TY - JOUR AU - Wu,, Yihao AB - SUMMARY Determining density structure of the Tibetan Plateau is helpful in better understanding of tectonic structure and development. Seismic method, as traditional approach obtaining a large number of achievements of density structure in the Tibetan Plateau except in the centre and west, is primarily inhibited by the poor seismic station coverage. As the implementation of satellite gravity missions, gravity method is more competitive because of global homogeneous gravity coverage. In this paper, a novel wavelet-based gravity method with high computation efficiency and excellent local identification capability is developed to determine multilayer densities beneath the Tibetan Plateau. The inverted six-layer densities from 0 to 150 km depth can reveal rich tectonic structure and development of study area: (1) The densities present a clockwise pattern, nearly east-west high-low alternating pattern in the west and nearly south-north high-low alternating pattern in the east, which is almost perpendicular to surface movement direction relative to the stable Eurasia from the Global Positioning System velocity field; (2) Apparent fold structure approximately from 10 to 110 km depth can be inferred from the multilayer densities, the deformational direction of which is nearly south-north in the west and east-west in the east; (3) Possible channel flows approximately from 30 to 110 km depth can also be observed clearly during the multilayer densities. Moreover, the inverted multilayer densities are in agreement with previous studies, which verify the correctness and effectiveness of our method. Gravity anomalies and Earth structure, Inverse theory, Asia 1 INTRODUCTION Density structure of the Earth is the essential information to study relevant geophysical and geodynamic problems (Hou & Yang 2011; Hsieh & Yen 2016). Nevertheless, density structure of the Tibetan Plateau (TP), the largest and highest plateau on the Earth (see Fig. 1), is still debatable so far, which is extremely complicated as a result of long-term continuous India-Eurasia convergence since ∼50 mya (Ma), the Eocene epoch (Gao et al.2009; Shin et al.2015; Yang et al.2015). The TP is referred to as ‘Golden key’ to insight into plate tectonics, continental collisions, orogeny, etc. (Tapponnier et al.1982; Gao et al.2013). Thus, determining density structure of the TP is very valuable and has been widely researched by scientists around the world. Figure 1. Open in new tabDownload slide Geological setting of the TP overlaying on topography (Modified from Gan et al.2007). The black dashed lines, black solid lines and white lines are bordering sutures, major active faults and national borders, respectively. Key to symbols: HB, Himalayan Block; LB, Lhasa Block; QTB, Qiangtang Block; KB, Kunlun Block; QDB, Qaidam Block; YGP, Yunnan-Guizhou Plateau; MBT, Main Boundary Thrust; IYS, Indus-Yarlung suture; BNS, Bangong-Nujiang suture; JS, Jinshajiang suture; AKMS, Anyimaqen-Kunlun-Mutztagh suture; F1, Jiali Fault; F2, Manyi Yushu Xianshuihe Fault; F3, Kunlun Fault; F4, Haiyuan Fault; F5, Altyn Tagh Fault; F6, Longmenshan Fault. Figure 1. Open in new tabDownload slide Geological setting of the TP overlaying on topography (Modified from Gan et al.2007). The black dashed lines, black solid lines and white lines are bordering sutures, major active faults and national borders, respectively. Key to symbols: HB, Himalayan Block; LB, Lhasa Block; QTB, Qiangtang Block; KB, Kunlun Block; QDB, Qaidam Block; YGP, Yunnan-Guizhou Plateau; MBT, Main Boundary Thrust; IYS, Indus-Yarlung suture; BNS, Bangong-Nujiang suture; JS, Jinshajiang suture; AKMS, Anyimaqen-Kunlun-Mutztagh suture; F1, Jiali Fault; F2, Manyi Yushu Xianshuihe Fault; F3, Kunlun Fault; F4, Haiyuan Fault; F5, Altyn Tagh Fault; F6, Longmenshan Fault. Two major approaches are usually employed to invert subsurface density structure: seismic method and gravity method. Seismic method determines density structure through the empirical correlation formula between rock density and seismic velocity. Recent seismic studies focusing on density structure in the TP are primarily investigated by seismic reflection, receiver function and seismic tomography, such as Bourjot & Romanowicz (1992), Tilmann et al. (2003), Huang & Zhao (2006), Wang et al. (2007), Xu et al. (2007), Chen et al. (2010), Yao et al. (2010), Zhang et al. (2011), Obrebski et al. (2012), Huang et al. (2015) and Li et al. (2016). However, because of the limited number and coverage of seismic stations in the TP, especially in the centre and west due to the rugged topography (see Fig. 1), the lateral spatial resolutions of density structure provided by these publications need to be improved further. Currently, gravity data in the TP are accurate and homogeneous as the implementation of the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE). In addition, gravity reflects density distribution of the Earth interior directly. Hence, gravity method is suitable for studying density structure of the TP and can provide more details. Fang & Xu (1997) obtained a 3-D lithospheric density structure beneath the TP and its adjacent area from seismic materials and terrestrial gravity