Three-dimensional direct gravity inversion for Moho and basement depths of the Tuchinh-Vungmay basin, offshore southeast Vietnam, incorporating a lithosphere thermal gravity anomaly correction

Abstract This paper presents the determination of the Moho and basement depths of Tuchinh-Vungmay basin (TCVMB) offshore southeastern Vietnam by the three dimension direct gravity inversion. The Moho depth was predicted from the mantle residual gravity anomaly with the lithosphere thermal gravity correction. The downward continuation of the basement residual gravity anomaly is also applied to enhance the basement topography’s resolution. The mean depths of the basement and Moho surfaces were constrained by the power density spectrum (PDS) of the residual gravity anomalies and the oceanic bottom seismic (OBS) data. The predicted Moho depth varies from 13.5 km to 23 km and the basement depth is from some hundred meters to 8.5 km. The gravity basement topography has higher resolution and detail than the National Oceanic and Atmospheric Administration (NOAA) seismic basement.


Introduction
Marine satellite gravity data visually illustrates the spatial distribution of the earth's crustal structure, such as basins, graben, seamounts, buried volcanoes, faults, and so on, from the shallow to deep parts of the earth (Sandwell and Smith, 2009;Sandwell et al. 2014).The data covers the entire world sea area within a 1 0 x 1 0 data grid with an accuracy of 1 mGal (Sandwell et al. 2013(Sandwell et al. , 2014;;Emmanuel et al. 2014).Hence, it is a beneficial data source for creating a structural map of the sea at a medium scale (Nguyen et al. 2004(Nguyen et al. , 2020;;Braitenberg et al. 2006;Greenhalgh and Kusznir, 2007;Chappell and Kusznir, 2008;Nguyen and Nguyen 2013;Khalid et al. 2018Khalid et al. , 2022;;Casulla et al. 2022;Sahoo and Pal, 2022).The determination of the Moho depth, sedimentary basement depth, and crustal thickness are essential to understand the structure, evolutionary history, and geodynamic mechanism of the earth's crust, as well as the location of the oceanic-continental transition at the rifted continental margin.The age and amplitude of the lithospheric crust thinning influence the current lithosphere temperature of the rifted continental margin.Variation in lithosphere temperature causes changes in lithosphere density, creating a long-wavelength and a large-amplitude lithosphere thermal gravity anomaly.The lithosphere thermal gravity anomaly has maximum values reaching À380 mGal in the young oceanic crust (Greenhalgh and Kusznir, 2007;Chappell and Kusznir, 2008).Correction of lithosphere thermal gravity anomalies in the calculations of the Moho depths in the rifted continental margin, as well as the oceanic crust, has been used by several authors (Greenhalgh and Kusznir, 2007;Chappell and Kusznir, 2008;Sahoo and Pal, 2022).The results showed that the Moho depth calculation without considering the lithosphere thermal anomaly correction might get over/underestimate Moho depth (Greenhalgh and Kusznir, 2007;Chappell and Kusznir, 2008;Sahoo and Pal, 2022).
The Tu Chinh-Vung May basin (TCVMB) is located at the rifted continental margin of the East Vietnam Sea (South China Sea), offshore southeast Vietnam (Figure 1).In this area, the bathymetry varies from a few hundred meters to 2.3 km.It is bounded by the Nam Con Son basin to the west, Truong Sa archipelago to the east, the continentaloceanic transition zone linked to the seafloor spreading centre of the Southwest Sub-basin to the north, and the Natuna basin to the south.The lithospheric crust density in this area might be influenced by lithospheric thermal changes like other rifted continental margins in the sea world.Determining the depth of the Moho surface by inverting gravity Figure 1.Location of the studied area (red square) and major structural units of the studied regions.The black solid line is the magnetic isochrons line; the bold solid green line is the continental-oceanic boundary (COB); the red dots are the Oceanic Bottom Seismic point (OBS); the green dots are drill sites U1433 and U1434.The contour interval of the bathymetry is 500 m.
data without taking into account the lithosphere thermal gravity correction could lead to significant errors (Chappell and Kusznir, 2008, Greenhalgh and Kusznir, 2007, Sahoo and Pal, 2022), leading to low accuracy in determining of the other boundary.In this study, we applied the three dimension (3D) gravitation inversion method taking into account the lithosphere thermal gravity correction (Greenhalgh & Kusznir 2007) to improve the model of the Moho and the sedimentary surface depths on the TCVMB on the rifted continental margin of the East Vietnam Sea.The inversion procedure is employed the following steps: (1) Determinate the Moho depth without taking into account lithosphere thermal gravity anomaly correction; in this step, we used the National Oceanic and Atmospheric Administration (NOAA) seismic total sediment thickness and the General Bathymetric Chart of the Oceans (GEBCO) bathymetry data to define the mantle residual gravity anomaly and then inverted to Moho depth; (2) Calculate the lithosphere thermal gravity anomaly from the crust thickness that defined by the obtained Moho depth minus the NOAA seismic basement depth; (3) Determine the mantle residual gravity anomaly with the lithosphere thermal anomaly correction.Then determine the Moho depth by inverting this lithosphere thermal mantle residual gravity anomaly; (4) Determine the sedimentary basement depth by inverting the basement residual gravity anomaly.The inversion procedure is subsequently a recursive cycle of inverting for Moho and basement depth, calculating the lithosphere thermal gravity anomaly, and updating the mantle residual gravity anomaly until convergence is achieved.In step 4, the final basement residual gravity anomaly was continued downward before taking the inversion in order to enhance the resolution of the basement depth (Nguyen et al. 2020).The results show better predicted Moho and basement topography and offer insight into the earth crustal thickness development.Such information can provide important insights into how rifted continental margin has occurred and how sediments became deposited in the margin sea.

