity models on our inversion result. We also evaluated the effect of the lateral velocity variations in MTZ on the estimated topography of the 410 and 660 km discontinuities. [38] Our results show a few prominent features in the MTZ topography under the Tien Shan, which may reflect temperature variations in MTZ. The 410 km discontinuity becomes shallow and the 660 km discontinuity becomes deep beneath the south and east of Lake Issyk‐Kul, which

[39] To study the MTZ topography and structure, many researchers have used the common conversion point (CCP) stacking [e.g., Dueker and Sheehan, 1998; Kind et al., 2002; Ozacar et al., 2008]. A plane is assumed at a given depth, the piercing point of each receiver function (RF) is located on the plane, and the plane is divided into many cells. RFs with piercing points located in the same cell are stacked together to improve the signal‐to‐noise ratio. To ensure coherent stacking, a velocity model is used to remove the effect of the difference in the epicenter distance or to convert RF from the time domain to the depth domain. To measure or image the 410 and 660 km discontinuities, CCP stacking is often carried out for the depths of 410 and 660 or 530 km. Raypaths of RFs in a CCP stacking may be distributed over a large region (with a horizontal range of 200–300 km) in the crust and upper mantle; therefore, any lateral velocity variations above the depth of 410 km can debase coherent stacking. On the other hand, there is a horizontal offset of 60–120 km between the piercing points at the 410 and 660 km discontinuities for a RF (Figure A1). As a result, the CCP stacking yields a measurement of the MTZ thickness with low lateral resolution. [40] In an RF, the D660−410 is not sensitive to velocity heterogeneities above the 410 km discontinuity, since the raypaths of P410s and P660s are nearly identical above that depth. To image the 410 and 660 km discontinuities with a high spatial resolution, we measure the D660−410 along an RF. For improving the signal‐to‐noise ratio, a common raypath (CRP) stacking is introduced in this study (Figure A1). First, a RF is taken as the host, the piercing points of the host RF at the depths of 410 and 660 km are taken as the centers of two circles with a given radius (such as 25 km), which are introduced at the depth 410 and 660 km, respectively. Second, for other RFs, if their piercing points at the depths

Figure A2. An example of measuring D410 and D660 by the CRP stacking. The piercing points of the host RF and guest RFs are shown as a large black cross and small shaded crosses, respectively. The vertical dashed lines on the stack trace of RFs show the range of searching P410s or P660s. The arrows denote the maximum amplitude as D410 or D660. The numbers of RFs in the stacking are shown under the stack trace. Results of the CRP stackings with different radii are shown: (a–c) 150 km radius; (d–f) 100 km radius; (g–i) 75 km radius; (j–l) 50 km radius; and (m–o) 25 km radius. The 23 RFs used in the CRP stacking with a radius of 25 km are shown in Figure A2p, and the host RF is shown at the bottom. In Figure A2o, the open circles and the vertical bars represent the mean values and the standard deviations estimated by using the bootstrap resampling procedure [Efron and Tibshirani, 1986]. 14 of 20

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Figure 12

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Figure A3. Same as Figure A2, but for a poor example with large standard deviations.

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Figure A4. Histograms showing (a) the number of RFs in each CRP stacking, (b) depth measurements of the 410 km discontinuity, (c) depth measurements of the 660 km discontinuity, (d) difference in the depth measurements between the 410 and 660 km discontinuities, (e) STD in the depth measurements of the 410 km discontinuity, and (f) STD in the depth measurements of the 660 km discontinuity. 17 of 20

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of 410 and 660 km are located within the two circles, they are taken as the guest RFs. Finally, the guest RFs and the host RF are stacked after being converted from the time domain to the depth domain with the velocity model IASP91. [41] The CRP stacking looks like stacking in a narrow cylindrical bin along the raypath of the host RF between 410 and 660 km depths. The distance between the host RF ray and the guest RFs rays is lesser than or equal to the given radius in MTZ, but may be somewhat larger than the given radius in the crust and upper mantle. [42] As shown in Figure A2, to identify the P410s and P660s correctly, we perform CRP stacking with different radii (e.g., 150, 100, 75, 50, and 25 km) and identify the converted phases in the CRP stacking by comparing the results with different radii. When the radius is 150 km, the number of RFs in the CRP stacking is 2050. We first pick up the maximum amplitudes as the P410s and P660s in the depth ranges of 410 ± 30 km and 660 ± 30 km from the stacked trace and get D410 = 414 km and D660 = 668 km. When the radius is 100 km, the number of RFs in the CRP stacking is 1190, and we pick up the maximum amplitudes as the P410s and P660s in the depth ranges of 414 ± 20 km and 668 ± 20 km from the stacked trace and get D410 = 412 km and D660 = 669 km. When the radius is 75 km, the number of RFs is 743, and we pick up the maximum amplitudes as the P410s and P660s in the depth ranges of 412 ± 20 km and 669 ± 20 km from the stacked trace and get D410 = 407 km and D660 = 669 km. When the radius is 50 km, the number of RFs is 272, and we pick up the maximum amplitudes as the P410s and P660s in the depth ranges of 407 ± 20 km and 669 ± 20 km from the stacked trace and get D410 = 406 km and D660 = 665 km. When the radius is 25 km, the number of RFs is 23 in the CRP stacking, then we pick up the maximum amplitudes as the P410s and P660s in the depth ranges of 406 ± 20 km and 665 ± 20 km from the stacked trace and get D410 = 407 km and D660 = 659 km. [43] Another example is shown in Figure A3. The P410s and P660s can be measured accurately from the stacked trace when the CRP stacking radius is larger than 75 km, while they are measured with low reliability when a smaller radius is used because there are multiple wave peaks with comparable amplitudes in the search range. Such data, as shown in Figure A3, are not used in the further analysis and inversion. [ 44 ] The bootstrap resampling procedure [Efron and Tibshirani, 1986] was use to estimate the standard deviations (STDs) of the discontinuity depths for each CRP stacking. The STD, sD410 and sD660, are calculated using s = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P 1=ð M 1Þ M i¼1 Di D , where M is the number of bootstrap steps (which is taken as 40 in this study), Di is the resulting depth of the ith step, and D is the mean depth. The STDs of the D660−410 are calculated by using sD660‐410 = pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2D410 þ 2D660 . We reject those measurements with sD410 or sD660 larger than 10 km or with the number of RFs per stacking less than 10, such as the example shown in Figure A3 where sD410 = 13.4 km. As a result, we obtain 4738 measurements (see Figure A4 for details). The average number of RFs per stacking is 40. The averages of D410, D660, and D660−410 are 411, 667, and 255 km, respectively. The

