Moho Fold Structure Beneath the East China Sea and Its Tectonic Implications

Highlights

What are the main findings?

• According to the Moho fold structure, the South China Block has undergone vertical stress that has forced the mantle to subduct.
• The dominant force within the Ryukyu Arc is different in various regions. In the northeastern and central parts of the Ryukyu Arc, vertical subduction forces are dominant. In the southwestern part of the Ryukyu Arc, vertical subduction forces are in balance with another force associated with mantle upwelling.

What are the implications of the main findings?

• Combined with previous studies, it has been confirmed that the ancient subduction zone was situated roughly along the eastern coastline of the South China Block.
• The differing dynamical control mechanisms across distinct regions of the Ryukyu Arc have been revealed. In the northeast and central regions, the primary influence stems from the subduction system. In the southwest, the predominant effect arises from back-arc mantle activity impacting shallow tectonics.

Abstract

Moho fold structures provide critical insights into the tectonic evolution of the East China Sea. However, previous models exhibit substantial uncertainties, primarily resulting from the unaccounted gravitational effects of crustal sources and insufficient constraints on inversion parameters. In this study, we applied wavelet multi-scale analysis and the power spectrum method to remove crustal contributions, combined with an improved Bott’s method to achieve robust hyperparameter estimations. The Moho topographic model obtained through this method exhibits a significantly enhanced accuracy, with a root mean square deviation from seismic control points reduced by approximately 30% compared to other models. The resulting Moho fold structure reveals three key findings: (1) The South China Block has undergone vertical stress that forced the mantle to subduct. (2) In the northeastern and central parts of the Ryukyu Arc, vertical subduction forces are dominant. In the southwestern part of the Ryukyu Arc, vertical subduction forces are in balance with another force associated with mantle upwelling. (3) There is no interplate stress beneath the Okinawa Trough, and its crustal thinning may have been influenced by upwelling in the mantle.

1. Introduction

The East China Sea, located on the eastern side of the South China Block, is a typical marginal sea, surrounded by the Taiwan Island, the Korean Peninsula, the Ryukyu Islands and the Kyushu Islands. Geologically, it is located at the junction of the Philippine Sea plate and the Eurasian Plate. As a result of the subduction of the Philippine Sea plate, the East China Sea has formed a complete trench–arc–basin system, comprising such tectonic units as the continental shelf basin, the Okinawa Trough Basin, the Diaoyudao uplift Belt and the Ryukyu Island Arc. As an important window for the tectonic formation and evolution of the Western Pacific Marginal Sea, the East China Sea remains a focal point for tectonic research. Several scientific questions remain controversial in the region, e.g., where is the location of the subduction of the Palaeo-Pacific Plate to the Eurasian Plate [1,2]? What is the reason for the crustal thinning beneath the Okinawa Trough [3,4]? Addressing these issues requires a more precise characterization of deep crustal architecture, particularly an accurate Moho topography model and clearer delineation of Moho fold structures, which are critical for elucidating the deep-seated processes shaping the region. Previously, several scholars have used seismic profiles to investigate the deep structure of the East China Sea and adjacent regions, which include the Moho topography [5,6]. Based on multi-channel seismic reflection profiles, Arai et al. [3] revealed the crustal structure in the southern part of the Okinawa Trough and found that there is crustal thinning in the region. Similarly, Nishizawa et al. [6] analyzed 17 seismic lines distributed across the Okinawa Trough. The results showed that crustal thinning in the Okinawa Trough is different in the south and north. In particular, the Moho depth is near 25 km in the north and 13 km in the south. By analyzing the wide-angle reflection seismic profiles ECS2017 and ECS2019, Wei et al. [5] suggested that the thickness of the crust decreases gradually from the Zhe-Min uplift Belt to the continental shelf basin. Despite these valuable insights, the sparse distribution of seismic profiles limits the ability to comprehensively characterize the deep structure and tectonic deformation across the entire East China Sea.

Compared with seismic profiles, satellite gravity data—with its global coverage—offers distinct advantages for reconstructing regional Moho topography. Xuan et al. [7] used the Parker–Oldenburg method [8,9] (one of the classic frequency-domain algorithms) to obtain the Moho topography of the East China Sea and its surrounding areas. Using interfacial inversion with a variable density model, Chen et al. obtained the Moho depth of the Okinawa Trough [10]. Xue et al. reconstructed the Moho depth in China and its neighboring regions using Bott’s regularization method [11]. Nevertheless, these gravity-based models face two major limitations: potentially biased inversion parameters and the omission of intra-crustal gravity effects. Both factors can significantly compromise the accuracy of the derived Moho topography.

The Moho fold structure is defined as the deviation between the Moho topography and the isostatic model. This structural residual has been widely used as an indicator of regional tectonic deformation [12,13]. In addition to the Moho topographic model, an accurate isostatic model is required before obtaining the Moho fold structure. The computation of the isostatic model depends critically on parameters such as the average compensation depth and topographic density. In previous studies, these parameters were often assigned based on a priori information [7,14]. While this conventional approach is computationally straightforward, it lacks rigorous physical constraints, potentially compromising the reliability of the resulting isostatic model and the subsequent fold structure analysis.

To solve the problems mentioned above, this study employs a multi-faceted geophysical approach. First, wavelet multi-scale analysis and the radial power spectrum method are applied to separate the gravity anomalies at different depths and to deduct the gravity effects from the crust. Then, an improved Bott’s method is implemented, incorporating seismic profiles as constraints, to obtain more reliable inversion parameters and to derive an accurate Moho topography. Finally, using the Moho topography as a constraint, we iteratively searched for the optimal isostatic model and obtained the Moho fold structure. Based on these refined models, we further revealed the deep structure as well as the deformation characteristics of the East China Sea.