Geological setting
The TCVMB is located at the rifted continental margin southwest of the East Vietnam Sea (EVS).It was influenced by the opening of the EVS.Recent researches indicate that the EVS started opening by $ 32-33 Ma in the Northwest of the EVS (Taylor and Hayes 1983;Briais et al. 1993;Hall 2002;Li et al. 2014), and the terminal age of seafloor spreading is 15-16 Ma (Li et al. 2014).The TCVMB is located in the interaction area between two tectonic provinces: the Truong Sa archipelago in the east, the edge of the Southeast Vietnamese continental shelf in the west, and the Sunda shelf in the south (Figure 1).The Truong Sa archipelago is the continental crust, which extended during the Eocene-Oligocene (Taylor and Hayes, 1983;Schluter et al. 1996).Sediment in this area is relatively thin, and the source of sedimentary material is mainly from Boneo and the Mekong River (Hutchison and Vijayan 2010).The Nam Con Son and Cuu Long basins were formed due to crustal stretching before the seafloor spreading in the Southwest of the EVS.These sedimentary basins were filled with sediments closely related to sea level fluctuations and materials from the Mekong River.The early rifting stage of the Nam Con Son basin began in the Early Eocene-Oligocene and accelerated during the Miocene (Matthews et al. 1997;Lee et al. 2001;Nguyen 2009), while the stretch and subsidence were interrupted by the influence of tectonic inversion in the middle Miocene (Matthews et al. 1997;Hutchison 2004;Nguyen 2009).Although crustal stretching has ceased since 16 Ma, moderate-intensity magma activity still affects the East Vietnam Sea.Volcanic magmatic activities of 8-12 million years old and Pliocene-Pleistocene were recorded in the studied area and various places in the East Vietnam Sea (Lu et al. 2013, Yeh et al. 2012).The sedimentary basement in the TCVMB varies from a few km in the high zones to 6-8 km in the grabens and half-grabens (Nguyen 2009;Lu et al. 2013;Straume et al. 2019;Xiaodong et al. 2020).The studied area consists of four main structural zones, including Bac Huyen chan trough (BHCT), Tu Chinh -Phuc Tan Height (TC-PTH), Vung May trough (VMT), and Vung May-Da Lat height (VM-DLH).The BHCT is located in the north of the study area.It is adjacent to the TC-PTH to the south and the Southwest Sub-basin in the north.The seafloor depth is 2-2.3 km.It is the deepest sea in the study region.The TC-PTH is adjacent to the Nam Con Son basin to the west and the VMT to the south (Figure 1).The TC -PTH is oriented in the northeast-southwest direction.The seafloor depth is the shallowest in the study area (0-1.5 km).The VMT lies between the TC-PTH in the west and the VM-DLH in the east.The seafloor depth varies from 1 to 2 km.The VMT has two main structural directions: the northeast-southwest direction in the southwest-northeast of the trough and the sub-meridian direction in the south, as well as the VM-DLH in the eastern boundary of the VMT.The main structural direction of this study is sub-meridian.