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averages of sD410, sD660, and sD660‐410 are 3.0, 4.3, and 5.7 km, respectively.

Appendix B: Relationship Between the MTZ S‐Velocity Anomaly and the MTZ Topography [45] We define the relationship between the S‐wave velocity anomaly in MTZ and the depth of the 410 or 660 km discontinuities as c = (DVS/VS)/DD ≈ dVS/dT · dT/dP · dP/dD · 1/VS = dVS/dT · (dP/dT · dD/dP · VS)−1, where dD/ dP = 0.03 km/MPa. For the 410 km discontinuity, dP/dT = 3.1 MPa/K [Katsura and Ito, 1989; Bina and Helffrich,1994], VS = 5.07 km/s [Kennett and Engdahl, 1991], dVS/dT = −0.33 to −0.384 m/s/K [Sinogeikin et al., 2003; Jackson et al., 2005], and c410 = −0.0008 km−1. For the 660 km discontinuity, dP/dT = −2.0 MPa/K [Katsura and Ito, 1989; Bina and Helffrich,1994], V S = 5.6 km/s [Kennett and Engdahl, 1991], dVS/dT = −0.33 to −0.384 m/s/K [Sinogeikin et al., 2003; Jackson et al., 2005], and c660 = 0.0011 km−1. [46] By comparing the MTZ thickness measured from RFs with S‐wave velocity estimated from a regional tomographic model, Lebedev et al. [2003] suggested that the MTZ thickness and the seismic velocity within the MTZ correlate with a slope of 0.19 ± 0.09 km/(m/s). Considering the Clapeyron slopes (3.1 and −2.0 MPa/K at 410 and 660 km discontinuities, respectively) [Katsura and Ito, 1989; Bina and Helffrich,1994], dD/dVS values are −0.114 and 0.076 km/(m/s) for the 410 and 660 km discontinuities, respectively. Using c = (DVS/VS)/DD ≈ dVS/dD · 1/VS = (dD/dVS · VS)−1, we obtain c410 = −0.0017 km−1 and c660 = 0.0023 km−1.

Appendix C: Equation for the Depth Measurements Considering Lateral S‐Velocity Variations in MTZ [47] By dividing the raypath of a converted wave in MTZ into J segments (in this study J = 5) and using the IASP91 velocity model, the travel time of the converted wave can be expressed as t¼

J X li ; Vs i i¼1

where li and Vsi are the length of the raypath and the average S‐wave velocity in the ith segment, respectively. [48] If there is a velocity anomaly in MTZ and the real velocity is V′S, we have DVs = DVS/VS = (V′S − VS)/VS. If |DVs| 1, and we can neglect the difference in the raypath between the IASP91 model and the real velocity structure. Then the real travel time of the converted wave is expressed as 0

t ¼

J J X X li li : 0 ¼ Vs ð 1 þ DVsi Þ Vs i i i¼1 i¼1

Assume that the error of the measurement DD660−410 is −"V, p = 1/Vs and Dp = −DVs, then we have "V ¼

J t t0 250 X 250 ¼ 250 J li pi 1 Dpi : P t li pi i¼1 i¼1

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Assume c0 = 250/

J P

li pi; then

i¼1

"V ¼ c0

J X i¼1

li pi Dpi :

Assume c410 = −Dp410/DD410 and c660 = −Dp660/DD660; we can get Dp410 = −c410 · DD410 and Dp660 = −c660 · DD660. Expressing Dpi using a linear interpolation function from eight grid nodes (four grid nodes at the 410 km discontinuity and four grid nodes at the 660 km discontinuity), we have "V ¼ c0

" J X i¼1

þ

8 X

li pi

4 X n¼1

wi;n c410 DD410 ði; nÞ !#

wi;n c660 DD660 ði; n 4Þ

;

n¼5

where w is the weight for the linear interpolation. Thus equation (2) can be rewritten as follows: DD660 ð x6k ; y6k Þ DD410 ð x4k ; y4k Þ þ "V ¼ DD660410 ðk Þ:

[49] Acknowledgments. The IRIS Data Center provided the waveform data for this study. We are grateful to L. Vinnik and Jianshe Lei for providing their velocity models. We thank editors Patrick Taylor and Jeanette Panning as well as two anonymous reviewers for their constructive comments and suggestions, which improved the manuscript. This research was supported by grants from the Chinese National Natural Science Foundation (40504005 and 40974025 to X.Tian, and 40721003 to Z.Zhang) and a grant from Japan Society for the Promotion of Science to D.Zhao (Kiban‐ A 17204037). Most of the figures were generated by using the Generic Mapping Tools software package [Wessel and Smith, 1998].

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