2. Study Area and Data

The study area of this paper is the East China Sea (latitude and longitude ranging from 118°E to 130°E and 21°N to 34°N), as shown in Figure 1. The East China Sea is located in the eastern part of the South China Block. It is bounded on its southwestern side by Taiwan Island and the South China Sea, on its northern side by the Yellow Sea, on its northwestern side by Japan and the Sea of Japan and on its southeastern side by the Philippine Sea (divided by the Ryukyu Arc and the Ryukyu Trench). As the junction of the Eurasian Plate and the Philippine Sea plate, tectonic activity is more active here. This has resulted in significant variations in seafloor topography and geomorphology in the region, ranging from the continental shelf in the west (near 200 m of water depth) to the Okinawa Trough in the east (over 1000 m of water depth). Of these, the continental shelf can be divided into three main areas, the Zhe-Min uplift Belt, the continental shelf basin and the Diaoyudao uplift Belt. Earthquakes with a magnitude greater than 5, totaling 658 over two decades (the period spans from 1 January 2005 to 1 January 2025, according to https://www.usgs.gov/programs/earthquake-hazards, accessed on 19 January 2026), are illustrated in Figure 1. In terms of distribution, the earthquakes are mainly located in the eastern part of Taiwan Island, the Okinawa Trough and the Ryukyu Arc. The Moho fold structure is induced by internal stresses, which also constitute one of the primary causes of major earthquakes. From the distribution of earthquakes, the Moho fold structure within the study area is notably pronounced and holds significant research value.

The main data used in this paper are free-air gravity anomalies, topography, sediment thickness and seismic control points. The free-air gravity anomaly is the XGM2019e_2159 model (http://icgem.gfz-potsdam.de/tom_longtime, accessed on 19 January 2026), as shown in Figure 2a. This is the global gravity field model published by Zingerle et al. [15] with a spatial resolution of 5′ × 5′, which has the advantage of a high spatial resolution, with comprehensive and well-integrated data sources. In Figure 2a, the free-air gravity anomalies in the study area range from −231.2 to 385.4 mGal. Among them, the positive gravity anomalies are mainly distributed on Taiwan Island and the negative gravity anomalies are mainly distributed near the Ryukyu Trench. The free-air gravity anomalies in the East China Sea range from 0 to 160 mGal, and the overall variation is not drastic.

The topographic data are from the ETOPO1 model (https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO1/data/, accessed on 19 January 2026), as shown in Figure 1. This is a global topographic model published by the National Oceanic and Atmospheric Administration, with a spatial resolution of 1′ × 1′ [16]. Based on the ETOPO1 model and assuming that the corrected density is constant (2.67 g/cm³ for land and 2.67–1.03 g/cm³ for ocean, which is the correction standard of the International Centre for Global Earth Models), the corrected Bouguer gravity anomaly is obtained as shown in Figure 2b. In Figure 2b, the Bouguer gravity anomalies in the study area range from −88.3 to 467.1 mGal. Among them, the negative gravity anomalies are mainly distributed in the South China Block and Taiwan Island, with values generally ranging from −80 to 0 mGal. The positive gravity anomalies are mainly distributed in the Philippine Sea, with values greater than 320 mGal. In terms of distribution, the Okinawa Trough, Ryukyu Arc and Ryukyu Trench are the middle zone of positive and negative gravity anomalies. The gravity anomalies in this region range from 0 to 240 mGal with significant numerical variations. The Bouguer gravity anomaly is a signal of internal structure, and differences in internal structure (sedimentary layers, crust, Moho topography, etc.) can cause “jumps” in the Bouguer gravity anomaly. From this point of view, the eastern coastal region of the South China Block, the southeastern part of Taiwan Island, the Okinawa Trough, the Ryukyu Arc and the Ryukyu Trench are all areas of intense internal tectonic movement.

In order to extract deeper gravity anomalies, the effect from sediments needs to be deducted here. The sedimentary layer model used in this paper is the Globsed-v3 model, as shown in Figure 3a [17]. In Figure 3a, the sediments are mainly distributed in the East China Sea and the South China Sea. Among them, the continental shelf basin has the thickest sediments, with a depth of nearly 10.5 km. Based on Xuan et al. [7], the density of the sediment layer here is assumed to be 2.54 g/cm³. With this, we used Parker’s method to forward the gravity effect from the sediments [8], as shown in Figure 3b. In Figure 3b, the lowest gravity effect is −49 mGal. Numerically, gravity effects (from sediments) are very small in most areas, generally within 10 mGal, except in some sedimentary basins. On the basis of the Bouguer gravity anomaly (Figure 2b), we subtracted the gravity effect from the sediments to obtain the gravity anomaly without sediments, as shown in Figure 3c.

3. Methods

There are four main methods in this paper, including wavelet multi-scale analysis, the radial power spectrum method, the improved Bott’s method and the iterative method for Moho fold structure. The computational flow of the Moho fold structure is shown in Figure 4. Figure 4 is divided into four main sections: data preprocessing, signal extraction, Moho topographic inversion and calculation of the Moho fold structure.