data using damped least-squares method. Bai et al. (2013) presented a 3-D crustal density structure beneath Himalaya and Lhasa blocks by forward modelling method using satellite and terrestrial gravity data. Yang et al. (2015) revealed 3-D density disturbances and channel flows of the TP using a generalized inversion technique based on satellite and terrestrial gravity data, providing some novel evidences for understanding the deep structure. Li et al. (2017) inverted the lithosphere density structure beneath the eastern margin of the TP from GOCE gradients through damped least-squares method. Yet, these studies have created differing 3-D density structures for the TP possibly due to their dissimilar assumptions and initial models, different approaches to inversion or use of various gravity databases. Therefore, in the present study, a novel wavelet-based gravity method is designed to invert multilayer densities beneath the TP for advancing the knowledge of tectonic structure and development, the correctness and effectiveness of which are validated by results derived from previous researches. Compared with aforementioned gravity inversion approaches, this method has the advantages of computation efficiency and local identification capability. To begin with, the complete Bouguer gravity anomalies of the TP are decomposed using wavelet multiscale analysis. Next, the corresponding mean source depths of the decomposed gravity anomalies are estimated by power spectrum analysis. Finally, according to the decomposed gravity anomalies and their corresponding source depths, the subsurface structure is layered and multilayer densities are inverted through Tikhonov regularization method. 2 GEOLOGICAL SETTING AND BOUGUER GRAVITY ANOMALY The history of the TP can trace back to 400–500 Ma in the Ordovician period. Approximately 240 Ma, northward extrusion of the Indian plate began to happen and caused uplift of the Kunlun Mountains and Hoh Xil area in the northern TP. After that, crustal rise and fall for parts of the TP constantly took place during the Himalayan movement period (Li 2011). In the Cretaceous time, thrust faulting, folding and crustal thickening occurred in the central plateau, and the southern and central plateau were elevated above sea level (Royden et al.2008). As the India–Eurasia collision continued into the Cenozoic period, the TP was further uplifted, shortened and thickened. Approximately 10 thousands of years ago, the TP was uplifted at the velocity of 7 centimeters per year and became ‘Roof of the World’ (Li 2011). Average elevation of the TP is 4–5 km. Its surface is principally formed by low mountains, hills and wide valley basins. Overall, the TP can be distinguished into northern high plateau, southern valley and eastern mountain-canyon region (see Fig. 1). Its terrain inclines gradually from 5 km in the north and west towards 4 km in the south and east. Moreover, the TP mainly consists of five nearly east-west stretching tectonic blocks, namely the HB, LB, QTB, KB and QDB from south to north, which are separated by four bordering sutures, namely the IYS, BNS, JS and AKMS, respectively. The major faults (F1–F6) are exactly located at the margin of these tectonic blocks. In this paper, WGM2012 Earth's gravity anomaly model is adopted, which is released by the Bureau Gravimétrique International (BGI) and can be downloaded from http://bgi.omp.obs-mip.fr/data-products/Grids-and-models/wgm2012 (Bonvalot et al.2012). This model provides the global complete Bouguer gravity anomalies on the geoid after terrain correction, plate correction, free-air correction and normal correction. Its effective spatial resolution is 5΄ by 5΄, which is helpful in revealing refined density structure of the Earth. Fig. 2 is the complete Bouguer gravity anomaly of the TP, extracted from WGM2012. The Bouguer gravity anomalies are low in the TP and high in the surrounding areas. The gravity high-low transfer zones exactly depict the outline of the TP. The negative anomalies of the TP indicate density deficits in the present region, which is in agreement with the isostatic model (Higher mountains correspond to lower densities) (Heiskanen & Moritz 1967). Overall, the gravity anomalies in the TP are divided into three regions: high-low alternating patterns in the north, nearly east-west trending folds in the west and nearly south–north trending folds in the east. These distributions are approximately perpendicular to surface movement directions derived from the GPS (see Fig. 2). In the west, surface movement direction is nearly south–north, while in the east the direction becomes nearly east–west. This phenomenon is consistent with the south–north crustal shortening and material eastward extrusion under the force of India–Eurasia convergence. Besides, the gravity anomalies in the TP are corresponding with the terrain (Fig. 1). Higher mountains in the west correspond to lower gravity anomalies and the basins, such as SB and TB, are located at gravity highs. In summary, high-resolution Bouguer gravity anomalies can provide rich knowledge of the major large-scale tectonic structure and development. To reveal refined subsurface density structure at different depths, the Bouguer gravity anomalies should be decomposed further. Figure 2. Open in new tabDownload slide Complete Bouguer gravity anomaly of the TP on the geoid. Blue vectors are the Global Positioning System (GPS) velocity field of crustal motion in the TP relative to the stable Eurasia. The major tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Key to symbols: TB, Tarim Basin; QB, Qaidam Basin; SB, Sichuan Basin. Figure 2. Open in new tabDownload slide Complete Bouguer gravity anomaly of the TP on the geoid. Blue vectors are the Global Positioning System (GPS) velocity field of crustal motion in the TP relative to the stable Eurasia. The major tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Key to symbols: TB, Tarim Basin; QB, Qaidam Basin; SB, Sichuan Basin. 