The methodology
The gravity data reflects the vertical structural features rather vaguely, so using prior information to build a hypothetical geological structure model is necessary for the inverse interpretation process.The structural model of the earth crust of the stretching continental margin is assumed to consist of four primary layers: the water layer on top, the second layer as sediment, and the third layer as the crystalline basalt crust and the mantle.In addition, at the rifted continental margin, there are lateral thermal variations in the lithosphere crust due to crustal stretching that form the lithosphere thermal gravity anomaly as described above (Greenhalgh & Kusznir 2007).Therefore, the observed free-air gravity anomaly at the sea level includes the following components: where g faa is the free air gravity anomaly, g top is the gravity effect of the seafloor topography; g s is the gravity effect of the basement topography; g mra is gravity effect of the Moho topography (or the mantle residual gravity anomaly) and g t is the lithosphere thermal gravity anomaly.
The observed gravity data is processed for inverting the residual gravity anomaly to determine the depth of Moho and the sedimentary basement, as shown in Figure 2. The steps of gravity anomaly correction and gravity inversion are calculated as follows (Figure 2): Determine the lithosphere thermal mantle residual gravity anomaly: According to the formula (1), the gravity effect of the Moho topography is defined by the free air gravity anomaly minus the gravity effect of seafloor topography (g top ), the basement topography (g s ), the lithosphere thermal gravity anomaly (g t ) (known as the lithosphere thermal mantle residual gravity anomaly): Determine the residual gravity effect of the sedimentary basement: the residual gravity effect of the sedimentary basement is calculated by the free air gravity anomaly minus the gravity effect of the seafloor topography (g top ) and the Moho topography (g Moh ): where g Moh is the gravity effect of the Moho topography that it is inverted from the lithosphere thermal mantle residual gravity anomaly.
Gravity effects of the density boundaries like seafloor or Moho topographies are calculated by Parker's 3D forward problem method (Parker, 1972): where F [] denotes the 2D forward Fourier transform; Dg is gravity effect of the seafloor or Moho surface in mGal, G is the universal gravitational constant (¼ 6.67 10 À (N.cm 2 g Àg ); Dq is density contrast between seawater and sediment, between sediment and crust or between mantle and crust (in g/cm 3 ); k is wavenumber; d 0 is the mean depth of the boundary (in cm), and h(x, y) is the topography of the boundary measured from a plane at mean depth of the boundary (d 0 ) below the observation plane.
In this calculation, seawater-sediment density contrast is referenced in the down-hole gamma-ray logging data at well sites U1433 and U1434 (Expedition 349 Scientists 2014) in the Southwest Sub-basin (see location in Figure 1).According to the gamma-ray measured data, the bulk density of sediments increases with depth from 1.4 to approximately 2 g/cm 3 in the uppermost 150 m (meters below the seafloor).The entire sediment layer's average bulk density is estimated at 1.97 g/cm 3 (Nguyen et al. 2020).Therefore, if the density of seawater is chosen to be 1.03 g/cm 3 , the density contrast of the seafloor surface is determined to be 0.94 g/cm 3 .The density contrast of the Moho surface was chosen to be 0.44 g/cm 3 (Nissen and Hayes, 1995;Mooney and Kaban, 2010;Kaban and Walter, 2001;Nguyen and Nguyen, 2013;Nguyen et al. 2020).To improve the resolution of the basement topography obtained from the basement residual gravity anomaly, we also perform calculations for the downward continuation of the basement residual gravity anomaly before calculating inversion.In this calculation, we use Tran and Nguyen's downward continuation algorithm, which gives high accuracy and stability results (Tran and Nguyen, 2020).
Determine the lithosphere thermal gravity anomaly: The lithosphere thermal gravity anomaly can be estimated from McKenzie's the cooling plate model (McKenzie, 1978).In present work, we use the formula of Greenhalgh and Kusznir (2007) for calculating the lithosphere thermal gravity anomaly: where: G is the universal gravity constant (6.67 10 À8 (N.cm 2 g À2 ); a is the lithosphere thickness and is equal to 125 km; a is the coefficient of thermal expansion and as equal as 3.28 10 5 0 C À1 ; q ¼ 3.3 g. cm 3 is the lithosphere density; T m ¼ 1300 0 C is the base lithosphere temperature; s ¼ 65 Ma, is the lithosphere cooling thermal decay constant and t is the lithosphere thermal equilibration time (Ma).b is the lithosphere stretching factor which is the ratio of the initial continental crustal thickness (ct 0 ) to the present continental crustal thickness (ct now ) in the case of continental margin lithosphere (b ¼ ct 0 /ct now ).The magnitude of gravity anomaly g t in formula ( 5) is generated by b and t.
In formula (5) for calculating the lithospheric thermal gravity anomaly (g t ), it is necessary to determine the lithosphere stretching factor, that is, to know the present crust thickness (ct mow ) and the initial continental crustal thickness (ct 0 ).To overcome this problem, we use the procedure of the recursive cycle of inversion proposed by Chappell and Kusznir (2008).We first reverse the mantle residual anomaly to determine the Moho depth without the lithosphere thermal gravity anomaly correction.We initially estimate the crust thickness to calculate the lithosphere thinning factor with the initial continental crustal thickness (ct 0 ) is 30 km (Nguyen et al. 2004, Nguyen andNguyen 2013).We then calculate the initial lithosphere thermal gravity anomaly according to formula (5) and subtract this value from the mantle residual anomaly to get the lithosphere thermal mantle residual gravity anomaly.The inversion is subsequently a recursive cycle of inverting for Moho and basement depth, calculating the lithosphere thermal gravity anomaly, and updating the mantle residual gravity anomaly until convergence is achieved (Figure 2).In the study area, the time of lithosphere thermal equilibrium (t) was chosen to equal the time of the sea opening of the East Vietnam Sea.According to Briais et al. (1993) and Li et al. (2014), the East Vietnam Sea started opening about 32-33 Million years ago, so in this calculation, we chose t as 32 Ma.Determine the Moho and sedimentary basement depths from the residual gravity anomaly: The basement residual gravity anomaly (g s ) and the mantle residual gravity anomaly (g mra ) are inverted by three-dimensional direct inversion algorithm mentioned in the previous works (Oldenburg, 1974, Chamot-Rooke et al., 1997, Huchon et al., 1998, Fu and Cazenave, 2001, Nguyen and Nguyen, 2013, Sahoo and Pal 2021): where: h(x, y) is the topography undulation of the sedimentary basement; F Àe is the two dimension inverse Fourier transform; F is the two dimension forward Fourier transform; g s is the gravitational effect of the sedimentary basement or Moho; In formula ( 6), the mean depth of the basement surface (d 0 ) and the density contrast (Dq) are two quantities that need to be known in advance.In this calculation, the initial mean depth (d 0 ) is determined by the power density spectrum (PDS) of the residual gravity anomaly.The PDS (Spector andGranti, 1970, Blakely 1995) is a valuable method to estimate objectively the mean depth of the density boundary from the relation of the slope of the logarithm of the PDS of the gravity anomaly and the wavenumber that doesn't require any prior knowledge of the source body.The initial density contrast (Dq q ¼ 0.24 g/ 3 ) referenced to the published data in the offshore basins and the studied area (Mooney andKaban, 2010, Kaban andWalter, 2001;Braitenberg et al. 2006, Huchon et al. 1998, Nguyen and Nguyen, 2013).The final density contrast (Dq) and mean depth of the boundaries (d 0 ) are constrained by the published OBS data in the region (Xiaodong et al. 2020).

