1 Introduction

The Ying-Qiong Basin is located where the Indochina Block intersection the South China Continental Block. The complex geological structure in the region includes the confluence of strike-slip and extensional continental margins to the northwest of the South China Sea. It also represents an area of tectonic extrusion or escape related to the collision of the India-Australian and Eurasian plates, and a subduction-related tectonic stretching zone in the paleo-South China Sea (Zhang, 2013). Since 50 Myr, the processes including the oblique convergence of the Indian and Eurasian plates, rapid trench retreat of the Pacific subduction zones, and the nearly south-north expansion of the South China Sea basin have caused the gradual disintegration of the northwestern continental margin of the South China Sea and the formation of the Ying-Qiong Basin.

The formation of the Yinggehai Basin is related to the collisional belt between the Indian and Eurasian plates, whereas the formation of the Qiongdongnan Basin is related to the subduction-stretching zone of the paleo-South China Sea. The research into the internal fault structure of the Ying-Qiong Basin is of great significance for understanding the structural attributes, evolution history, and formation process of petroliferous basins in the northern margin of the South China Sea.

Predecessors have conducted a sizable amount of work on the structural evolution history of the Ying-Qiong Basin, the characteristics of the regional stress field, the strength of extensional crustal deformation, and the geometry, activity rate, and stress state of principal faults in the basin (Sun et al., 2003, 2015; Clift and Sun, 2006; Li et al., 2006; Zhu et al., 2009; Song, 2012; Xie et al., 2015).

Previous researchers have also reported a series of basic geophysical studies in the Ying-Qiong Basin. The wideangle seismic profiles in the Yinggehai Basin have been processed and analyzed to obtain the velocity structure characteristics of the basin sediments (Xia et al., 1998; Wu et al., 2009). The Ocean Bottom Hydrophones (OBHs) seismic data were integrated by the two-dimensional (2D) raytracing program to study variations in the characteristics of the Moho depth, upper crustal thickness, and Cenozoic sediment thicknesses from the northeast to southwest boundary of the Yinggehai Basin (Liu et al., 2011). The seismic data and satellite altimetry gravity anomaly data were combined to study the deep crust structural characteristics of the Yinggehai-Songhong Basin (Luo et al., 2014). Zhao et al. (2019) utilized the ambient noise tomography method to perform relevant processing on the seismic station data in the South China Sea area, along with three-dimensional Swave velocity structures from the seafloor to the depth of 60 km obtained by inversion.

Zhang et al. (2009) used the stack velocity spectrum dataset of near-vertical deep reflection profiles implemented in the deep water area of the Zhujiang River Estuary and the Qiongdongnan Basin to analyze the spatial variation of P-wave velocities at different depths, as well as characteristics of the stratified crustal geometry in the basin. Shan et al. (2011) calculated Moho surface temperatures and determined the thermal structure of the sedimentary cover, upper crust, lower crust, and the high-speed layers in the lower crust based on the submarine heat flow data and related petrological thermal properties of strata in the Qiongdongnan Basin. Zhao et al. (2011) used deep seismic reflection profiles and gravity data in the basin to obtain the crustal density structure in the study area by using a joint gravity and seismic data inversion method, and the rock composition of the upper crust of the Qiongdongnan Basin was estimated. Based on seismic reflection profiles, layer velocities and gravity data, velocity and density structures were calculated for the sedimentary basement of the Qiongdongnan Basin (Qiu et al., 2013, 2014).

At present, the researches on the faults in Yinggehai Basin are mainly about their active periods (Zhu et al., 2009), activity intensity (Lei et al., 2015) and their controlling effect on the basin formation (Clift and Sun, 2006; Cui et al., 2008; Lei et al., 2015). Few studies have focused on the depth of fault activities. The main faults in the Yinggehai Basin were mainly active during Oligocene to early Miocene (30 – 16 Myr), middle to late Miocene (16 – 5.5 Myr), and Pliocene to Holocene (after 5.5 Myr) (Zhu et al., 2009; Yang et al., 2013). These faults mainly break the sediment sequences older than 13.8 Myr (Lei et al., 2015).

Similarly, the researches on faults in Qiongdongnan Basin are mostly about their active periods (Liao et al., 2012), activity intensity (Xie et al., 2007; Yin et al., 2010; Li et al., 2011; Bo et al., 2013; Liu et al., 2015) and their controlling effect on the basin formation (Sun et al., 2005; Zhao et al., 2018). Few studies have focused on the depth of fault activities.

In summary, previous researchers have conducted extensive works on the structural evolution, the characteristics of faults, the velocity structure, the density structure, the crustal morphology, and the depth of the Moho surface in the Ying-Qiong Basin. In these works, active source seismic data were most often analyzed, and partially supplemented by gravity or magnetic data. However, the limited detection depth and coverage of seismic exploration methods make it difficult to determine the active depth range of the main faults controlling the deeper parts of basin structures. Therefore, the Bouguer gravity anomaly data are used to study the active depth range of the principal faults in the Ying-Qiong Basin by wavelet multi-scale analysis and power spectral methods in this paper.

2 Geological Setting 2.1 Red River Fault Zone

The Red River fault zone (RRFZ) is one of the largest strike-slip fault zones in Asia. It starts from the eastern edge of the Tibetan plateau and extends along the edge of the South China Block to Hainan Island, separating the South China Block from the Indochina Block. The RRFZ is a strong ductile shear zone. Zhu et al. (2009) believed that the offshore part of the RRFZ has experienced three consecutive deformation periods: first a 30 – 16 Myr leftlateral movement stage, followed by a 16 – 5.5 Myr slip reversal stage. During this period, the shear sense of RRFZ changed from sinistral to dextral one. Finally, during the period of 5.5 – 3.6 Myr, dextral displacement reached a peak and then ceased.