3 METHOD Complete Bouguer gravity anomalies primarily reflect superposition of all anomalous bodies within the Earth interior. Consequently, they should be decomposed to determine anomalous densities at different depths in the crust and upper mantle. At present, separating methods for gravity data chiefly include trend analysis, high-order derivative, analytic continuation, running average, wavelet multiscale analysis, etc. In recent years, wavelet multiscale analysis, well capable of local identification in spatial and temporal domain, has been proved to be a powerful tool for separation of gravity anomaly and successfully applied to relevant geophysical interpretation (Fedi & Quarta 1998; Alp et al.2011; Xu et al.2015; Xu et al.2017a; Xu et al.2017b). In this study, the complete Bouguer gravity anomalies |$\Delta g(\varphi ,\lambda )$| on the geoid (spherical approximation is assumed and the undulation of the geoid is neglected in this paper) are decomposed into wavelet approximation |${A_S}(\varphi ,\lambda )$| and wavelet details |${D_s}(\varphi ,\lambda )$| using wavelet multiscale analysis (Mallat 1989; Xu et al.2017a): \begin{equation*} \Delta g(\varphi ,\lambda ) = {A_S}(\varphi ,\lambda ) + \sum\limits_{s = 1}^S {{D_s}} (\varphi ,\lambda ) \end{equation*} (1) where \begin{equation*} \left\{ \begin{array}{@{}l@{}} {A_S}(\varphi ,\lambda ) = \sum\limits_{k \in Z} {\sum\limits_{l \in Z} {{m_{S,k,l}}{\phi _{S,k}}(\varphi ){\phi _{S,l}}(\lambda )} } \\ {D_s}(\varphi ,\lambda ) = \sum\limits_{k \in Z} {\sum\limits_{l \in Z} {n_{s,k,l}^{HH}{\psi _{s,k}}(\varphi ){\psi _{s,l}}(\lambda )} } + \sum\limits_{k \in Z} {\sum\limits_{l \in Z} {n_{s,k,l}^{LH}{\psi _{s,k}}(\varphi ){\phi _{s,l}}(\lambda )} } + \\ \quad \quad \quad \quad \,\,\sum\limits_{k \in Z} {\sum\limits_{l \in Z} {n_{s,k,l}^{HL}{\phi _{s,k}}(\varphi ){\psi _{s,l}}(\lambda )} } \end{array} \right. \end{equation*} (2) in which |$(\varphi ,\lambda )$| is geodetic latitude and longitude on the geoid, |$\phi $| and |$\psi$| denote respective scaling function and wavelet function, |$m$| and |$n$| are coefficients and |$S$| is the decomposed maximum order. |${A_S}(\varphi ,\lambda )$| can be regarded as regional anomaly caused by deep and large-scale geological bodies, which is usually removed to study the structure of crust and upper mantle. |${D_s}(\varphi ,\lambda )$| is local anomaly derived from shallow and small-scale heterogeneous materials. To determine the density structure at different depths, the corresponding source depths of all decomposed gravity anomalies |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,S)$| must be estimated. According to the solution to 2-D Laplace's equation, each |${D_s}(\varphi ,\lambda )$| can be expressed as (Spector & Grant 1970; Syberg 1972; Cianciara & Marcak 1976) \begin{equation*} {D_s}(\varphi ,\lambda ) = \sum\limits_\varphi ^{} {\sum\limits_\lambda ^{} {{T_K}{e^{i2\pi ({K_\varphi }\varphi + {K_\lambda }\lambda )}}{e^{2\pi KH}}} }, \end{equation*} (3) where |${T_K}$| denotes the amplitude, |$K = \sqrt {{K_\varphi }^2 + {K_\lambda }^2}$| is the wave number and |$H$| is the elevation of |${D_s}(\varphi ,\lambda )$|⁠. Thus, |${T_K}$| can be determined by \begin{equation*} {T_K} = \sum\limits_\varphi ^{} {\sum\limits_\lambda ^{} {{D_s}(\varphi ,\lambda ){e^{ - i2\pi ({K_\varphi }\varphi + {K_\lambda }\lambda )}}{e^{ \pm 2\pi KH}}} }. \end{equation*} (4) When |$H = 0$|⁠, eq. (4) is written as \begin{equation*} {({T_K})_0} = \sum\limits_\varphi ^{} {\sum\limits_\lambda ^{} {{D_s}(\varphi ,\lambda ){e^{ - i2\pi ({K_\varphi }\varphi + {K_\lambda }\lambda )}}} }. \end{equation*} (5) Inserting eq. (5) into eq. (4), |${T_K}$| is rewritten as \begin{equation*} {T_K} = {({T_K})_0}{e^{ \pm 2\pi KH}}. \end{equation*} (6) Hence, \begin{equation*} {P_K} = {({P_K})_0}{e^{ \pm 4\pi KH}} \end{equation*} (7) where |${P_K} = {({T_K})^2}$| is the power. Then, \begin{equation*} \ln {P_K} = \ln {({P_K})_0} \pm 4\pi KH \end{equation*} (8) in which |$\ln {P_K}$| is natural logarithm of |${P_K}$|⁠. Based on the linear correlation between |$K$| and |$\ln {P_K}$| in eq. (8), the corresponding average source depth |${h_s}$| of |${D_s}(\varphi ,\lambda )$| relative to the geoid can be estimated exactly \begin{equation*} {h_s} = \frac{{\Delta \ln {P_K}}}{{4\pi \Delta K}}, \end{equation*} (9) where |$\Delta \ln {P_K}$| and |$\Delta K$| are rates of change for |$\ln {P_K}$| and |$K$|⁠, respectively. In this manner, the