Used data and initial gravity correction
In this study, we collect the bathymetry data from GEBCO's current gridded bathymetry data set at the website https://www.gebco.net/data_and_products/gridded_bathymetry_data/ (Figure 1).It is a global terrain model for ocean and land providing elevation data in meter, on a 15 arc-second interval grid.The bathymetry ranges from 0 to 2.3 km in the study area.The satellite gravity data sources are collected from the website https://topex.ucsd.edu/cgi-bin/get_data.cgi,(Sandwell et al. 2014, Emmanuel et al. 2014, Sandwell and Smith, 2009).The gravity data is derived from the cryosat-2, Enivsat and Hason-1 satellite altimeter data sources with a data grid of 1 0 x 1 0 and a maximum accuracy of 1 mGal (Emmanuel et al. 2014).Most of the data are upscale in the anomalous band with wavelengths from 12-40 km, corresponding to structures usually about 6 km in size.Figure 3a is a free-air gravity anomaly map of the studied area.The gravity anomaly value ranges from À25 to 100 mGal.Many positive isometric anomalies with amplitudes from 20 to 40 mGal appear on the free air gravity anomaly map, especially, the highest block up to 100 mGal in the VM-DLH.The gravity anomalies are oriented mainly northeast-southwest and north-south directions.The north-south oriented gravity anomaly occurs in the south and northeast of the VMT.The northeast-southwest oriented gravity anomalies occur in the TC-PTH, notably in the northeast and southwest of the studied area.Figure 3b is the gravity effect of the seafloor topography is calculated by the formula (4) with the seawater-sediment density contract of 0.94 g/cm 3 .The total sediment thickness of the study area is collected from the published database of the World's Oceans and Marginal Seas (Straume et al. 2019) at the NOAA website https://ngdc.noaa.gov/mgg/sedthick/.The sediment thickness data is updated from many sources with a data grid of 5-arc-minute.The initial sedimentary basement depth is defined equally as the seafloor depth plus the total sediment thickness, as shown in Figure 3c.The seismic sedimentary basement depth in the study area varies from 2.5 km in the TC-PTH to 7.5 km in the VMT and the mean basement depth of 5 km.The gravity effect of the sedimentary basement topography is calculated by the formula (4) as shown in Figure 3d.Bouguer gravity anomaly defined from the free air gravity anomaly subtracting the gravity effect of the seafloor topography (Dg faa -g top ), as shown in Figure 3e.The Bouguer gravity anomaly in the studied area ranges from À40 mGal to 60 mGal.The TC-PTH has the smallest anomalous value being from À40 to 0 mGal.The largest anomalous value ranges from 20 to 60 mGal in the north of the study area.In the VMT, the gravity anomaly is from 0 to 30 mGal.The mantle residual gravity anomaly without lithosphere thermal correction (LTC) is calculated by the Bouguer gravity anomaly subtracting the gravity effect of the basement topography (Figure 3g).The mantle residual gravity anomaly ranges from À40 to À10 mGal in the TC-PTH and VM-DLH to 10-30 mGal in the VMT and 20-60 mGal in the BHCT.southern half of the study area.The initial earth crustal thickness was determined by the Moho depth without the LTC minus the sedimentary basement depth (Figure 5b).