2.2 Yinggehai Basin

The Yinggehai Basin is located between the Hainan Island and the Indochina Peninsula. It is tectonically located in the South China Block and is a southeast-striking fusiform basin with a length of about 500 km and a maximum width of about 150 km. Separated by reverse faults, it has the characteristics of a strike-slip basin. The Yinggehai Basin is characterized by rapid filling, rapid subsidence, high temperatures, and high pressures, and diapiric structures that mostly occur in the middle of the basin (Zhu et al., 2009). The Yinggehai Basin opened at about 44 Myr and mainly experienced tensile deformation in the initial stage. At 21 – 14 Myr, the basin experienced continuous structural inversion at first, followed by a gradual decrease in subsidence rate (Clift and Sun, 2006). The Yinggehai Basin successively developed synrift strata and post-rifting strata. Zhu et al. (2009) considered the two boundary faults in the basin (fault No.1 and the Yingxi fault) and the two central faults to be the major offshore extensions of the RRFZ. Same as Zhu et al. (2009) in terms of the numbering of the main fault systems in the Yinggehai Basin, we name the fault No.1 and the Yingxi fault as faults A and D, respectively, and the two main faults in the center of the Yinggehai Basin as faults B and C, respectively. The positions of the four faults, A, B, C, and D are marked in Fig.1.

Fault A separates the Yinggehai Basin from the Beibu Gulf and the Qiongdongnan Basin. Its trajectory is nearly a straight line, extending from the Beibu Gulf to the Zhongjian Ridge, with a total length of about 420 km. The strike of fault A is NE-SW in the north and N-S in the south. It is a southwestward-dipping, high-angle normal fault, whose displacement decreases with time (Zhu et al., 2009). The fault A (No.1) cuts through the crust at a depth of 8 – 9 km. The structure on both sides of the fault A in the crust is greatly different, and the thickness of the crust suddenly decreases from 25 km to 6 – 7 km. That means the fault No. 1 may extend to greater depths, or even the entire crust (Wu et al., 2009).

Fault B runs from the Gulf of Tonkin and goes through the center of the Yinggehai Basin to the south, with a total length of about 450 km. It may extend all the way to the vicinity of the Zhongjian Ridge. The north segment of fault B strikes in the direction of N-S, but it bends to NW-SE in the south Zhu et al. (2009). Based on the seismic profile data, fault B is a high-angle reverse-slip fault in the northern part of the Yinggehai Basin and is inferred as a deep fault (Zhu et al., 2009).

Fault C starts from the Gulf of Tonkin, cuts across the center of the Yinggehai Basin, and extends southward to the Zhongjian Ridge, with a total length of about 480 km. The overall trend of fault C is NW-SE. In terms of its sense of displacement, fault C significantly changes from a reverse fault in the northern basin to a normal one in the southern basin (Zhu et al., 2009).

Fault D extends along the western edge of the Yinggehai Basin, with a length of about 500 km. In the northern part of the basin, the fault D strikes in a N-S direction and becomes NW-SE in the southern part of the basin. At the same time, the inclination and properties of fault D also significantly change from north to south. The northern segment is a high-angle reverse fault with the fault plane dipping to the northeastward, accompanied by positive flower structures. The southern segment of fault D is a high-angle normal fault dipping northeastward (Zhu et al., 2009).

2.3 Qiongdongnan Basin

The Qiongdongnan Basin is located at the passive continental margin on the west side of the northern South China Sea. It is a Cenozoic rift basin with an average water depth of more than 2500 m and is northeast-trending (Xie et al., 2007; Bo et al., 2013). The formation and evolution of the Qiongdongnan Basin have been affected by both the RRFZ and the spreading of the South China Sea (Han et al., 2016). There are five major depocenters in the Qiongdongnan Basin: the Ledong sub-basin (LDS), the Lingshui sub-basin (LSS), the Beijiao sub-basin (BJS), the Baodao sub-basin (BDS), and the Changchang sub-basin (CCS), from west to east (Bo et al., 2013). These sub-basins are all formed during the rifting stage and are bounded and controlled by faults (Xie et al., 2007).

In the Qiongdongnan Basin, there is a fault zone formed during the rifting stage, which has a planar width of about 50 – 100 km and a length of about 400 km. The fault zone appears as an arc and can be divided into three parts: the western, middle, and eastern sections (Bo et al., 2013). These fault zones are covered by thick sedimentary layers (Bo et al., 2013). The layout of the main faults in the Qiongdongnan Basin is shown in Figs.1, 2, 4 and 5 (Bo et al., 2013). In order not to be confused with the fault numbers in Yinggehai Basin, the fault numbers in Qiongdongnan Basin has been partially modified, that is: Fault C and Fault D on the north side of Lingshui sub-basin (LSS) in the literature were changed into faults M and N, respectively. En Echelon fault zone B and En Echelon fault zone A on the north and south sides of Changchang sub-basin (CCS) were changed into fault zones L and H, respectively.