corresponding average source depths |${h_s}\,\,(s = 1,2, \cdots ,S)$| of all decomposed gravity anomalies |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,S)$| can be obtained. After that, the crust and upper mantle can be divided into |$S$| spherical layers according to |${h_s}\,\,(s = 1,2, \cdots ,S)$|⁠. The thickness of the |$sth$| layer (spherical shell) is |$\Delta {r_s}$|⁠. Then, each layer is gridded at |$\Delta \varphi$| and |$\Delta \lambda$| intervals along |$\varphi$| and |$\lambda$| using spherical tesseroids (the notion was introduced by Anderson (1976) and Heck & Seitz (2007)). Based on the Newtonian gravitational law, the relation between |${D_s}(\varphi ,\lambda )$| on the geoid and anomalous densities |$\Delta {\rho _s}({\varphi _0},{\lambda _0})$| of the tesseroids in the |$s\mathrm{ th}$| layer can be expressed as (Heck & Seitz 2007): \begin{equation*} {D_s}(\varphi ,\lambda ) = \sum\limits_{{\varphi _0}}^{} {\sum\limits_{{\lambda _0}}^{} {G\Delta {\rho _s}({\varphi _0},{\lambda _0})\Delta {r_s}\Delta \varphi \Delta \lambda \left[ {{L_{000}} + \frac{1}{{24}}({L_{200}}\Delta {r^2} + {L_{020}}\Delta {\varphi ^2} + {L_{002}}\Delta {\lambda ^2}} \right]} } \end{equation*} (10) where |$G$| is the gravitational constant, |$({\varphi _0},{\lambda _0})$| is the centre geodetic latitude and longitude of the tesseroids, and |${L_{000}}$|⁠, |${L_{200}}$|⁠, |${L_{020}}$| and |${L_{002}}$| are respectively: \begin{equation*} {L_{000}} = \frac{{r_0^2(R - {r_0}\cos {\psi _0})\cos {\varphi _0}}}{{l_0^3}} \end{equation*} (11) \begin{equation*} \begin{array}{@{}l@{}} {L_{200}} = \frac{{R\cos {\varphi _0}}}{{l_0^3}}\{ 2 - \frac{{3{r_0}}}{{l_0^2}}\left[ {5{r_0} - (2R + 3{r_0}\cos {\psi _0})\cos {\psi _0}} \right]\\ \quad \quad \quad + \frac{{15r_0^3}}{{l_0^4}}{\sin ^2}{\psi _0}({r_0} - R\cos {\psi _0}) \end{array} \end{equation*} (12) \begin{equation*} \begin{array}{@{}l@{}} {L_{020}} = {\left( {\frac{{{r_0}}}{{{l_0}}}} \right)^3}\cos \varphi (1 - 2{\sin ^2}{\varphi _0})\cos \delta \lambda + \frac{{{r_0}^2}}{{{l_0}^5}}\{ - R({R^2} + {r_0}^2)\cos {\varphi _0}\\ \quad \quad \quad + {r_0}\sin \varphi [ - R{r_0}(\sin \varphi \cos {\varphi _0} - \cos \varphi \sin {\varphi _0}\cos \delta \lambda ) + \\ \quad \quad \quad \sin {\varphi _0}\cos {\varphi _0}(2{R^2} + 4{r_0}^2 - 3R{r_0}\sin \varphi \sin {\varphi _0})] + \\ \quad \quad \quad {r_0}^2\cos \varphi \cos \delta \lambda (1 - 2{\sin ^2}{\varphi _0}) \times [{r_0} + R\cos \varphi \cos {\varphi _0}\cos \delta \lambda ]\\ \quad \quad \quad + R{r_0}^2\cos \varphi \sin {\varphi _0}\cos {\varphi _0}\cos \delta \lambda [3\sin \varphi \cos {\varphi _0} - 4\cos \varphi \sin {\varphi _0}\cos \delta \lambda ]\} \\ \quad \quad \quad + \frac{{5R{r_0}^3}}{{{l_0}^7}}\{ - R({R^2} + {r_0}^2)\sin {\varphi _0} + {r_0}^2\cos \varphi \sin {\varphi _0}\cos {\varphi _0}\cos \delta \lambda \times \\ \quad \quad \quad ({r_0} + R\cos \varphi \cos {\varphi _0}\cos \delta \lambda ) + {r_0}\sin \varphi [2{R^2} - {r_0}^2 - R{r_0}\cos {\psi _0} + {\sin ^2}{\varphi _0}\\ \quad \quad \quad \times ({R^2} + 2{r_0}^2 - R{r_0}\sin \varphi \sin {\varphi _0})]\} \times (\sin \varphi \cos {\varphi _0} - \cos \varphi \sin {\varphi _0}\cos \delta \lambda ) \end{array} \end{equation*} (13) \begin{equation*} \begin{array}{@{}l@{}} {L_{002}} = {\left( {\frac{{{r_0}}}{{{l_0}}}} \right)^3}\cos \varphi {\cos ^2}{\varphi _0} \times \{ \cos \delta \lambda - \frac{{3R}}{{{l_0}^2}}[2{r_0}\cos \varphi \cos {\varphi _0}{\sin ^2}\delta \lambda \\ \quad \quad \quad + (R - {r_0}\cos {\psi _0})\cos \delta \lambda ] + \frac{{15{R^2}{r_0}}}{{{l_0}^4}}\cos \varphi \cos {\varphi _0}(R - {r_0}\cos {\psi _0}){\sin ^2}\delta \lambda \}, \end{array} \end{equation*} (14) where |$R$| is the average radius of the Earth, |${r_0} = R - {h_s}$|⁠,|$\delta \lambda = {\lambda _0} - \lambda$|⁠, |${l_0} = \sqrt {{R^2} + r_0^2 - 2R{r_0}\cos {\psi _0}}$| and |$\cos {\psi _0} = \sin \varphi \sin {\varphi _0} + \cos \varphi \cos {\varphi _0}\cos \delta \lambda$|⁠. Further, eq. (10) can be written in matrix form: \begin{equation*} {{{\bf D}}_s} = {{\bf B\Delta }}{{{\boldsymbol \rho }}_s} \end{equation*} (15) where |${{\bf B}}$| is the matrix of the sensitive function between the density and gravity anomaly. Solving eq. (15) using Tikhonov regularization method, anomalous densities |${{\bf \Delta }}{{{\boldsymbol \rho }}_s}$| of the |$s\mathrm{ th}$| layer are (Tikhonov & Arsenin 1977) \begin{equation*} {\bf \Delta}{\boldsymbol \rho }_{s} = ({\bf B}^{\rm T}{\bf B} + \alpha {\bf I})^{ - 1}{\bf B}^{\rm T}{\bf D}_{s}, \end{equation*} (16) where |${{\bf I}}$| is identity matrix and |$\alpha$| denotes regularization parameter, which can be estimated by L-curve approach (Hansen & O'Leary 1993). Lastly, absolute densities |${{{\boldsymbol \rho }}_s}$| of the |$s\mathrm{ th}$| layer can be determined by \begin{equation*} {{{\boldsymbol \rho }}_s} = {{\bf \Delta }}{{{\boldsymbol \rho }}_s} + {{{\boldsymbol \rho }}_r}, \end{equation*} (17) where |${{{\boldsymbol \rho }}_r}$| is the corresponding reference mean density of the |$sth$| layer from apriori information, such as seismic results (Dziewonski & Anderson 1981; Laske et al.2013). In this way, multilayer densities |${{{\boldsymbol \rho }}_s}(s = 1,2, \cdots ,S)$| of study area can be achieved. According to above analysis, this method can absorb fully merits of the lateral resolution from homogeneous gravity data and the vertical identification capability from wavelet multiscale analysis. Therefore, it can give more details for the 3-D density structure of the Earth interior, which is very valuable for advancing the knowledge of tectonic structure and development. In addition, compared with the other approaches (e.g. Bai et al.2013; Li et al.2017), our method inverts the densities of each layer singly, which reduces density parameters, avoids complex computation and improves simultaneously the stability of solutions. In the following, multilayer densities of the TP are inverted by this approach. 