Lithosphere thermal corrected Moho depth
After several iteration calculations to determine the most suitable lithospheric thermal corrected Moho depth value, we found that the RMS error between the two iterations was getting bigger and bigger after each iteration.For example, after the first iteration, the root mean square error is 0.36 km, the second iteration is 0.45 km, and the third iteration is 0.48 km.Therefore, we stopped at the first iteration to calculate the lithospheric thermal corrected Moho surface depth.Figure 6 shows the lithospheric thermal gravity anomaly (Figure 6a) and the lithospheric thermal mantle residual gravity anomaly (Figure 6b).The mean depth of the Moho surface of the study area determined from the PDS of the lithosphere thermal mantle residual gravity anomaly is 17.9 km (Figure 7).We inverted the lithosphere thermal mantle residual gravity anomaly with the estimated mean Moho depth (d 0 ) of 17.9 km, and the Moho depth was determined, as shown in Figure 8. Figure 9 presents the OBS profile (Xiaodong et al. 2020) that consists of the Moho and basement depths from the OBS inversion (green square dots), the Moho without the LTC (red square dots) and the lithosphere thermal corrected Moho (black dashed line).The comparison between gravity Moho depth and OBS Moho depth reveals that the 3D gravity inverted results are quite consistent with the OBS analysis results (Figure 9).The RMS error between the lithosphere thermal corrected Moho and OBS Moho is 1.9 km.The lithosphere thermal corrected Moho depth varies from 23 km to 13.5 km.The most profound Moho depth is 20-23 km in the TC-PTH, and the shallowest Moho depth is 13.5-15 km in the VMT.

Basement residual gravity anomaly
The gravity effect of the sedimentary basement is determined by subtracting the gravity effect of the Moho surface with the lithosphere thermal gravity correction from Bouguer gravity anomaly.Figure 10 shows the basement residual gravity anomaly at the sea level and at 3 km downward continuation.The value of the residual basement anomaly at sea level varies from 10 mGal to 50 mGal in the TC-PTH and VM-DLH (Figure 10a).In the  VMT, the residual gravity anomaly varies from À40 to 10 mGal.The residual gravity anomaly varies from 20 to 30 mGal in BHCT. Figure 10b is the basement residual gravity anomalies that are continued downward to 3.2 km.The residual gravity anomaly at the 3.2 km downward continuation varies from 20 to 70 mGal in the TC-PT and VM-DL heights and from 10 to À50 mGal in the VMT.Thus, the amplitude of the basement residual gravity anomaly at 3.2 km is 10-30 mGal larger than that at the sea level.On the map of the basement residual gravity anomaly at the 3.2 km downward continuation, the gravity anomaly exhibits a higher resolution than the gravity anomalies at the sea level.For instance, the local, separate gravity anomalies, such as saddle structures, peaks, and sags appear clearly on the basement residual gravity anomaly at 3.2 km downward continuation but they appear very faint in the basement residual gravity anomaly map at the sea level (Figure 10).