3.1. Wavelet Multi-Scale Analysis

Gravity anomalies are a combination of signals from topography, sediments, crust, Moho topography and deeper structures. Currently, based on the publicly available topographic model and sedimentary layer model, the corresponding gravity effects can be obtained by forward modeling, whereas gravity effects from the crust cannot be obtained by forward modeling due to the lack of a reliable crustal model. In order to invert a more rigorous Moho topographic model, gravity effects from the crust need to be subtracted. Previously, Mallat [18] proposed the classical algorithm for signal separation, i.e., wavelet multi-scale analysis. And later the method was applied to the processing of field data such as gravity and magnetic data several times [19,20]. Wavelet multi-scale analysis decomposes the original function into projections in different spaces, which contain the high-frequency signal $D_m\left(\phi ,\lambda \right)$ and the low-frequency signal $C_m\left(\phi ,\lambda \right)$, as shown in Equation (1). According to the potential field theory, signals from different frequency bands originate from materials at varying depths. High-frequency signals primarily originate from shallow materials, whilst low-frequency signals primarily originate from deep materials.

$$g_s\left(\phi ,\lambda \right)=C_M\left(\phi ,\lambda \right)+{\displaystyle \sum _{m=1}^M{D}_m\left(\phi ,\lambda \right)}$$

(1)

where $g_s\left(\phi ,\lambda \right)$ is the sediment-free gravity anomaly (obtained by subtracting the gravity effect corresponding to sediment from the Bouguer gravity anomaly). $\phi$ and $\lambda$ are the longitude and latitude, respectively. $M$ is the decomposition order, which is taken as 8 in this paper [21].

3.2. Radial Power Spectrum Method

After separating the high-frequency signals $D_m\left(\phi ,\lambda \right)$ of different orders, it is necessary to determine their corresponding depths in order to deduct the crustal signals. Based on the proposed radial power spectrum method [22,23,24,25], the relationship between $D_m\left(\phi ,\lambda \right)$ and its corresponding depth $H$ can be constructed, as shown in Equation (2).

$$D_m\left(\phi ,\lambda \right)={\displaystyle \sum _{\phi }{\displaystyle \sum _{\lambda }{A}_k{e}^{i2\pi \left(k_{\phi }\phi +k_{\lambda }\lambda \right)}}}{e}^{2\pi kH}$$

(2)

where $A_k$ is the amplitude, and the wave number $k=\sqrt{k_{\phi }^2+k_{\lambda }^2}$. From Equation (2), the following can be derived:

$$A_k={\displaystyle \sum _{\phi }{\displaystyle \sum _{\lambda }{D}_m\left(\phi ,\lambda \right)e^{-i2\pi \left(k_{\phi }\phi +k_{\lambda }\lambda \right)}}}{e}^{-2\pi kH}$$

(3)

Substituting $H=0$ into Equation (3), we obtain

$${\left(A_k\right)}_0={\displaystyle \sum _{\phi }{\displaystyle \sum _{\lambda }{D}_m\left(\phi ,\lambda \right)e^{-i2\pi \left(k_{\phi }\phi +k_{\lambda }\lambda \right)}}}$$

(4)

Based on Equation (4), Equation (3) can be changed to

$$A_k={\left(A_k\right)}_0{e}^{\pm 2\pi kH}$$

(5)

Squaring both sides of the equation together, we obtain

$$P=P_0{e}^{4\pi kH}$$

(6)

where $P$ is the power. Taking logarithms on both sides of the equation, we obtain

$$\ln P=\ln P_0+4\pi kH$$

(7)

From Equation (7), it can be deduced that

$$H={\displaystyle \frac{\mathsf{\Delta }\ln P}{4\pi \mathsf{\Delta }k}}$$

(8)

Based on Equation (8), we are able to determine the average field source depth $H$ corresponding to high-frequency signals at different orders. Based on a priori models, such as CRUST 1.0, GEMMA, etc., it is possible to determine which orders are from the crust [26]. That is to say, the role of the prior models here is to provide a reference depth, with approximations below this reference depth being treated as crustal signals. By comparing this with the depth model derived from the power spectrum, signals originating from the crust can then be subtracted. According to Equation (1), these high-frequency signals can be stripped from the sediment-free gravity anomalies, which in turn yields gravity anomalies $g_0^{obs}$ from the Moho topography.

3.3. Improved Bott’s Method

After obtaining the gravity anomalies from the Moho topography, the next thing that needs to be determined is the inversion parameters, i.e., the average Moho depth and the Moho density contrast. Within the surveying field, it is recognized that the measurement of data itself inherently carries a systematic bias. However, traditional linear regression methods fail to account for the impact of this systematic bias. Li et al. [27] proposed an improved Bott’s method. The core of this method lies in introducing two systemic biases, $\mathsf{\Delta }\rho =\tilde{\rho }-\widehat{\rho }$ ($\tilde{\rho }$ is the true Moho density contrast and $\widehat{\rho }$ is the estimated Moho density contrast) and $\mathsf{\Delta }m=\tilde{m}-\widehat{m}$ ($\tilde{m}$ is the true Moho topography and $\widehat{m}$ is the estimated Moho topography). Furthermore, by subtracting the impact of systematic biases on the inversion process, unbiased estimation is achieved. Firstly, based on the gravity anomaly $g_{cp}^{obs}$ at the seismic control point and the Moho topography ${\tilde{m}}_{cp}$ at the seismic control point (here, the data at the seismic point is used as the true value for constraining the estimation of the inversion parameters), a linear equation for the two can be obtained, as shown in Equation (9).