The western section of the fault zone is mainly composed of some normal faults with the E-W orientation, including fault F and the LDS (Bo et al., 2013). The middle part of the fault zone is composed of a number of long, linear, NE-ENE-oriented tensional boundary faults, including faults 5, 2, 6, 11, M, N, E, and so on (Bo et al., 2013). In seismic profiles, these faults all have fault planes with large dip angles accompanied by normal fault displacement, which do not show strike-slip characteristics. The middle part of the fault zone also contains the LSS, BJS, and BDS. The No.5 fault was less active during the Eocene, while in the early Oligocene its activity rate increased with the maximum slip of 4290 m. In the late Oligocene, the basin was in the fault-depression transition period with the maximum slip of 3732 m. In the period of Sanya formation, the activity rate further decreased with the maximum slip of 1395 m. The No.2 fault had a low activity rate in Eocene, with a maximum slip of 3615 m; in early Oligocene, it had a maximum slip of 6800 m; in late Oligocene, strong activities caused a maximum slip of 6413 m; in Miocene, it had a low activity rate, with a maximum slip of 1006 m. In the Eocene, the activity rate of No.6 fault was low and the maximum slip was 2532 m. In the early Oligocene, the fault activity was significantly increased and the maximum slip was 3992 m. In the late Oligocene, the maximum slip was 3109 m. The slip of No. 11 fault is 3000 m in Eocene and 9000 m in early Oligocene, and its fault activity was the most intense in the late Oligocene, with a slip of 8607 m. After the Miocene (12 Myr), the fault activities stopped (Yin et al., 2010). The lengths of faults M, N and E are all about 40 km, and the maximum normal displacement is 1800, 3700 and 4900 m, respectively (Bo et al., 2013).

The eastern section of the fault zone is mainly composed of the CCS and fault zones L and H (Bo et al., 2013), which are located on the north and south sides of the CCS. The faults that make up these fault zones are mostly large left-lateral strike-slip faults with E-W or nearly E-W orientations and internal faults in E-W or nearly NE orientations. The maximum normal fault displacement in fault zones H and L is 3200 and 5100 m, respectively (Bo et al., 2013).

The large, deep, NE-trending faults exert the main controls on the strike and basin shape of the Qiongdongnan Basin (Xie et al., 2007; Zhang et al., 2013). The faults in NE-SW, E-W, and NW-SE directions in the Qiongdongnan Basin ceased to be active after 23 Myr (Zhao et al., 2016). The Paleogene rifting stage also ended around 23 Myr, so the faults mainly controlled the strata formed during the rifting period.

3 Data Acquisition and Methods 3.1 Data

The research area of this study is between 15.3˚ – 22˚N in latitude and 105˚ – 113˚E in longitude. The data used in this paper is the Bouguer gravity data provided by the Bureau Gravimetric International with a resolution of 2΄× 2΄ (Bonvalot, 2012). The data have been processed by terrain correction, height correction, normal field correction, middle layer correction, and atmospheric correction (eliminating the influence of atmospheric mass on gravity) based on the original gravity data.

As shown in Fig.2, the Bouguer gravity anomaly values are low, close to 0 mGal, in the northwest of the Yinggehai Basin and gradually increase to 100 mGal toward the southeast direction. Near the Zhongjian Ridge, there is a gravity anomaly gradient belt with the north-south direction. From its west side to the east, the Bouguer gravity anomaly values gradually increase. The Bouguer gravity anomaly in the Qiongdongnan Basin gradually increases from the northwest to the south and most are greater than 150 mGal.

3.2 Methods

The Bouguer gravity anomaly includes not only the influence of various ore bodies and structures that deviate from the normal density distribution in the crust but also the influence of the undulation of the lower crustal interface and large losses or surpluses of upper mantle mass in the lateral direction. Using wavelet multi-scale decomposition of the Bouguer gravity field and extracting gravity anomaly information at different frequencies, we focus on analyzing the field details (the second- to sixth-order details). This method is called the 2D discrete wavelet transform. The average bottom interface depth was obtained from each level of field detail after decomposition, and the gravity response of the faults in each level of field detail was analyzed.

This paper aims to characterize the large faults that control the formation of the basin. They have long active times, large penetration depths, and significant gravity anomalies, and involve the formation of synrift strata. Therefore, the depth range of such fault activities has a certain degree of continuity in space. As the decomposition order increases, low-frequency information in the reconstructed detailed field increases, and the proportion of the reflected deep field source information gradually increases. Consequently, it is possible to study the gravity anomaly response of faults at different depths in the Ying-Qiong Basin based on the detailed field information of different decomposition orders.

3.2.1 Two-dimensional discrete wavelet transform

In 1984, French geophysicists Grossman and Morlet proposed the concept of the wavelet transform. They then established the theoretical system of wavelet transforms using translation and expansion invariance, and cooperated to complete the theoretical work of continuous wave

let transforms and inverse transforms (Grossmann and Morlet, 1984). The wavelet transform method has been applied in many disciplines (Chen and Feng, 1999; Feng et al., 2002). Mallat (1989) developed this theory in 1989 and first proposed the concept of multi-resolution analysis. The reconstruction formula for a 2D discrete wavelet transform is as follows:

$ f(x, y) = \sum\limits_{m, n \in Z} {A_{{2^J}}^d} f{\Phi _{{2^j}}}(x, y) + \sum\limits_{j = 1}^J {\sum\limits_{m, n \in Z} {\left[ {D_{{2^j}}^1f\Psi _{{2^j}}^1(x, y) + D_{{2^j}}^2f\Psi _{{2^j}}^2(x, y) + D_{{2^j}}^3f\Psi _{{2^j}}^3(x, y)} \right]} } . $

(1)

The term $A_{{2^j}}^d$ (where j represents the jth-order approximation part of the wavelet decomposition) represents the low-frequency approximation in the 2D multi-scale analysis space, and the terms $D_{{2^j}}^1$, $D_{{2^j}}^2$, and $D_{{2^j}}^3$ represent the high-frequency details in the horizontal, vertical, and diagonal directions, respectively. They are calculated by the following formulas:

$ A_{{2^j}}^df = {\left({\left\langle {f(x, y), {\phi _{{2^j}}}(x {2^{ j}}n, y {2^{ j}}m)} \right\rangle } \right)_{(n, m) \in {Z^2}}}, $

(2)

$ D_{{2^j}}^1f = {\left({\left\langle {f(x, y), \Psi _{{2^j}}^1(x {2^{ j}}n, y {2^{ j}}m)} \right\rangle } \right)_{(n, m) \in {Z^2}}}, $

(3)

$ D_{{2^j}}^2f = {\left({\left\langle {f(x, y), \Psi _{{2^j}}^2(x {2^{ j}}n, y {2^{ j}}m)} \right\rangle } \right)_{(n, m) \in {Z^2}}}, $

(4)

$ D_{{2^j}}^3f = {\left({\left\langle {f(x, y), \Psi _{{2^j}}^3(x {2^{ j}}n, y {2^{ j}}m)} \right\rangle } \right)_{(n, m) \in {Z^2}}}, $

(5)

where ${\phi _{{2^j}}}$ is the scaling function, and $\Psi _{{2^j}}^1$, $\Psi _{{2^j}}^2$, and $\Psi _{{2^j}}^3$ are the wavelet functions in the horizontal, vertical, and diagonal direction, respectively. The terms n and m represent the discrete coordinate values of two dimensions in the x and y directions, respectively. Using the gravity anomaly data on the grids as the coefficients {S⁰} of the spatial scale function, we can calculate the coefficients {S^j} of the other spatial scale functions and the coefficients {d^{h, j}}, {d^{v, j}}, and{d^{d, j}} of the wavelet function to realize the multi-scale decomposition of the 2-D gravity anomalies. This decomposition is simply written as follows:

$ \Delta g(x, y) = {A_6}G + {D_6}G + {D_5}G + {D_4}G + {D_3}G + {D_2}G + {D_1}G, $

(6)

where A₆G is the sixth-order approximation part of gravity anomalies obtained by the wavelet decomposition and D_jG are the sums of the three detail parts, namely, horizontal, vertical, and diagonal components. On a low-order wavelet detail map, the anomalies represent density anomalies in the shallow crustal layer, while high-order details represent the density structures in the deeper crustal layers. The average depth of the field source can be estimated by power spectrum analysis.

3.2.2 Power spectrum method

The average depth of the field source in detailed maps derived from wavelet decomposition can be estimated by using the power spectrum method (Hannan, 1966; Cianciara and Marcak, 1976; Pal et al., 1978; Tselentis et al., 1988; Tanaka et al., 1999; Bansal and Dimri, 2001; Liu et al., 2013; Tian et al., 2017, 2020). According to Hou and Li (1988) and Li et al. (1998), the bottom depth of a prism can be estimated based on the formula to calculate the gravity anomaly from a rectangular prism in the frequency domain derived by Bhattacharyya (1966). The bottom depth can be written as follows:

$ h = \frac{1}{2}\frac{{\ln Z(s)}}{s}, $

(7)

where Z(s) is the power spectrum and s is the circular wave number. The power spectra and average depths derived from the first- to sixth-order detailed wavelet field (1-D – 6-D) are shown in Fig.3 and Table 1.

4 Results 4.1 Second-Order Detailed Field Characteristics

The average depth of the bottom interface of the field source of the second-order detailed field is 8 km (Fig.3b), which may be the shallow, dense and inhomogeneous objects. As shown in Fig.4a, in the Yinggehai Basin, the positive gravity anomalies in the second-order detailed field are distributed in equiaxial or banded pattern, whereas the obvious gravity anomaly gradient belt which may indicate the four main faults (A, B, C, and D) in the basin has not been found. In the western Qiongdongnan Basin, the gravity anomalies are also equiaxial or banded, whereas along the northern and southern boundaries of the basin, two gravity gradient belts and beaded anomalies with nearly NE and E-W strikes occur, which indicate the boundary faults in the northern basin (such as faults 5, 6, 2, and F, and fault zone H), and the southern basin (such as the gravity anomaly response of fault zone L and fault 11).

4.2 Third-Order Detailed Field

The average depth of the bottom interface of the field source of the third-order detailed field is 15 km (Fig.3c), being approximate to the previous result (Gao and Liu, 2014). As shown in Fig.4b, in the central Yinggehai Basin, positive gravity anomalies are distributed in a wide band or an equiaxial shape. Beaded anomalies occur at the eastern boundary of the basin and at the location of fault A; and a gravity gradient belt occurs at the southern end of fault A, near the Zhongjian Ridge. There are also weak beaded anomalies at the western boundary of the basin, namely, at the location of fault D. In the Qiongdongnan Basin, the gravity anomalies have obvious linear characteristics and are distributed in bands. In the northwest part of the basin, the gravity anomalies are close to NE-striking, whereas in the east of the basin they are close to EW-striking. According to the projection results for faults in the Qiongdongnan Basin from the third-order detailed field, these gravity gradient belts are the responses of faults F, 5, 6, 2, M, N, E, and 11, and fault zones H and L.

4.3 Fourth-Order Detailed Gravity Field

The average bottom interface depth of the fourth-order detailed gravity field source is 26.5 km (Fig.3d).