Basement depth and sedimentary thickness
Figure 11 presents the PDS of the basement residual gravity anomaly of the studied area.The PDS graph reveals a distinct linear segment that is fitted by a linear regression equation Y =-63.864Ã X presents the PDS 2 ¼ 0.98).The mean basement depth is estimated by 5.1 km.This mean basement depth is the initial mean basement depth in the inversion of the basement residual gravity anomaly.A combination of the mean basement depth (d 0 ) and density contrast (Dq) is adjusted until the calculated gravity basement depths are closest to the OBS basement depths.We finally determined an acceptable combination of the density contrast Dq q ¼ 0.3 g/ 3 and mean basement depth d 0 ¼ 4.9 km.The comparison between gravity basement depth and OBS basement depth reveals that the 3D gravity inverse analysis results are quite consistent with the OBS results (Figure 9).
The basement depth is obtained from the 3D inversion of basement residual gravity anomaly at the sea level is presented in Figure 12.The obtained basement map imaged well the depressions and heights in the studied area (Figure 12).At the northwestern edge of the studied area, the basement depth depth varies from 5-7.5 km and the sediment thickness is 4-7 km.In the TC-PTH, the basement topography is oriented northeastsouthwest direction.It appears there are alternating heights and depressions.The depth of  the basement varies from 0-2.5 km in the heights and to 3-4 km in the depression zones.The sedimentary thickness varies from 0 to 3.5 km.Here, the high chains that are formed extend in the northeastsouthwest direction.In the VMT, the basement depth varies from 4 -8.5 km and sedimentary thickness ranges from 3 to 7 km.The basement depth lifts up to 3-6 km in the east while lowers to 6-8.5 km in the south of the VMT.In the BHCT, the basement depth varies from 3 to 4.5 km corresponding to the sediment thickness from 1 to 2.5 km.We can see that the sedimentary thickness is the thinnest in the TC-PTHs and BTC trough and the thickest in the VMT.

Crustal thickness
Figure 13 shows the map of the earth crustal thickness calculated by subtracting the basement depth from the Moho depth.The crust thickness in the studied area varies from 9.5 to 22 km.The crust thickness varies from 16 to 21 km in the TC-PTH and VM-DLH.This is the largest crust thickness in the study area that forms a thick crust extending NE-SW across the study area.The BHCT is a thin crust zone with the thickness of 12-15 km.The VMT is the thinnest crust zone varying from 9.5 to 14.5 km.The thinnest crust (9.5-11 km) is in the south of the VMT.Sandwiched between the NE-SW thickest crust ranges are two zones with the thinnest crust (9.5-14 km), which are the VMT in the southeast and the BHCT in the north.