$${\tilde{m}}_{cp}=g_{cp}^{obs}\cdot slop+{\mathrm{z}}_0$$

(9)

where $slop$ is the linear slope. Based on Equation (9), the intercept of the linear regression line is the average Moho depth ${\mathrm{z}}_0$. Next, the initial model ${\widehat{m}}_0$ is constructed, as shown in Equation (10).

$${\widehat{m}}_0=g_0^{obs}\cdot slop+{\mathrm{z}}_0$$

(10)

By forwarding the gravity anomaly $g_0^{obs}$ corresponding to ${\widehat{m}}_0$, it follows that

$${\widehat{\rho }}_0\cdot F({\widehat{m}}_0,1)=g_0^{obs}$$

(11)

where $F\left({\widehat{m}}_0,1\right)$ is the gravity anomaly relative to ${\widehat{m}}_0$ at unit density. The parameters used in Equation (11) are the estimated Moho density contrast and Moho topography. If it is realistic that there is no bias, then Equation (11) can be rewritten as

$${\tilde{\rho }}_0\cdot F({\tilde{m}}_0,1)=g_0^{obs}$$

(12)

The equation can be transformed into

$$\mathsf{\Delta }{\rho }_0\cdot F({\tilde{m}}_0,1)+{\widehat{\rho }}_0\cdot F({\tilde{m}}_0,1)=g_0^{obs}$$

(13)

Solving $F({\tilde{m}}_0,1)$ linearly using Taylor expansion (retaining up to first-order derivatives) gives the following:

$$F({\tilde{m}}_0,1)\approx F({\widehat{m}}_0,1)+{\displaystyle \frac{\partial F(m,1)}{\partial m}}\cdot \mathsf{\Delta }m$$

(14)

where ${\displaystyle \frac{\partial F(m,1)}{\partial m}}=-2\pi G$ ($G$ is Newton’s gravitational constant). Substituting Equation (14) into Equation (13) yields

$${\widehat{\rho }}_0\cdot F({\widehat{m}}_0,1)-2\pi G\cdot \mathsf{\Delta }m\cdot {\widehat{\rho }}_0+\mathsf{\Delta }\rho \cdot F({\tilde{m}}_0,1)=g_0^{obs}$$

(15)

Here, replacing the variables in Equation (15) with seismic control points then gives

$${\widehat{\rho }}_0\cdot F({\widehat{m}}_{cp},1)-2\pi G\cdot ({\tilde{m}}_{cp}-{\widehat{m}}_{cp})\cdot {\widehat{\rho }}_0+\mathsf{\Delta }\rho \cdot F({\tilde{m}}_{cp},1)=g_{cp}^{obs}$$

(16)

Substituting $F\left({\tilde{m}}_{cp},1\right)=g_{cp}^{obs}/{\tilde{\rho }}_0$ into Equation (16) gives

$$-{\widehat{\rho }}_0\cdot g_{cp}^{obs}={\tilde{\rho }}_0\cdot \mathsf{\Delta }{g}_{cp}(\widehat{m},{\widehat{\rho }}_0)$$

(17)

where

$$\mathsf{\Delta }{g}_{cp}(\widehat{m},{\widehat{\rho }}_0)=-{\widehat{\rho }}_0\cdot F({\widehat{m}}_{cp},1)+2\pi G\cdot ({\tilde{m}}_{cp}-{\widehat{m}}_{cp})$$

(18)

Here, the robust linear regression method is used to solve Equation (17) [28]. The values of $-{\widehat{\rho }}_0\cdot g_{cp}^{obs}$ and $\mathsf{\Delta }{g}_{cp}\left(\widehat{m},{\widehat{\rho }}_0\right)$ in Equation (17) can be calculated. Based on this, robust linear regression is employed to compute the true Moho density contrast ${\tilde{\rho }}_0$. Based on the method proposed by Bott [27,29,30], the initial model $m^0$ of the Moho topography can be expressed as

$$m^0={\displaystyle \frac{g_0^{obs}}{-2\pi G{\tilde{\rho }}_0}}+{\mathrm{z}}_0$$

(19)

In order to reduce the discrepancy between the predicted and observed gravity values, an iterative formula is used here:

$$m^k=m^{k-1}+{\displaystyle \frac{g_0^{obs}-F(m^{k-1},{\tilde{\rho }}_0)}{-2\pi G{\tilde{\rho }}_0}}$$

(20)

Adding the fitted parameters and the regularization term to Equation (20), we obtain

$$m^k=m^{k-1}+{\displaystyle \frac{g_0^{obs}-F(m^{k-1},{\tilde{\rho }}_0)-\lambda D(m^{k-1})}{s^{k-1}}}$$

(21)

where $D$ is the second order Laplace operator ($D$ is the core operator of the regularization term, whose function is to constrain the spatial continuity and smoothness of the Moho topography), and $\lambda$ is the regularization parameter. $s^k$ is the positive real value (where $s^0=-2\pi G{\tilde{\rho }}_0$) calculated as follows:

$$s^k=\left\{\begin{array}{c}\begin{array}{cc}{s}^{k-1}\cdot r_1,& {\tau }_2^{k-1}<{\tau }_2^{k-2}\end{array}\\ \begin{array}{cc}{\displaystyle \frac{s^{k-1}}{r_1\cdot r_2}}& {\tau }_2^{k-1}\ge {\tau }_2^{k-2}\end{array}\end{array}\right.$$

(22)

where ${\tau }_2^{k-1}$ and ${\tau }_2^{k-2}$ represent the 2-norm of the residual gravity for the $k$-first iteration and the $k$-second iteration, respectively. Both $r_1$ and $r_2$ are fitting parameters, taking values in the range $(0,1]$ (the final values of $r_1$ and $r_2$ must satisfy the following: gravitational residuals must decrease continuously throughout the iteration process, whilst maintaining reasonable spatial continuity of the Moho topography; following testing, we have determined that $r_1$ is 0.9 and $r_2$ is 0.1). After $k$ iterations, the Moho topography $m^k$ can be calculated.