4 RESULTS 4.1 Decomposed gravity anomalies In the first place, the complete Bouguer gravity anomalies |$\Delta g(\varphi ,\lambda )$| (see Fig. 2) in the TP are decomposed by eq. (1) with |$\psi = Coif3$| as the wavelet function referring to Xu et al. (2017a), though the differences by using various wavelet functions are very small and can be neglected. Decomposed gravity anomalies |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,S)$| are shown in Fig. 3. Subsequently, radially averaged logarithm power spectrum (see Fig. 4) of |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,S)$| is calculated using eq. (9) to determine their corresponding mean source depths. And the estimated mean depths |${h_s}\,\,(s = 1,2, \cdots ,S)$| are listed in Table 1. Mean source depth of the sixth-order wavelet detail is 130 km, which has reached the upper mantle. Hence, the decomposed maximum order |$S$| is fixed as 6 in the present study. Figure 3. Open in new tabDownload slide Decomposed gravity anomalies of the TP. (a)–(f) are the first- to sixth-order wavelet details. White circles represent distribution of earthquake epicentres with moment magnitudes larger than 5.0 in each layer, whose records are provided by the China Earthquake Data Center (CEDE). The major tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Figure 3. Open in new tabDownload slide Decomposed gravity anomalies of the TP. (a)–(f) are the first- to sixth-order wavelet details. White circles represent distribution of earthquake epicentres with moment magnitudes larger than 5.0 in each layer, whose records are provided by the China Earthquake Data Center (CEDE). The major tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Figure 4. Open in new tabDownload slide Radially averaged logarithm power spectrum of the decomposed gravity anomalies in the TP. (a)–(f) are the first- to sixth-order wavelet details consistent with subfigures (a)–(f) of Fig. 3. Red lines represent rates of change for logarithmic power relative to wave number. Figure 4. Open in new tabDownload slide Radially averaged logarithm power spectrum of the decomposed gravity anomalies in the TP. (a)–(f) are the first- to sixth-order wavelet details consistent with subfigures (a)–(f) of Fig. 3. Red lines represent rates of change for logarithmic power relative to wave number. Table 1. Estimated mean source depths of the decomposed gravity anomalies in the TP. Subfigures of Fig. 4 (a) (b) (c) (d) (e) (f) Mean source depth (km) 3 8 20 50 90 130 Subfigures of Fig. 4 (a) (b) (c) (d) (e) (f) Mean source depth (km) 3 8 20 50 90 130 Open in new tab Table 1. Estimated mean source depths of the decomposed gravity anomalies in the TP. Subfigures of Fig. 4 (a) (b) (c) (d) (e) (f) Mean source depth (km) 3 8 20 50 90 130 Subfigures of Fig. 4 (a) (b) (c) (d) (e) (f) Mean source depth (km) 3 8 20 50 90 130 Open in new tab The first- and second-order wavelet details (see Figs 3a and b) with respective mean source depths 3 and 8 km primarily reflect density distribution of the upper crust. The distribution of gravity anomalies at the margin of the TP and the major blocks is more dispersed than that in the centre. And the most dispersed gravity anomalies are located at the southeastern margin (25°N–32°N, 97°E–103°E). It demonstrates that the long-term India–Eurasia collision causes severe deformation of the upper crust at the boundary of the TP and the major blocks. It also induces a large number of earthquakes (see the white circles in Figs 3a and b). The mean source depths of the third- and fourth-order wavelet details (see Figs 3c and d) are respectively 20 and 50 km, which are corresponding with depths of the middle crust and lower crust. Positive–negative alternating gravity belts are apparent, the directions of which are nearly east–west in the western area and nearly south–north in the eastern area. They are almost perpendicular to the GPS velocity field of crustal motion. It indicates that mass movement pattern of the middle-lower crust may be revealed by the decomposed gravity anomalies. The basins (TB, QB and SB) are located at gravity highs, which can be observed obviously. The major faults (F1–F6) are consistent with gravity high-low alternating zones. In addition, the majority of earthquakes occurred in the middle crust. At the depths of 90 and 130 km respectively, corresponding to the fifth- and sixth-order wavelet details (see Figs 3e and f), gravity anomalies are