As shown in Fig.4c, positive gravity anomalies in the Yinggehai Basin are distributed in strips, striking NW to N-S. Fault A starts from the location where the RRFZ enters the sea, which is the eastern boundary of the basin, and extends southward to the vicinity of the Zhongjian Ridge. In the fourth-order detailed maps of the Bouguer gravity anomaly, a large-scale banded gravity gradient belt was identified. In the northern part of the basin, banded negative gravity anomalies occur between faults D and C, corresponding to the graben structure between the faults D and C with the opposite dip directions. In the southern part of the basin, there is a similar graben between the faults A and D according to the negative gravity anomaly strip. In the central part of the basin, fault B is shown as N-Strending banded negative gravity anomalies and fault C is marked by a gravity anomaly gradient belt.

In the Qiongdongnan Basin, the fourth-order detailed gravity field is dominated by banded gravity anomalies with NE and E-W strikes. For example, the large banded negative gravity anomaly at the northern boundary of the basin starts from the western segment of fault M and extends to the east of the basin along faults 5, M, 6, and 2, and fault zone H. In the south of the basin beaded anomalies start from fault E and propagate eastward along fault 11 and fault zone L. These faults are located at the edges of the banded gravity anomalies.

4.4 Fifth-Order Detailed Gravity Field

The average bottom interface depth of the fifth-order detailed gravity field source is 39 km (Fig.3e).

As shown in Fig.4d, the fifth-order detailed Bouguer gravity anomalies in the Yinggehai Basin display a banded distribution pattern with the NW strike. Near the Hainan Island, which is in the eastern side of the basin, there is a band of positive gravity anomalies with the nearly NW strike between faults A and B. The banded negative gravity anomaly between faults C and D in the west of the basin starts from the estuary of the RRFZ and extends southward along the tracks of faults C and D. Finally, all four faults (faults A, B, C, and D) converge in the negative gravity anomaly area on the west side of the Zhongjian Ridge.

There are two large banded gravity anomaly areas in the Qiongdongnan Basin, one of which is inverted L-shaped at the northern boundary of the basin. It starts from the west side of Hainan Island and extends southeast along the boundary of the Yinggehai Basin. Beyond that, it extends northeastward along fault F and faults 5 and 6 in the Qiongdongnan Basin. Finally, it continues to extend eastward along the fault zone H. The other area starts from the LDS, which is marked by the banded positive gravity anomalies, continues to extend eastward along the northwest boundary of fault E, faults M and N, and the BJS. After passing through the LSS and BDS, it reaches the CCS and extends eastward along the strike of fault zones H and L. The boundaries of these two large banded gravity anomaly areas are consistent with those of the deep and shallow water areas in the basin. According to isostatic gravity field theory, the depth of the Moho surface is shallower in the areas of deep water, and the upwelling of mantle materials leads to positive Bouguer gravity anomalies.

4.5 Sixth-Order Detailed Gravity Field

The average bottom interface depth of the sixth-order detailed gravity field source is 187 km (Fig.3f). As shown in Fig.4e, on the sixth-order detailed maps of the Bouguer gravity anomaly, in addition to the banded positive gravity anomalies striking NW along the east coast of Vietnam, the northwest basin of the South China Sea displays six groups of bimodal banded features with NE-trending alternating positive and negative gravity anomalies. Because the main controlling faults in the Yinggehai Basin strike in NW direction, which is perpendicular to the trends of the gravity anomalies, the long banded gravity anomalies in the basin are not inferred to be caused by faults. Compared with the fifth-order detailed gravity field, the positive gravity anomaly zone in the Qiongdongnan Basin has a greater area, which is supposed to be related to the distribution of deep mantle materials. Therefore, the formation of this zone is not considered to be related to the faults. In conclusion, the active depth of the fault system in the YingQiong Basin is less than the average depth of the sixth- order detailed gravity field sources.

5 Discussion 5.1 Gravity Response Characteristics of Controlling Faults in the Yinggehai Basin

Fault A is divided into three parts: north, middle, and south. The northern segment forms the boundary between the Yinggehai Basin and the Beibu Gulf Basin, the middle segment separates the Yinggehai Basin from the Hainan Island, and the southern segment is the boundary fault of the Zhongjian Ridge.

The first- to second-order detailed fields mainly reflect the gravity anomalies of shallow objects with different densities. A very thick sedimentary strata formed after the end of fault A (Clift and Sun, 2006; Bo et al., 2013; Yang et al., 2013), and this sediment cover masks the fault A to make its gravity response less distinct. Fault A was mainly active in sedimentary strata formed before 13.8 Myr (Lei et al., 2015) and cut through the sedimentary basement (Song et al., 2002; Lu et al., 2015). In the third-order detailed field, the beaded anomalies occur along the strike of the north and middle segments of fault A (Zhu et al., 2009); therefore, the beaded anomalies represent the gravity response of fault A. Along the southern segment of fault A, a nearly N-S banded negative gravity anomaly zone with the same strike, greater than −10 mGal, is also observed. The banded positive gravity anomalies display on both sides of fault A. In the fourth-order detailed field, the position of fault A and the gravity gradient zone are basically coincident. A gravity gradient zone with NNW strike appears in the north and middle sections of fault A, whereas the banded gravity anomaly, which is thought to be related to the Zhongjian Ridge based on its scale, occur along the southern segment of fault A. In the fifth-order detailed field, the large banded gravity anomaly along the north and middle segments of fault A is related to the eastern boundary of the Yinggehai Basin. According to the tomography (Wu et al., 2009), in the center of the basin and near the Hainan Island, the crustal thickness on the right side of fault A is about 25 km, whereas the crustal thickness on the left side is about 6 – 7 km thinner than that on the right side, displaying as banded gravity anomalies. The southern segment of fault A is the boundary fault of the Zhongjian Ridge (Sun et al., 2005), along which low negative gravity anomaly values were found. In conclusion, based on the gravity anomaly characteristics of fault A in the third- to fifthorder detailed fields, we speculate that its active depth range is 15 – 39 km. However, the tomography results indicate that the active depth of fault A in the crust near the northwestern part of Hainan Island ranges from 5 to 30 km, cutting across the Moho surface (Wu et al., 2009). The difference between the two sets of results is related to the method used. The tomography results are more accurate in shallow regions, but due to the low signal-to-noise ratio of seismic data, the tomography method cannot describe fault activities deeper than 30 km. Therefore, the active depth of fault A may range from 5 to 39 km.