Discussion
According to the formula (5), the magnitude of the lithosphere thermal gravity anomaly g t is governed by the lithosphere stretching factor (b ¼ ct 0 /ct now ) and in fact when t and ct 0 are constants, g t is depended only ct now .When the present continental crustal thickness (ct now ) is small (Moho surface uplifted), it will produce a large amplitude of lithosphere thermal anomaly and vice versa.So the lithosphere thermal factor causes the lithosphere thermal mantle residual gravity anomaly to have a larger value in the uplifted Moho area and smaller value in the sunk down Moho area.Therefore, calculating the Moho surface depth without the thermal correction is necessary to achieve as much reliability and accuracy as possible.The mean Moho depth estimated by the PDS of the mantle residual gravity anomaly with and without the lithosphere thermal correction gives almost the same value (17.98 À 17.91 km).However, the value of Moho depth determined from these two mantle residual gravity anomalies has a clear difference.In the area of deep Moho depth, for example, in the TC-PTH, the LTC Moho depth is about 1.5-2 km deeper than the Moho depth without the LTC.In contrast, in the uplifted Moho area, such as the south of the VMT, the LTC Moho depth is about 1.5 km shallower than the Moho without the LTC.The lithosphere thermal factor in the stretching continental margin has made the Moho surface structure more curved than the Moho surface in the continental crust without stretching.On the OBS line section, the Moho depth without the LTC has the RMS error of 1.5 km compared with the OBS Moho, while the LTC Moho surface depth has the RMS error of 1.9 km.However, the LTC Moho is different from the Moho without the LTC.The LTC Moho surface is better constrained by the isotactic compensation model where the seabed topography and the basement surface are uplifted, while the OBS Moho does not consistent well with the isotactic compensation model.For example, at the beginning of the OBS line (from km 50 to km 200), the seabed's topography and the basement are elevated, and the OBS Moho is also raised.In contrast, the LTC Moho in this area is lowered, consistent well with the isotactic compensation model.With this comparison, we assume that the OBS Moho in this case is not really a good result.It could be shallower than it really is.
The south and central area of the VMT has the most uplifted Moho surface and forms a thin crust zone extending from the northeast to the southwest and from the north to the south of the studied area.The southwest and northeast areas of the VMT have the thinnest earth crustal thickness and forms a thin crust zone extending from the northeast to the southwest and from the north to the south in the VMT (see Figure 13).We suggest that the TCVM basin could be formed and developed in two stages.In the first stage, the TCVM basin was formed and evolved in the NE-SW direction during the opening of the Southwest Sub-basin (Nguyen 2009).As a result, the grabens and half-grabens were formed in the northeast-southwest direction.The second stage of the rifting process was redirected to the east-west to create the thin crust zone in the North-South direction.In the TC-PTH area, the deepest Moho depth (22-23 km) is reflected by the lowest Bouguer gravity anomaly values (-20-0 mGal), and the highest Moho surface (13.5-15 km) in the VMT is reflected by the high positive Bouguer gravity anomaly (10-30 mGal).Figure 14a is a map of magnetic field anomalies in the study area (Takemi and Toshihiro, 2021).The magnetic anomaly field has high anomalous amplitude (100-200 nT).Here appear pairs of high negative-positive magnetic anomalies that characterize the appearance of magma masses (Figure 14a).This high-amplitude magnetic anomaly may be related to intrusive/eruptive magmatic activities that cause the Moho to rise up in these areas.The seismic cross-section in the VMT also clearly shows the activities of erupting/instructing magma (Figures 14b and 15b).We suggest that the magmatic activity greatly affects the rock composition of the basement in this area.This may explain the density contrast thru the basement surface in this area rise up to 0.3 g/cm 3 .The basement depth map obtained from the gravity anomaly inversion has the main structures and depth is quite similar to the basement depth map produced from the NOAA total sediment thickness database (Figures 3c and 12a).However, the sedimentary basement depth inverted from the basement residual gravity anomaly has a much higher resolution and detail than the NOAA seismic basement map.The local structural zones, such as uplift zones or grabens, are shown very clearly on the basement map according to gravity inversion.In contrast, these local structural zones were invisible on the NOAA seismic basement map (see Figure 3c).The low resolution and poor detail of the NOAA seismic basement map can be seen more clearly on seismic lines in the study area.For example, according to the seismic sections AB and CD (Figure 15a, b), the basement topography includes clear uplift and graben zones.The  NOAA seismic basement surface is relatively smooth and hardly shows these uplift and graben zone structures (Figure 15c, d).While the gravity basement boundaries show these uplift and graben zone structures well (Figure 15c, d).It is clear that although the NOAA sediment thickness data is of low detail, it is a valuable initial input in the gravity anomaly inversion to determine the Moho and the sedimentary basement depths.The sedimentary basement map obtained from gravity anomaly inversion has greater detail and reliability.The local structural units are shown quite clearly on the map of the sedimentary basement.The inverse results from the gravity anomalies at the sea level and at different downward continuation levels show that the basement topography map calculated from the continued downward gravity anomaly has a higher resolution than that from the gravity anomaly at the sea level (see Figure 16).On the basement map from the 3.2 km continued downward gravity anomaly, small-sized structures such as saddleshaped structures or protrusions can be identified, while they are poor visible on the basement map of the gravity anomaly at the sea level.Figure 15c and d shows that the basement surface determined from the 3.2 km continued downward basement residual gravity anomaly (blue dash line) reflects the basement structure better, i.e., the structure of uplifts and depressions, compared to the basement boundary determined by the basement residual gravity anomaly at sea level.The uplifts and depression block structures according to the downward continuation residual gravity anomaly are clearly shown in accordance with the seismic section, while the basement boundary according to the residual gravity anomaly at sea level shows faintly.It is clear that the downward continuation of the residual gravity anomaly near the basement gave a much better deconstruction of the basement than that from the gravity anomaly at the sea level.

Conclusion
The major conclusions of this study are the following: Moho depth in the TCVMB varies from 13.5 to 23 km.The deepest Moho surface is located in the TC-PTH (23-19 km) and the area with the most elevated Moho surface is in the VMT (13.5-15 km) and the BHCT (14-15 km).The basement depth of the TCVMB is from 0.5 to 8.5 km.The deepest basement depth is in the south of the VMT (5-8.5 km) and the shallowest basement depth is in TC-PTH (1-4 km).The basement terrain is oriented towards the NE-SW direction in the TC-PTH and northwest of the VMT, the N-S direction in the south of the VMT and the northwest of the study area.The earth crust ranges from 9.5 to 21 km.The TC-PTH and VM-DLH zone are the largest earth crust thickness (16-21 km) and the thinnest crust in the VMT (9.5-14 km).The TCVMB is a rifted continental slope basin has been formed and evolved on the thin and weak earth crust and in two stages: stage 1 begins forming in the NE-SW direction during the opening of the Southwest sub-basin and stage 2, the process of rifting is redirected in the East -West, forming the North -South direction thin crust.The inversion procedure applied to gravity data in this work allows to determine rapidly and in detail the structural characteristics of the sedimentary basement utilizing the worldwide published data as satellite gravity, bathymetry and sediment thickness.This opens up the possibility of building a worldwide map of the sedimentary basement depth with more detail and reliability than the currently published seismic data.The inverse interpretation from the downward continuation gravity anomaly in the sediment basin areas could provide a more detailed and resolution basement topography than that from the gravity anomaly at sea level.The lithosphere thermal gravity anomaly has a great influence on gravity inversion to determine the deep crustal structure in the rifted continental margin.The correction of lithospheric thermal gravity anomalies in determining the Moho surface depth at the rifted continental margin is necessary.However, calculating the Moho depth without the thermal correction necessarily achieve as much reliability and accuracy as possible.