smooth, which primarily reflect density distribution of the lower lithosphere. The lateral density inhomogeneity is attenuating. The major tectonic blocks and basins can be still identified clearly. Few earthquakes occurred in these layers. To sum up, the decomposed gravity anomalies (the first- to sixth-order wavelet details) are basically consistent with the tectonic features at different depths in the crust and upper mantle. It shows that the decomposed method (eq. 1) and depth estimation (eq. 9) are effective and their results can be employed to invert multilayer densities in the TP. 4.2 Multilayer densities from decomposed gravity anomalies Based on the decomposed gravity anomalies |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,6)$| (Fig. 3) and their corresponding mean source depths |${h_s}\,\,(s = 1,2, \cdots ,{\rm{6}})$| (Table 1), the crust and upper mantle of the TP are divided into |$S = 6$| layers (see Table 2). The thicknesses |$\Delta {r_s}(s = 1,2, \cdots ,6)$| of the six layers are 6, 4, 20, 40, 40 and 40 km, respectively. Their average depths are in agreement with |${h_s}\,\,(s = 1,2, \cdots ,{\rm{6}})$| (3, 8, 20, 50, 90 and 130 km) of |${D_s}(\varphi ,\lambda )\,\,(s = 1,2, \cdots ,6)$|⁠. Subsequently, each layer is gridded at |$\Delta \varphi = 0.{\rm{5}}^\circ$| and |$\Delta \lambda = 0.{\rm{5}}^\circ$| intervals along |$\varphi$| and |$\lambda$|⁠. Anomalous densities |${{\bf \Delta }}{{{\boldsymbol \rho }}_s}$| of each layer can be inverted using eq. (16). Lastly, multilayer densities |${{{\boldsymbol \rho }}_s}(s = 1,2, \cdots ,6)$| of the TP are determined by eq. (17). The reference mean densities |${{{\boldsymbol \rho }}_r}$| of the corresponding layers are listed in Table 2. According to the Preliminary Reference Earth Model (PREM; Dziewonski & Anderson 1981), densities from Moho depth to 220 km depth change slightly. Thus, |${{{\boldsymbol \rho }}_r}$| of Layer 4, Layer 5 and Layer 6 are all fixed to 3.36 g cm−3. Fig. 5 shows the inverted multilayer densities |${\rho _s}(s = 1,2, \cdots ,6)$| of the TP where the regularization parameters |$\alpha$| are 8 × 10−13, 8 × 10−13, 7 × 10−12, 3 × 10−10, 1 × 10−10 and 1 × 10−11, respectively. Figure 5. Open in new tabDownload slide Inverted multilayer densities of the TP. (a)–(f) are Layer 1 through Layer 6, whose mean depths are 3, 8, 20, 50, 90 and 130 km, respectively. Thick dashed lines are possible low-density channel flows. The main tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Figure 5. Open in new tabDownload slide Inverted multilayer densities of the TP. (a)–(f) are Layer 1 through Layer 6, whose mean depths are 3, 8, 20, 50, 90 and 130 km, respectively. Thick dashed lines are possible low-density channel flows. The main tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Table 2. Layered model of the crust and upper mantle in the TP. Number Depth range (km) Reference mean density (g cm−3) Layer 1 0–6 2.55 Layer 2 6–10 2.65 Layer 3 10–30 2.80 Layer 4 30–70 3.36 Layer 5 70–110 3.36 Layer 6 110–150 3.36 Number Depth range (km) Reference mean density (g cm−3) Layer 1 0–6 2.55 Layer 2 6–10 2.65 Layer 3 10–30 2.80 Layer 4 30–70 3.36 Layer 5 70–110 3.36 Layer 6 110–150 3.36 Reference mean density of each layer is derived from the PREM and the CRUST1.0 (Laske et al.2013). Open in new tab Table 2. Layered model of the crust and upper mantle in the TP. Number Depth range (km) Reference mean density (g cm−3) Layer 1 0–6 2.55 Layer 2 6–10 2.65 Layer 3 10–30 2.80 Layer 4 30–70 3.36 Layer 5 70–110 3.36 Layer 6 110–150 3.36 Number Depth range (km) Reference mean density (g cm−3) Layer 1 0–6 2.55 Layer 2 6–10 2.65 Layer 3 10–30 2.80 Layer 4 30–70 3.36 Layer 5 70–110 3.36 Layer 6 110–150 3.36 Reference mean density of each layer is derived from the PREM and the CRUST1.0 (Laske et al.2013). Open in new tab Densities of Layer 1 and Layer 2 (see Figs 5a and b) primarily reflect material distributions of 0–6 km depth and 6–10 km depth in the upper crust, respectively. Densities of these two layers range from 2.52 to 2.67 g cm−3, indicating strong lateral density inhomogeneity existing in the upper crust (Yang et al.2015). Fig. 5(c) presents the mean density distribution from 10 to 30 km depth, corresponding to the depth of the middle crust. The minimum and maximum densities are 2.72 and 2.86 g cm−3, respectively. Obvious high-low alternating patterns exist, whose directions are nearly east–west in the western TP and almost south–north in the east. Their boundary is approximately 95° E. The nearly east-west, high-low patterns in the LB and QTB can provide indirect evidence for crustal folding and shortening under south-north convergence between the India and Eurasia plates (Royden et al.2008; Shin et al.2015; Yang et al.2015; Xu et al.2017a). The nearly south–north, high-low patterns in the eastern TP indicate that materials are flowing eastwards (Royden et al.1997, 2008; Clark & Royden 2000; Li et al.2016). Due to the obstacle presented by the stable SB, materials further flow to the YGP (99° E–104° E, 25° N–30° N). Overall, the densities present almost a clockwise pattern, which is nearly perpendicular to surface movement direction from the GPS (Fig. 1). It shows that the inverted