The northern part of fault B, near the Beibu Gulf Basin, is adjacent and parallel to fault A. The middle and southern sections of fault B are mainly active in the depocenter of the Yinggehai Basin. Some faults are related to the diapir structure (Lei et al., 2011), and the overlying sedimentary layer is very thick (Clift and Sun, 2006; Zhu et al., 2009); therefore, their gravity anomaly response in the second- and third-order detailed fields (Figs.4a – b) are very weak. A large amount of crustal gas contained in the diapir structure has migrated up through fault B, indicating that fault B has a greater active depth. In the fourthorder detailed field, near the Beibu Gulf Basin, fault B is located on a gravity gradient belt, whereas the middle and southern sections of fault B are located on a negative gravity anomaly belt with the SE strike, which is inferred to be related to the diapir structure in the area near fault B. In the fifth-order detailed field, the northern sections of faults B and A together form the boundary between the Hanoi depression and the Beibu Gulf Basin, giving rise to a gravity gradient zone; the gravity response characteristics of the middle and southern sections of fault B are very weak. In summary, the active depth range of fault B is inferred to be 26.5 – 39 km based on the gravity anomaly response characteristics in the fourth- to fifth-order detailed fields.

Fault C can be divided into three sections according to changes in strike: north, middle, south sections. The north section extends southward from the Gulf of Tonkin to the middle of the Yinggehai Basin with a strike of nearly N-S; the middle section runs through the middle of the Yinggehai Basin, and its strike is NW-SE (Zhu et al., 2009); the southern section is located in the south of the Yinggehai Basin and is N-S-striking. In the second-order detailed field, the influence of small density inhomogeneities in the shallow part obscures the gravity anomaly response characteristics of fault C. In the third-order detailed field, fault C passes through a small negative gravity anomaly zone in the north section and corresponds to a series of small beaded gravity anomalies in the middle section, whereas the response of the gravity anomaly for the south section is not obvious. In the fourth-order detailed field, the north section of fault C is located in a gravity gradient belt with an approximately S-N strike. On its west side is a negative gravity anomaly area, and on its east side is a positive anomaly area. A gravity gradient belt with a NW strike appears in the middle section of fault C. The southern section of fault C is located in an approximately N-S-trending negative gravity anomaly zone. In the fifth-order detailed field, fault C is located in a strip of negative gravity anomalies whose shape is basically consistent with that of fault C. In conclusion, according to the gravity anomaly response characteristics of fault C in the third- to fifth-order detailed fields, the active depth of fault C is inferred to be 15 – 39 km.

In the second-order detailed field, the gravity anomaly response of fault D is very small, without any obvious gravity anomaly characteristics. The third-order detailed field contains obvious beaded anomalies in the north and middle sections of fault D, and the response in the south is chaotic. In the fourth-order detailed field, negative banded gravity anomalies occur in the north of the Yinggehai Basin between faults C and D, which is located on the west side of the gravity anomaly belt. In the south-central part of the Yinggehai Basin, positive banded gravity anomalies appear between faults C and D, where faults C and D become NE-dipping normal faults. In the fifth-order detailed field, faults C and D are located in a negative gravity anomaly strip whose shape is roughly same as that of fault D. In conclusion, we infer the active depth range of 15 – 39 km for fault D according to its gravity anomaly response characteristics in the third- to fifth-order detailed fields.

In summary, the Yinggehai Basin contains four deep faults striking in the NNW direction referred to as A, B, C, and D, from east to west, which has influenced the formation of the Yinggehai Basin. According to the results of the above analysis, the active depth range of fault A is 5 – 39 km and the active depth of faults C and D ranges from 15 to 39 km, with the gravity response mostly reflected in the third- to fifth-order detailed fields (Table 2). The active depth range of fault B is smallest (26.5 – 39 km), and its gravity response is mostly reflected in the fourth- and fifth-order detailed fields (Table 2).

5.2 Gravity Response Characteristics of Controlling Faults in the Qiongdongnan Basin

The response characteristics of fault F are not obvious in the Bouguer gravity anomaly (Fig.2), whereas fault 5 is located on a gravity gradient belt with a NEE trend. In the second- and third-order detailed fields, faults F and 5 correspond to gravity anomaly gradient zones with the nearly ENE trend. The south and north sides of the gravity gradient zone are negative and positive gravity anomaly zone, respectively. The gradient zone is more obvious in the thirdorder detailed field, and the negative gravity anomaly strip becomes wider on its south side. In the fourth-order detailed field, the gravity response on the west side of fault 5 is weakened, but the response remains obvious on the east side. In the fifth-order detailed field, faults F and 5 are located on a large ENE-oriented negative gravity anomaly strip, but there is no sharp gravity anomaly change. Therefore, based on the gravity anomaly characteristics of faults F and 5 in the second- to fourth-order detailed fields, their fault activity depth range is inferred to be 8 – 26.5 km (Table 3).