3.4. An Iterative Method for Moho Fold Structure

The isostatic model is the Moho depth in isostatic state, free from external disturbances. Here, we adopted the Airy isostatic theory to obtain the isostatic model $m_I$, as shown in Equation (23).

$$m_I=H_c-{\displaystyle \frac{{\rho }_t}{\tilde{\rho }}}h$$

(23)

where $h$ is the topographic load, taken as the terrain height. $H_c$ and ${\rho }_t$ are the average compensation depth and terrain density, respectively. Gao et al. [14] suggested that the Moho topography and isostatic model are consistent in the absence of vertical stress effects. Here, it is assumed that the difference between $m_I$ and $m^k$ is minimized. That is, based on different $H_c$ and ${\rho }_t$, we computed various isostatic models. By comparing $m^k$, we obtained its corresponding root mean square error, selecting $m_I$ where the root mean square error is minimal. Based on this, the Moho fold structure $m_F$ can be calculated, as shown in Equation (24).

$$m_F=m^k-m_I$$

(24)

4. Results

4.1. The Airy Isostatic Model

Based on the sediment-free gravity anomaly, the next step to be calculated is the gravity anomaly from the Moho topography, which requires the deduction of gravity effects from the crust. Here, the wavelet basis we adopt is “coif3” [20]. We used Equation (1) to separate the wavelet details at the first eight orders, as shown in Figure 5, where Figure 5a–h represent the 1st to 8th order wavelet details, respectively. Wavelet details at different orders are located in different frequency bands. According to field theory, wavelet details at different orders are mainly caused by structures at different depths. In Figure 5, the gravity anomalies of the first- and second-order wavelet details range from −4 to 4 mGal. From Figure 5c, the signal is mainly distributed in the Philippine Sea, which may be from the remaining sediments. The signals in Figure 5d–h are mainly distributed in the Okinawa Trough, Ryukyu Arc and Ryukyu Trench. This confirms that, compared to other neighboring regions, their structural heterogeneity is markedly pronounced. This structural heterogeneity comes from the crust, the Moho topography and the mantle, and is generally higher than 50 mGal, which has a large impact on the inversion of the Moho topography.

Figure 5 shows that there is some horizontal variability in the structure at different depths, and the next thing that needs to be determined is the average field source depth corresponding to the wavelet details at different orders. We plotted the radially averaged logarithm power spectrum, as shown by the blue line in Figure 6. Based on Equation (8), the slope of blue line (red line in Figure 6), which is the average field source depth, can be calculated.

Table 1. The layered model in ECS.

Layer	Average Depth (km)	Range of Depth (km)
D1	0.42	0.0~0.84
D2	2.18	0.84~3.52
D3	4.93	3.52~6.34
D4	8.22	6.34~10.1
D5	15.84	10.1~21.58
D6	28.88	21.58~36.18
D7	45.72	36.18~55.26
D8	70.08	55.26~84.9

lists the corresponding average field source depths from D1 to D8, which are 0.42 km, 2.18 km, 4.93 km, 8.22 km, 15.84 km, 28.88 km, 45.72 km and 70.08 km, respectively. Based on this, we classified the subsurface structure of the study area into eight layers, and the depth ranges of layers 1 to 8 were 0~0.84 km, 0.84~3.52 km, 3.52~6.34 km, 6.34~10.1 km, 10.1~21.58 km, 21.58~36.18 km, 36.18~55.26 km and 55.26~84.9 km, respectively (first, we determined the depth range for the first layer; the upper bound of the first layer is the ground level at 0 km, with an average depth of 0.42 km, yielding a lower bound of 0.84 km; the lower bound of the first layer serves as the upper bound of the second layer, and so on, thereby determining the depth ranges for all layers). Based on Equation (1), the remaining signal (eighth order wavelet approximation) is mainly from structures at depths greater than 84.9 km.

Previously, Xuan et al. [7] had used the CRUST 1.0 model as a constraint to calculate a regional average Moho depth of 23.5 km. The CRUST 1.0 model also shows that the average Moho depth in this region is 25.7 km. Based on the depth range in Table 1, it can be judged that D1 to D5 are signals from the crust. Therefore, we deducted these signals and retained their residual signals (fifth-order wavelet approximation), regarding their residual signals as gravity anomalies from the Moho topography, as shown in Figure 7.

In Figure 7, the gravity anomalies in the study area range from −78.8 to 421.9 mGal. Among them, the gravity anomalies of the South China Block and Taiwan Island are the lowest, and most of the area is below 0 mGal. The Philippine Sea has the highest gravity anomaly, which is around 400 mGal in most areas. In addition, the gravity anomaly of the Okinawa Trough, a typical back-arc basin, is elevated compared to other areas in the East China Sea, ranging from 160 to 240 mGal. Since this is a gravity anomaly from Moho topography, the difference is most directly due to crustal thickness. The high gravity anomaly in Figure 7 corresponds to a thinner crust and the low gravity anomaly corresponds to a thicker crust.