densities are well consistent with the regional tectonic movements. In addition, the basins (TB, QB and SB) are in agreement with density highs. The major faults are primarily located at high-low alternating zones. Depth range of Layer 4 (see Fig. 5(d)) is 30–70 km, which corresponds to Moho relief in the TP (Braitenberg et al. 2000a, Braitenberg et al. 2000a, 2000b; Shin et al.2007, 2009, 2015; Tenzer & Chen 2014; Guo et al.2015; Tenzer et al.2015; Eshagh et al.2016; Xu et al.2017a). Hence, densities of this layer primarily reflect the structure of the lower crust and upper mantle. Their range is 3.34–3.38 g cm−3. The correlation between density distribution and the major tectonic elements becomes stronger. The basins (TB, QB and SB) still correspond to density highs. The major faults are yet consistent with high-low alternating zones. The nearly east–west crustal fold structure in central LB and QTB can be inferred clearly from the east–west, high-low alternating density patterns. Similarly, the nearly south–north crustal fold structure in the eastern TP can be also identified through the nearly south-north, high-low alternating density patterns. Moreover, possible low-density channel flows can be observed in this layer (see the thick dashed lines in Fig. 5d). Low densities in the LB of the southern TP form a passageway, in which low-density materials flow from west to east under the long-term south–north India–Eurasia convergence (Royden et al.1997, 2008; Li et al.2016; Xu et al.2017a). Because of the obstacle of the high-density material in (99° E, 29° N) and (102° E, 28° N), the channel is divided into two channels, which has been also observed by Li et al. (2016) and Xu et al. (2017a) using seismic data and gravity data, respectively. In the northern TP, another possible low-density channel flow can be identified (see the thick dashed lines in Fig. 5(d)). Under the long-term south–north extruding force, low-density materials flow from (87° E, 36° N) to western TB and northern QB, respectively, which is consistent with the results provided by Xu et al. (2017a) derived from gravity data. Layer 5 (Fig. 5e) gives the mean density from 70 to 110 km depth, which corresponds to the depth of the upper mantle. Its range is 3.29–3.43 g cm−3. The major tectonic elements (blocks and basins) and low-density channel flows can be still identified from the density distribution. However, the fold is smoother than that of the lower crust (Fig. 5d). From 110 to 150 km depth, corresponding to the depth of the bottom of lithosphere, densities range from 3.17 to 3.52 g cm−3 (see Fig. 5f). The density in the TP, except that in central QTB and QB, is lower than that of surrounding area. The fold structure can no longer be observed at this layer. According to above analysis, the inverted multilayer densities of the TP can provide rich information for understanding tectonic structure and development. Possible low-density channel flows may occur from the middle crust (30 km depth) to the upper mantle (110 km depth) (see Figs 5d and e). Fold structure from 10 to 110 km depth is apparent in study area (see Figs 5c–e), the deformational direction of which is in good agreement with that of surface motion from the GPS. It demonstrates that the inverted method in the present study is correct and effective. 5 DISCUSSIONS To further validate our method, we compare the inverted multilayer densities with those provided by the CRUST1.0. The consolidated crystalline crust is divided into three layers in the CRUST1.0 (see Table 3). Lateral spatial resolution of each layer is 1° × 1°. Multilayer densities of the CRUST1.0 are shown in Fig. 6. Figure 6. Open in new tabDownload slide Multilayer densities from the CRUST1.0. (a)–(c) are Layer A to Layer C, whose mean depth ranges are 0.75–20.80, 20.80–36.21 and 36.21–47.74 km, respectively (see Table 3). The main tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Figure 6. Open in new tabDownload slide Multilayer densities from the CRUST1.0. (a)–(c) are Layer A to Layer C, whose mean depth ranges are 0.75–20.80, 20.80–36.21 and 36.21–47.74 km, respectively (see Table 3). The main tectonic elements (see Fig. 1) are overlain on the map for assistant analysis. Table 3. Layered model of the consolidated crystalline crust in the CRUST1.0. Number Mean depth range (km) Mean density (g cm−3) Layer A 0.75–20.80 2.80 Layer B 20.80–36.21 2.90 Layer C 36.21–47.74 3.36 Number Mean depth range (km) Mean density (g cm−3) Layer A 0.75–20.80 2.80 Layer B 20.80–36.21 2.90 Layer C 36.21–47.74 3.36 Open in new tab Table 3. Layered model of the consolidated crystalline crust in the CRUST1.0. Number Mean depth range (km) Mean density (g cm−3) Layer A 0.75–20.80 2.80 Layer B 20.80–36.21 2.90 Layer C 36.21–47.74 3.36 Number Mean depth range (km) Mean density (g cm−3) Layer A 0.75–20.80 2.80 Layer B 20.80–36.21 2.90 Layer C 36.21–47.74 3.36 Open in new tab Layer A presents the mean density distribution of the CRUST1.0 from 0.75 to 20.80 km depth (see Fig. 6a). The depth range of Layer A is consistent with Layer 1, Layer 2 and part of Layer 3 (see Figs 5a–c). It indicates that our results can give more knowledge of vertical density structure than what is