Faults 2 and 6 are parallel normal faults with opposite dip directions (Bo et al., 2013). Based on seismic interpretation, faults 2 and 6 were active in the upper Eocene and cut through the basement. The Yacheng formation and the Lingshui formation were formed during the rifting stage (Bo et al., 2013; Sun et al., 2015). Both faults 2 and 6 are located in the high gravity anomaly area (Fig.2). In the second-order detailed field (Fig.4a), the western section of fault 2 corresponds to negative beaded anomalies; the eastern section is located on a gravity gradient belt with an approximately NE trend, whose north and south sides are abnormal bands of positive and negative gravity anomalies, respectively. Fault 6 corresponds to beaded anomalies in a NE orientation. In the third-order detailed field (Fig.4b), faults 2 and 6 are located on the north and south edges, respectively, of a NE-trending negative gravity anomaly belt. It is speculated that this negative gravity anomaly belt is related to the horst structure formed between faults 6 and 2. In the fourth-order detailed field (Fig.4c), faults 2 and 6 are located on a NE-trending gravity anomalous gradient belt. In the fifth-order detailed field (Fig.4d), fault 2 is located near the boundary between positive and negative gravity anomaly strips, but with different strikes. Therefore, no gravity response of faults 2 and 6 is inferred from the fifth-order detailed field. Based on the gravity anomaly characteristics of faults 2 and 6 in the second- to fourth-order detailed fields, it is inferred that their fault activity depth range is between 8 and 26.5 km (Table 3).

The interpretations of seismic profiles indicate that fault E was active in the upper Eocene and cut through the basement. The Yacheng formation and the Lingshui formation are synrift deposition (Bo et al., 2013). The response of fault E in the second-order detailed field is beaded anomalies with a NE trend. In the third-order detailed field, fault E corresponds to a gravity gradient belt, whereas fault E has a weak response in the fourth-order detailed field. The western section of fault E is located at the transition zone between high and low positive gravity anomalies, constituting a small gravity gradient belt. The eastern section of fault E extends into the negative gravity anomaly zone. In the fifth-order detailed field, fault E is in the positive gravity anomaly zone, and there is no gravity response. Based on the gravity anomaly characteristics of fault E in the second- to fourth-order detailed fields, its fault activity depth range is inferred to be 8 – 26.5 km (Table 3).

According to the interpretation of seismic profiles, faults M and N were active in the upper Eocene and cut through the basement, and the Yacheng formation and the Lingshui formation were formed during the rifting stage (Bo et al., 2013). In the second-order detailed field, both faults M and N are located on the beaded anomalies with a NE orientation. In the third-order detailed field, faults M and N are located on a NE-trending gravity gradient zone. The fourth-order detailed field shows that the northeast section of fault M is located in a gravity gradient zone, whereas fault N is located in a zone with low positive gravity anomaly values, which infers that fault N has no gravity response characteristics. In the fifth-order detailed field, faults M and N are located at the edge of a large-scale NE-trending positive gravity anomaly belt. Based on the difference in scale between the fault and gravity anomaly belt, it is inferred that the gravity gradient belt at this location should be related to the distribution of materials in the deep mantle. In summary, the active depth ranges of faults M and N are 8 – 26.5 and 8 – 15 km, respectively (Table 3).

The seismic data interpretation indicates that fault 11 was active in the Sanya formation that formed in the postrifting stage, and active in the Yacheng formation and the Lingshui formation formed in the rifting stage during the upper Eocene, and also cut through the basement (Zhao et al., 2016). In the second-order detailed field, fault 11 is located on the beaded anomalies. In the third-order detailed field, fault 11 is located on a gravity gradient zone and on its north and south sides are banded positive and negative gravity anomalies, respectively. In the fourth-order detailed field, the western section of fault 11 is located in a banded negative gravity anomaly area, and the northeast section is located at the edge of the isometric positive gravity anomaly area in the BJS. Therefore, the gravity response of fault 11 in the fourth-order detailed field is weak. In the fifth-order detailed field, fault 11 is mainly located in a negative gravity anomaly zone, which may be related to the large-scale uneven distribution of materials in the mantle. Based on the gravity anomaly characteristics of fault 11 in the second- to fourth-order detailed fields, we speculate that its fault activity depth range is between 8 and 26.5 km (Table 3).

Fault zones H and L are in a set of en echelon fault zones with parallel strikes and opposite inclinations. The CCS was formed between the two fault zones (Bo et al., 2013). According to the seismic data interpretation, fault zones H and L were active in the deposition of the Eocene Yacheng formation and Lingshui formation, and furtherly cut through the basement. In the second-order detailed field, beaded gravity anomalies appear at the position of fault zone H. In the third-order detailed field, the responses of fault zones H and L are both beaded anomalies with the E-W trend. In the fourth-order detailed field, fault zones H and L are both located on an E-W-trending gravity gradient belt with equiaxial positive gravity anomalies between the two fault zones. The CCS is in a high-value positive gravity anomaly zone with an E-W trend in the fifthorder detailed field. The northern boun- dary of this anomaly zone corresponds to fault zone H, whereas fault zone L is located inside the positive gravity anomaly zone. There is no obvious gravity field response characteristic for either fault. The formation of this anomaly zone is related to the shallow depth of the Moho surface in the CCS (only 13.8 km) and the gradual deepening to the north and south sides (Zhang et al., 2013). Therefore, it is inferred that the active depth of the fault zone H is between 8 and 39 km and that of the fault zone L is between 8 and 26.5 km (Table 3).