4.2. The Moho Topography of ECS

After obtaining the gravity anomalies from Moho topography, what needs to be determined are the inversion parameters, i.e., the average Moho depth and Moho density contrast. Here, using seismic profiles and receiver function data as seismic constraints [5,31], we used Equation (9) to construct a linear regression between the gravity anomalies and the Moho topography, as shown in Figure 8a. In Figure 8a, the average Moho depth can be obtained from the intercept of the regression line, which is 22.74 km. Next, we used Equation (17) to construct a linear regression between $\mathsf{\Delta }{g}_{cp}\left(\widehat{m},\widehat{\rho }\right)$ and $-\widehat{\rho }\cdot g_{cp}^{obs}$, as shown in Figure 8b. In Figure 8b, the Moho density contrast can be obtained from the slope of regression line, which is 0.483 g/cm³. Previously, Xuan et al. [7] calculated the average Moho depth and Moho density contrast in the region to be 25.7 km and 0.55 g/cm³, respectively. This indicates that our results are close to Xuan et al. [7] in terms of inversion parameters. There are two differences: Firstly, the seismic data used for constraints are different; we used seismic profiles and receiver function data from the past few years, while Xuan et al. [7] used the CRUST 1.0 model. Secondly, the systematic bias is introduced in the method we used, which reduces the effect of the nonlinear term to some extent.

Based on Equation (21), we iteratively calculated the Moho topography of the study area, as shown in Figure 9. The Moho depth in the study area ranges from 9.2 to 33.4 km. Among them, in the East China Sea, the Moho topography shows distribution characteristics of a deep northwest and shallow southeast. The northwestern part of the East China Sea is mainly a continental shelf, including the Zhe-Min uplift Belt, the continental shelf basin and the Diaoyudao uplift Belt. The Moho depth in these areas ranges from 27 to 30 km. In terms of depth, this is a typical continental crust. On the western side of the East China Sea, the Moho depth of the South China Block is around 32 km. The difference in Moho depth between the East China Sea and the South China Block is a few kilometers, which suggests that the plates here have been, or are at present, subject to forces such as extrusion and subduction. Hilde et al. [1] proposed the existence of Mesozoic subduction in the eastern part of the South China Block. Regarding the location of the paleo-subduction zone, Niu et al. [2] suggested that the subduction spread roughly along the southeastern coastline of China. From the Moho topography, it is indeed possible that the southeastern coastline of China is the location of the paleo-subduction zone.

On the southeastern side of the East China Sea, i.e., the Okinawa Trough, Ryukyu Arc and Philippine Sea, the Moho topography shows a shallow–deep–shallow distribution. As a subducting plate, the Moho topography of the Philippine Sea is the shallowest, basically between 9 and 12 km. As a result of the subducting plate, the crust of the Ryukyu Arc is significantly thickened, and its Moho depth is between 25 and 30 km. The special point is that this thickening is not uniform. In the southwestern part of the Ryukyu Arc (near Taiwan Island), the Moho topography is shallow, with a depth of about 25 km. In the northeastern part of the Ryukyu Arc, the Moho topography is deeper, with a depth of about 30 km. Based on ocean bottom seismometer data, Arai et al. revealed that, in the southwestern part of the Ryukyu Arc and the subducting plate (Philippine Sea), the Moho depths are 25 and 10 km, respectively, which is in better agreement with Figure 9 [4]. As a back-arc basin, the Moho depth of the Okinawa Trough ranges from 18 to 25 km. Compared with the continental shelf on its northwestern side and the Ryukyu Arc on its southeastern side, the crustal thickness of the Okinawa Trough is reduced by about 5 km. Both Arai et al. [3] and Nishizawa et al. [6] detected the presence of back-arc uplift beneath the Okinawa Trough. While it is still not possible to determine here whether this uplift is active or passive, what can be determined is that the uplift leads to crustal thinning. In addition, there are differences in Moho depths in the north–south direction of the Okinawa Trough. Among them, the Moho topography in the north is deeper than that in the south, at around 25 km. This is in good agreement with the results of Nishizawa et al. [6].

To verify the reliability of the Moho topography in this paper, we chose two other models for comparison, the Moho model from Xuan et al. [7] and the CRUST 1.0 model, as shown in Figure 10. Figure 10a shows that the Moho depth of the study area ranges from 10.8 to 36.9 km. The distribution of deep Moho topography regions (South China Block, Taiwan Island and Ryukyu Arc) and shallow Moho topography regions (Philippine Sea) are similar compared to the model in this paper. There are two differences: One is that the Moho model from Xuan et al. [7] is too smooth, which is due to the low-pass filtering in the algorithm. The other is that the Moho topography of this model is overall 2–3 km deeper than the model in this paper, which is due to the difference in inversion parameters.

In order to show the differences in the three Moho models more intuitively, we compared the three Moho models with the seismic points [4,5,10,31,32], and the results are shown in

Table 2. Comparison of different Moho topography models and seismic Moho depths.