Figure 2 .
Figure 2. The inversion workflow for determining Moho and basement depths incorporating an iterative solution for the lithosphere thermal gravity anomaly.

Figure 3 .
Figure 3. (a) Free air gravity anomaly, (b) Gravity effect of the seabed topography, (c) Sedimentary basement depth and (d) Gravity effect of the sediment basement depth, (e) Bouguer gravity anomaly, (g) Mantle residual gravity anomaly without the lithosphere thermal correction.
4.1.1.Moho depth without lithosphere thermal correction Figure 4 presents the PDS of the mantle residual gravity anomaly of the studied area.The PDS graph reveals a distinct linear segment that is fitted by a linear regression equation Y =-225.86Ã X þ5.3398 (with R 2 ¼ 0.92).According to the PDS method (Spector and Granti 1970; Blakely 1995), the mean Moho depth is determined by 225.86/(4Ã p)¼17.98 km.The Moho depth showing in Figure 5a was determined by inverting the mantle residual gravity anomaly without the LTC, with the mean Moho depth (d 0 ) of $18 km.The root mean square (RMS) error between calculated Moho and the OBS Moho profile (Xiaodong et al. 2020) is 1.5 km.The obtained Moho depth without the LTC varies from 21 to 15 km.It is 20-21 km along the TC-PTH and VM-DLH and 15-17 km in the VMT and the north of the study area.Moho surface topography consists of two main structural directions: northeast-southwest in the northern half of the study area and north-south in the

Figure 4 .
Figure 4.The graphs of the PDS of the mantle residual gravity anomaly without the LTC (Figure 3h).The mean Moho depth is estimated at $18 km.

Figure 5 .
Figure 5. (a) The Moho depth from gravity inversion without the lithosphere thermal correction; (b) The initial crustal thickness is defined by Moho depth without the LTC subtracting the seismic basement depth.

Figure 6 .
Figure 6.(a) The lithosphere thermal gravity anomaly and (b) The lithosphere thermal mantle residual gravity anomaly of the study area.

Figure 7 .
Figure 7.The graphs of the PDS of the lithosphere thermal mantle residual gravity anomaly.The mean Moho depth is estimated being 17.9 km.

Figure 8 .
Figure 8.The Moho depth from inversion of the the lithosphere thermal mantle gravity residual anomaly.The lithosphere thermal corrected Moho depth is the range of 13.5-23 km.The contour interval is 1 km.

Figure 9 .
Figure 9.The Moho and basement depths are along the OBS profile (Xiaodong et al. 2020).The green square dots are the Moho and basement depths from the OBS data and red square dots are the Moho without the LTC.The black dash lines are the LTC Moho.The RMS error between lithosphere thermal corrected Moho and OBS Moho is 1.9 km.

Figure 10 .
Figure 10.(a) Basement residual gravity anomaly at sea level and (b) Basement residual gravity anomaly at 3.2 km downward continuation.

Figure 11 .
Figure 11.The PDS of the basement residual gravity anomaly.The mean basement depth estimated by the power density spectrum method is 5.1 km.

Figure 12 .
Figure 12.(a) Basement depth from the inversion of the basement residual gravity anomaly and (b) The sediment thickness.The contour interval is 1 km.

Figure 13 .
Figure 13.Crustal thickness of the study area.The contour interval is 1.0 km.

Figure 14 .
Figure 14.Magnetic anomaly and seismic lines in the studied area show a high magnetic range from the TC-PTH to the VMT and magmatic activities.

Figure 15 .
Figure 15.Seismic sections (a) and (b) show the topography of the sedimentary basement consisting of uplift blocks and grabens.Figures (c) and (d) show the basement boundary obtained from inversion of basement residual gravity anomalies at sea level and upward continuation of 0.8 km, 1.6 km, 2.4 km and 3.2 km (solid lines) and basement surface according to NOAA seismic total sediment thickness data (black, dashed line).

Figure 16 .
Figure 16.The map of the basement depth from inversion of the basement residual gravity anomaly at (a) 1.6 km downward continuation (a) and 3.2 km downward continuation.