In the Qiongdongnan Basin, the gravity response of the fault zone H is reflected in the second- to fifth-order detailed fields, and the active depth ranges is from 8 to 39 km. The gravity response of the fault N is reflected in the second- to third-order detailed fields indicating the depth range of 8 – 15 km. Aside from these two faults, the gravitational responses of the other faults are reflected in the second- to fourth-order detailed fields, and their active depths range from 8 to 26.5 km.

5.3 The Influence of Deep Fault Systems on Basin Structure

According to the wavelet multi-scale analysis mentioned above in the Yinggehai Basin, the four faults that constitute the offshore extension of the RRFZ have a maximum penetration depth of at least 39 km, which are classified as crustal-scale faults, cutting through the Moho. Under the continuous activities of this dominant fault zone, the basin has developed significant sediment deposition since the Cenozoic. As can be seen from Fig.5, the thickness of the strata in the sedimentary center of the basin reaches as much as 15 km. According to the theory of crustal equilibrium, the filling of a large amount of low-density sediments in the basin may cause feedback in the deep structure of the lithosphere. It can be seen that the Moho is uplifted in the central part of the basin, and the crust has been significantly thinned by 10 km, accounting for nearly 1/3 of the average crustal thickness of the basin (34 km). According to wavelet multi-scale analysis in the Qiongdongnan Basin, although there are significant spatial differences in the penetration depths of the faults, the crustpenetrating faults with an overall depth of nearly 40 km also developed. The basin has received a large amount of sediment deposition in relation to the trans-crustal faulting mentioned above, and the input of low-density sediments has also caused isostatic adjustment of the lithospheric structure. As shown in Fig.5, the thickness of the central strata in the west side of the Basin reaches as much as 10 km. Accordingly, the Moho has been uplifted by nearly 7 km, and the thickness of the crust has been reduced by approximately 1/4 of the total (27 km). The profile along Line 3 in the central part of the basin shows that, under the control of faults 2, 6, and 11, around 7 km of sedimentary strata has been deposited, and the Moho is uplifted 5 km, thinning about 1/5 of the crustal thickness (27 km). The profile along Line 4 on the east side of the basin shows that, under the main influence of the H and L fault zones, sediment accumulation in the center of the basin reaches 10 km in thickness, and the Moho is uplifted by 10 km, thinning 1/2 of the crustal thickness (22 km). Thus, the presence of low-density strata has also induced the adjustment in crustal structure, varied in space, under the dominance of the aforementioned main controlling faults in the Qiongdongnan Basin. Toward the east of the basin, the adjustment becomes larger. In particular, the comparison between sections along Line 1 and Line 4 reveals that the crustal thinning along Line 4 (by 1/2 of crustal thickness) was significantly greater than that along Line 1 (1/3 of crustal thickness), although the two sections were dominated by the same main trans-crustal faults and both were loaded with nearly 10 km of sedimentary strata. Compared to the Yinggehai Basin, the Qiongdongnan Basin gets the sufficient material supply from the areas such as the Sichuan-Yunnan region and Indosinian Blocks in southeastern Tibet, and from the Red River and other river systems. As the fault activity and the accommodating space increase, the thickness of the sedimentary strata is obviously thicken. However, the range of crustal adjustment in the Yinggehai Basin is less than that in the Qiongdongnan Basin. This difference may not be simply attributed to the Airy equilibrium model. This indicates that the crustal structure adjustment in the Qiongdongnan Basin is not only related to the accretion of sedimentary strata dominated by the basin faults, but is also closely related to magmatic activities and other factors. The eastern part of the Qiongdongnan Basin is adjacent to the northwest sub-basin of the South China Sea and near its expansion center. Therefore, the Moho is shallower and the crust has been significantly thinned due to the upwelling of deep mantle materials (Shi et al., 2005, 2017; Mi et al., 2009; Liu et al., 2015).

6 Conclusions

Previous studies in the Ying-Qiong Basin mainly focus on the active time and rate of the main faults and their relationship with the growth of the basin, but there are few studies on the depths of fault activities. Based on wavelet decomposition of the Bouguer gravity field and power spectrum analysis, this paper estimated the active depth ranges of the main controlling faults in the Yinggehai Basin and the Qiongdongnan Basin. In the Yinggehai Basin, the trending of the four main faults A, B, C and D is generally NW trending, and fault A has the largest activity depth range of 5 – 39 km. The active depth ranges of faults C and D are all 15 – 39 km, and their gravity responses are mostly reflected in the third- to fifth-order detailed fields. The active depth range of fault B is smallest between 26.5 and 39 km, and the gravity response is mostly reflected in the fourth- to fifth-order detailed fields. Compared with the Yinggehai Basin, the active depth of faults in the Qiongdongnan Basin is relatively shallow. Among them, the fault zone H with E-W strike is significantly marked in the second- to fifth-order detailed fields with an active depth range from 8 to 39 km. The gravity response of fault N is obvious in the second- to thirdorder detailed fields with an active depth range between 8 and 15 km. Aside from the first two, the gravity responses of the remaining faults are mostly reflected in the secondto fourth-order detail fields with the active depth range between 8 and 26.5 km.

The depths obtained by the gravity power spectrum method used in this paper are not accurate enough. It is suggested that joint inversion should be carried out in combination with gravity and seismic data in future.

Acknowledgements

We thank Wessel & Smith (https://www.soest.hawaii.edu/gmt) for the free use of GMT software, by which most figures in this paper were produced. This work was supported by the National Natural Science Foundation of China (Nos. 41530963, 91858215 and 41906048), the Fundamental Research Funds for the Central Universities (No. 201964015) and the Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology (No. MMRZZ201801).