Moho Models	Compare Objects	95% Confidence Interval (km)	STD (km)	RMS (km)
CRUST 1.0	All seismic points	[−9.71, 8.27]	4.45	4.62
Xuan et al. [7]		[−0.77, 11.83]	3.49	6.59
This paper		[−5.22, 6.95]	3.21	3.26

. Additionally, we have plotted the error distributions for these three Moho models, as shown in Figure 11. Table 2 shows that the 95% confidence interval of error between the CRUST 1.0 model and seismic points is [−9.71, 8.27] km. The 95% confidence interval of error between the model of Xuan et al. [7] and seismic points is [−0.77, 11.83] km. The 95% confidence interval of error between the model in this paper and seismic points is [−5.22, 6.95] km. The maximum and minimum values of the differences show that a few seismic points have large differences from the Moho model. Since this occurs in all three models, we believed it may be due to a bias in the interpretation of seismic data. Nevertheless, the inversion parameters estimated in this paper are still similar to the results of Xuan et al. [7]. In terms of outcomes, although employing different methods, the model in this paper aligns closely with that of Xuan et al. [7], which to some extent corroborates the reliability of the results. In addition, the RMS and STD corresponding to the CRUST 1.0 model are 4.62 km and 4.49 km, respectively, those corresponding to the model by Xuan et al. [7] are 6.59 km and 3.49 km, respectively, and the RMS and STD corresponding to the model in this paper are 3.26 km and 3.21 km, respectively. It can be seen that the model in this paper is the closest to the seismic points. That is to say, the model in this paper is a bit more accurate than the other two Moho models.

4.3. Moho Fold Structure in the ECS

After obtaining the Moho topography of the study area, a more accurate isostatic model is indispensable in order to judge the stresses on different plates. Previously, topographic density and compensation depth were derived from a priori information [12]. However, this may lead to large biases in the isostatic model in localized regions. Therefore, here, we used the Moho topography as a constraint, and, based on different topographic densities (2.0~3.0 g/cm³ with 0.1 g/cm³ spacing) and compensation depths (taking the range of 20~30 km with 0.1 km spacing), we used Equation (23) to compute the isostatic model that is subjected to global constraints (whose difference from the Moho topography with the RMS is minimum 2.79 km), as shown in Figure 12. The appropriate topographic density and compensation depth were calculated to be 2.62 g/cm³ and 27.8 km, respectively.

Figure 12 shows that, in the isostatic state, the Moho depth of the study area ranges from 6.4 to 44.5 km. Among them, in the continental shelf area of the East China Sea, the isostatic Moho depth is around 26 km. Unlike the continental shelf, the isostatic Moho depth of the Okinawa Trough is close to 20 km. In addition, the isostatic Moho depth is around 40 km for Taiwan Island and 34 km for the South China Block.

The Moho fold structure is a deviation between the Moho topography and the isostatic model, and this deviation is a product of tectonic movements such as plate extrusion. That is, it is by these stresses that the isostatic state is broken, resulting in the present Moho topography. To study the stresses, we used Equation (24) to obtain the Moho fold structure of the study area, as shown in Figure 13.

In Figure 13, the value of the Moho fold structure ranges from −13.5 to 11.2 km. It should be noted that, in the region of positive values, the Moho topography is deeper than the Airy isostatic model. In regions of negative values, the Moho topography is shallower than the Airy isostatic model. Positive values are mainly found in the South China Block, Ryukyu Arc and the western part of Taiwan Island. Among them, in the Ryukyu Arc, the Moho fold structure is the thickest, with a thickness ranging from 5 to 11 km. This phenomenon indicates that the region is subjected to a very intense stress that breaks the isostatic state of the region and forces the mantle to sink. Since the region is the junction of the Philippine Sea plate and Eurasian Plate, then it can be judged that the main component of this stress is subduction vertical force. Based on the thickness of the Moho fold structure, the Ryukyu Arc can be divided into three parts: southwest, central and northeast. The thickness of the southwestern part is the greatest, around 10 km. The thickness of the central part is the second thickest, around 7 km. The thickness of the northeastern part is the smallest, around 5 km.

In the South China Block, the Moho fold structure is around 3 km thick. This confirms that the region was subjected to stresses that forced the mantle to sink. Unlike the Ryukyu Arc, the Moho fold structure of the South China Block is thinner. This situation may be due to the fact that the South China Block has not been stressed for a long time, or was stressed a long time ago, but slow crustal rebound reduced this effect. Previous studies [1,2] indicate that Mesozoic subduction occurred in this region. Therefore, we hypothesize that this region may have been subjected to stress from Mesozoic subduction long ago, but prolonged crustal rebound has gradually diminished the Moho fold structure. In the central and eastern parts of Taiwan Island, the thickness of the Moho fold structure ranges from −5 to −13 km. Compared with the Airy isostatic model, the Moho topography here is significantly elevated. This mantle uplift suggests that the dominant stress here is horizontal squeezing between plates rather than subduction vertical forces. In the Okinawa Trough, the Moho fold structure is relatively insignificant. In contrast, the Moho topography of the region is shown to be uplifted in Figure 9. The most plausible explanation is that the upwelling flow in the mantle mentioned by Arai et al. [3] contributed to the uplift of Moho topography in the near absence of interplate stresses.

5. Discussion

5.1. Influential Factors in Algorithms

Regarding the method employed in the paper, there are several areas worthy of improvement. The first point is curvature. The paper employs an improved Bott’s method for Moho topographic inversion, which does not account for the influence of the Earth’s curvature. Li et al. [33] previously assessed the curvature effect on the Tibetan Plateau. Although this influence is not significant, it should nevertheless be considered in subsequent studies. The second point is the constraint provided by seismic points. The improved Bott method requires seismic points to serve as constraints. However, should the seismic points be of low accuracy or insufficient in number, the resulting constrained model will exhibit a certain degree of bias. Therefore, in practical applications, it is necessary to collect as many seismic points as possible to serve as constraints, thereby reducing this bias. The third point is signal separation. In this paper, signal separation employs wavelet multi-scale analysis and a radial power spectrum method. Presently, regardless of the pathway taken for signal separation, incomplete separation inevitably occurs. In the future, utilizing constraints from actual measurement data, such as deep drilling, could achieve a more precise signal separation. The final one is the isostatic model. Based on fixed compensation depth and crustal density, the isostatic model was calculated using the Airy isostatic theory. Although we constrain the selection of these two parameters using the Moho topographic model, a fixed compensation depth and crustal density may lead to localized model deviations. In the future, it will be necessary to consider lateral variations in crustal density and adaptive adjustments to compensation depth in order to enhance the accuracy of the isostatic model.

