Application of Geoid Anomalies to the Tectonic Research in the East Asian Continental Margin

WU Xiaoyang, XING Junhui, 3), *, LI Chaoyang, LIU Xinzhe, YANG Kai, CHEN Hongyan, and GONG Wei



Application of Geoid Anomalies to the Tectonic Research in the East Asian Continental Margin

WU Xiaoyang1), 2), XING Junhui1), 2), 3), *, LI Chaoyang1), 2), LIU Xinzhe1), 2), YANG Kai1), 2), CHEN Hongyan1), 2), and GONG Wei1), 2)

1),,266100,2),,266100,3),,266071,

In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral. The East Asian con- tinental margin was selected as the study area. The residual geoid anomalies have been calculated by programming.On the basis of residual geoid anomalies at various orders, the interlayer geoid anomalies at different depths were calculated to depict the spatial distribution characteristics of the residual geoid. Finally, we conducted a detailed geophysical interpretation for the study area according to the geoid anomalies in combination with other geophysical datasets. Four conclusions can be outlined as follows: 1) it is impracticable that geoid anomalies are used in the interpretation of the shallow objects due to the influence of the terrain; 2) the anomalies of residual geoid can reflect the intensity of small-scale mantle convection in the asthenosphere; 3) the interlayer geoid anomalies can reflect the magmatic activities associated with the mantle convection and mantle plume in different scales; 4) the study of the geoid may provide an approach for the research of the subduction zone, mantle convection and mantle plume.

EGM2008 gravity field model; geoid anomalies; the East Asian continental margin; structural interpretations

1 Introduction

The marine geoid, as the manifestation of the gravity field, is an important reference information for marine geodetic and oceanographic researches. It implies a wealth of tectonic dynamics information (Lu, 2002). In addition, the geoid is more sensitive to the density distribution of the earth’s interior.The densities of the earth’s interior materials are closely related to the shape, formation and evolution of the earth, plate movement, isostatic adjustment, geodynamics processes and the distribution of mineral resources. Therefore, the geoid anomalies can be used to study the interior structural features of the earth (Sree- jith., 2013).Based onthe characteristics of wavelength, the geoids at three different wavelengths can be extracted: 1) the long wavelength geoid reflecting the distribution of deep mantle materials and the undulation of core-mantle boundary; 2) the medium wavelength geoid reflecting the undulation of Moho and the distribution of upper mantle materials; 3) the short wavelength geoid reflecting the influence of terrain and the uneven distribu-tion of the crust (Featherstone, 1997; Fang, 2006; Kamguia., 2008).

The undulation of the geoid corresponds tothe gravity anomalies, which is the comprehensive reflection of the uneven distribution of the earth’s interior materials. According to Newton’s Gravitational Formula (the Bruns Formula), the geoid anomalies contain the information of the earth’s interior. The gravity anomalies are inversely proportional to the square of the depth of field source. The gravity anomalies change drastically with the increase of the depth of the field source (Ke., 2009). The geoid is also inversely proportional to the depth of field source while it decreases relatively slowwith the increase of the depth of field source. Therefore, the geoid has more advantages than gravity when it is used to reflect the tectonic features of the earth’s interior.Since the 1980s, the geoid data has been used for detecting the sea- mounts (Lazarewicz and Schwank, 1982), predicting the submarine volcano (Anny and Kien, 1984) and studying the subduction zones (Mcadoo, 1981). The current researches mainly focus on the depth of field source (, Ebbingand Olesen, 2005; Lin., 2012), the power pattern of structure (, Bowin, 1983; Jin and Gao, 2001; Fang and Hsu, 2002; Gao and Jin, 2003) as well as the inversion of density structure of the earth’s interior (, Featherstone., 2001; Bhattacharyyaand Majumdar, 2006; Cornaglia., 2009; Świeczak.,2009; Wang and Fang, 2014).

Although the previous studies have extracted residual geoid anomalies and introduced the concept of depth in such researches, they do not achieve the separation and extraction of the deep and shallow anomalies. The subduction zones in the East Asian continental margin are the frontiers of scientific research, which have complex structural features, evolutionary history and subduction patterns (Wu and Liu, 2004). However, subduction patterns and processes still need further study in some areas. So the East Asian continental margin as the study area in the present paper is characterized by island-arc-trench system.The field sources at different depths are studied by combining the gravity geoid, the gravity field model, and the residual geoid anomalies. The interlayer geoids of the target depths are extracted by separating the residual geoids of different order windows. Finally, the characteristics of these anomalies are analyzed based on other related geological and geophysical data. The feasibility of using geoid to interpret the plate tectonic features in the East Asian continental margin is also discussed.