available from the CRUST1.0. In Fig. 6(a), the basins (TB and SB) are located at density highs. Outline of the TP is depicted obviously by density lows. Large-scale spatial patterns of densities from the CRUST1.0 and this study are similar. Nevertheless, the lateral spatial resolution of our results in the central TP is higher than that of CRUST1.0, which implies that the homogeneous gravity data can provide more lateral details than the sparse seismic data in the TP. From 20.80 to 36.21 km depth, the spatial pattern of Layer B (Fig. 6b) is also in agreement with that of Layer 3 (Fig. 5c). Similarly, our results can reflect more tectonic structure. For example, the east–west crustal fold in the west and south–north fold in the east can be identified obviously in Fig. 5(c), while they cannot be observed in the CRUST1.0. In addition, QB corresponds to density high in Fig. 5(c), but it cannot be identified in Fig. 6(b). Fig. 6(c) shows the density structure from 36.21 to 47.74 km depth, which corresponds to part of Layer 4 (30–70 km depth) of this study exactly (Fig. 5d). In Fig. 6(c), the east–west high-low alternating pattern in the west and south–north high-low alternating pattern in the east can be observed vaguely, which can be identified clearly in Fig. 5(d). Besides, the basins (TB, QB and SB) are corresponding with density highs both in this study and the CRUST1.0. All these demonstrate that our results are consistent with those from the CRUST1.0. However, there are also some differences between these two models. For example, the CRUST1.0 presents density high in central LB, while this study gives density low. High-density material in (102° E, 28° N) can be observed in this study, but it is not obvious in the CRUST1.0. These differences need to be researched further in the future. According to above analysis, the spatial patterns of these two models can match each other basically, which verifies the correction and effectiveness of our method. The lateral and vertical spatial resolution of this study is higher than that of CRUST1.0, which can provide more details of density structures for advancing the knowledge of tectonic structure and development in the TP. 6 CONCLUSIONS In this paper, the decomposed gravity anomalies and their corresponding average source depths in the TP are calculated by wavelet multiscale analysis and power spectrum analysis, respectively. There are strong correlations between the decomposed gravity anomalies and the tectonic features at different depths in the crust and upper mantle. The first- and second-order wavelet details demonstrate that the deformation at the margin of blocks in the upper crust is severer than that in the centre. The third- and fourth-order wavelet details may reveal the material movement pattern in the middle-lower crust. The fifth- and sixth-order wavelet details reflect the attenuating lateral density inhomogeneity in the lower lithosphere. Moreover, six-layer densities of the TP with the lateral spatial resolution of 0.5° × 0.5° are inverted based on the decomposed gravity anomalies. The inverted multilayer densities provide a clear 3-D model to further insight into the tectonic structure and development. Densities of Layer 1 and Layer 2 imply strong lateral density inhomogeneity existing in the upper crust. From Layer 3 to Layer 5, fold structure and possible channel flows can be identified. Layer 6 gives smooth density distribution at the bottom of lithosphere. Our results are consistent with those from previous studies. It shows that the wavelet-based gravity method developed in the present study is correct and effective. It is worth nothing that although our method has only been used to determine density structure in the TP, it can be employed to investigate structures of the Earth interior all around the globe. ACKNOWLEDGEMENTS The authors would like to express their sincere thanks to the BGI for providing gravity data and the CEDE for supplying earthquake data. The figures were made using Generic Mapping Tools (GMT). This research is supported by the National Natural Science Foundation of China (Grant Nos. 41504015 and 41704012), the Open Research Fund Program of the State Key Laboratory of Geodesy and Earth's Dynamics (Grant Nos. SKLGED2018-1-3-E and SKLGED2018-1-2-E) and the China Postdoctoral Science Foundation (Grant Nos. 2015M572146, 2016M592337 and 2016M602301). REFERENCES Alp H. , Albora A.M. , Tur H. , 2011 . A view of tectonic structure and gravity anomalies of Hatay Region Southern Turkey using wavelet analysis , J. Appl. Geophys. , 75 , 498 – 505 . Google Scholar Crossref Search ADS WorldCat Anderson E.G. , 1976 . The effect of topography on solutions of Stokes' problem , Unisurv S-14, Rep, School of Surveying, University of New South Wales , Kensington . 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TI - Multilayer densities using a wavelet-based gravity method and their tectonic implications beneath the Tibetan Plateau JF - Geophysical Journal International DO - 10.1093/gji/ggy110 DA - 2018-06-01 UR - https://www.deepdyve.com/lp/oxford-university-press/multilayer-densities-using-a-wavelet-based-gravity-method-and-their-yvrH0uHdzW SP - 2085 VL - 213 IS - 3 DP - DeepDyve ER -