5.2. Primary Stresses Within Different Regions

Gao et al. [14] proposed that, when vertical stresses act upon the crust, the isostatic model deviates from the Moho topography. From this, a general formula for vertical stress, denoted as $P_{vertical}=\left(m^k-m_I\right){\tilde{\rho }}_{0}g$, was derived. Shin et al. [34] employed the Moho fold structure to investigate the internal deformation of the Tibetan Plateau. This demonstrates that employing Moho fold structures to investigate stress conditions within the deep structure is theoretically feasible.

Differences in the thickness of the Moho fold structure across the Ryukyu Arc reflect variations in the tectonic stresses acting on this region, and two scenarios can explain this phenomenon (linked to the role of subduction vertical forces): 1. The subduction vertical force is the absolutely dominant control on crustal thickness. 2. The subduction vertical force is not the sole dominant factor, and additional forces act locally across the Ryukyu Arc (superimposed on the subduction vertical force). For example, in the central and northeastern Ryukyu Arc, the Moho topography corresponds to significant crustal thickening—this observation directly links to the dominant role of subduction vertical forces in driving crustal deformation here. In contrast, the southwestern Ryukyu Arc shows a paradox: the strongest subduction vertical force coincides with the thinnest crust (Moho depth ~25 km). This inconsistency implies that a more dominant internal force (driving mantle uplift) must operate here, overriding the effect of the subduction vertical force.

In the central/northeastern Ryukyu Arc, the dominance of subduction vertical forces (coupled with crustal thickening) aligns with typical arc–continent subduction behavior. Here, the subducting slab’s downward pull drives crustal stacking and thickening. In the southwestern Ryukyu Arc, the “strong subduction force + thin crust” anomaly (driven by mantle uplift) suggests a transition in the tectonic regime: this region may be influenced by back-arc extension (or slab rollback) that triggers mantle upwelling. The upwelling mantle thins the crust, even as subduction vertical forces act. This implies a complex interplay between slab-driven compression and mantle-driven extension in the southwestern arc.

5.3. Profilic Structure of the Ryukyu Arc

To illustrate the internal structure of the Ryukyu Arc, we have extracted three profiles, Line AB, Line CD and Line EF, whose positions are indicated by the red lines in Figure 13. Among these, line AB lies in the southwestern part of Ryukyu Arc, line CD in the central part and line EF in the northeastern part. The Moho topography and isostatic models for these three profiles are shown in Figure 14. Figure 14 demonstrates that, across various locations within the Ryukyu Arc, the Moho topography is generally deeper than the isostatic model. In Figure 14a, the maximum thickness of the Moho fold structure is approximately 8.1 km. In Figure 14b, the maximum thickness of the Moho fold structure is approximately 6.5 km. In Figure 14c, the maximum thickness of the Moho fold structure is approximately 5.7 km. Moreover, in the central and northeastern parts of the Ryukyu Arc, the Moho topography exhibits a pronounced subsidence, with the deepest point approaching 30 km. In contrast, in the southwestern section of the Ryukyu Arc, the subsidence of the Moho topography is somewhat “inhibited”, corroborating our earlier analysis of stress.

6. Conclusions

Based on the XGM2019e_2159 gravity field model and seismic data, we calculated the Moho topography and Moho fold structure beneath the East China Sea. The results show that the Moho topography of the study area ranges from 9.2 to 33.4 km. In the continental shelf area of the East China Sea, the Moho depth ranges from 27 to 30 km. Of these, the Moho topography in the north is around 25 km and the Moho topography in the south is around 18 km. In the South China Block, the Ryukyu Arc and the western part of Taiwan Island, the Moho topography is deeper than the Airy isostatic model. In the central and eastern parts of Taiwan Island, the Moho topography is shallower than the Airy isostatic model. Derived from these results, we presented several conclusions.

(1)

There are traces of downward stress inside the South China Block, which is very consistent with the subduction of the palaeo-Pacific to the Eurasian Plate. The distribution of the Moho fold structure shows that the location of the palaeo-subduction zone is in the eastern coastal zone of the South China Block.

(2)

In different regions of the Ryukyu Arc, the internal structures are subjected to different subduction vertical forces. The most exceptional of these is the southwestern part of the Ryukyu Arc (near Taiwan Island). Here, the Moho fold structure is the thickest, approaching 10 km. However, compared to other areas of the Ryukyu Arc, the crust here is the thinnest, with a Moho depth of about 25 km. In other words, the subduction vertical force is not dominant here, and therefore does not cause significant crustal thickening.

(3)

As a back-arc basin, the Moho topography of the Okinawa Trough is elevated, with depths ranging from 18 to 25 km. However, the Moho fold structure is almost non-existent here. This confirms the point that, in the absence of interplate stresses, it may be upwelling flow in the mantle that contributes to crustal thinning.