2 Geological Setting

The study area (0˚–45˚N, 100˚–150˚E, Fig.1) is located in the continental margin of East Asia, which is a typical trench-arc-basin system at the junction of the Pacific plate, the Philippine plate and the Eurasian plate. The topography of the study area is complex. It has island arcs, trenches, back arc basins, ridges, plateaus, basins, troughs and other elements of topography. The deepest site is located in the south of Mariana Trench which is >10000m in depth. The depth of the Pacific Ocean is deeper than 6000m generally. There are two group different water depths of the Philippine Sea. The water depth is >5000m to the west of Kyushu Palau Ridge, while the water depth is <5000m to the east of the ridge. The water depths of the first island chain including the Japan Sea, the Okinawa Trough and the South China Sea are about 2000m, and the water depths of the other areas are <1000m (., Li., 2000).

The East Asian continental margin is the interaction zone of the Eurasian plate, the Philippine Sea plate and the Pacific plate, which had experienced a complex evolu- tion process. In Jurassic period, the Pacific plate began to develop and subduct underneath the Eurasian plate (Li., 2013). Subsequently there had been many major changes in the direction of movement. The subduction changed from the direction of SW to NW, then to NNW, and eventually back to NW. It was accompanied by the roll-back of subduction plates, regional extension and more active magma activities (Koppers., 2001; Sharp and Clague, 2006; Zhang., 2008; Sun., 2008). Due to the influence of the convergence of plates, the Philippine Sea began to expand and develop in the late Eocene. Two tectonic extension activities in the N–S direction and the E–W direction formed a series of basins and Mid-ocean Ridges (Zang and Ning, 1996; Sdrolias.,2004; Yin, 2010; Zhang., 2014; Zhang and Zhang, 2015). Since the Quaternary, the trenches, island arcs and sea basins in the East Asian continental margin have reached the pre- sent position. A typical trench-arc-basin system has formed.

Fig.1 Bathymetric map with major tectonic units in the East Asian margin. Data sources: https://www.ngdc.noaa.gov/ mgg/global/global.html. Data accuracy is 1˚×1˚. The division of tectonic units of the East Asian margin is derived from Wu and Liu (2004). Double dashed lines denote Mid-ocean Ridges. Black lines with triangles show the distribution of subduction zones.

The structural boundaries between the Eurasian plate and the Philippine Sea plate are the Ryukyu Trench subduction zone, the Manila Trench subduction zone and the Philippine Trench subduction zone. The Philippine Sea plate dives to the Eurasian plate along the Ryukyu Trench and the Philippine Trench (, Fukao., 1992; Kodaira., 1996; Kubo and Fukuyama, 2003; Fan, 2013; Shang, 2014), while the Eurasian plate subducts underneath the Philippine Sea plate along the Manila Trench (Li., 2013). The tectonic boundary between the Pacific plate and the Philippine Sea plate consists of the Izu-Bonin- Mariana subduction zone, which are formed by the subduction of the Pacific plate towards the Eurasian plate and the subduction of the Caroline plate towards the Philippine Sea plate, respectively (Zang and Ning, 2002). The Japanese Trench subduction zone and the Yap-Palau Trench subduction zone extend to the north and south of this boundary, respectively.

3 Data and Methods

3.1 Data

The Earth Gravitational Model (EGM2008) used in this study was released by the National Geospatial Intelligence Agency (NGA) (http://bgi.omp.obs-mip.fr/data-products/ Toolbox/EGM2008-anomaly-map-visualization). The co- efficient of gravity field of the earth is the main parameter of gravitational potential. If we want to express the gravitational potential of the earth, we must derive the coefficients accurately.Usually, the coefficients can be only determined by the finite order.Therefore, the higher order of the coefficients, the more likely the earth’s gravitational potential can be approximated. EGM2008 is complete to degree and order 2159, and contains additional coefficients up to degree 2190 and order 2159, which is equivalent to the about 9km spatial resolution of the model.The resolution of this model is 5˚×5˚. Over areas covered with high quality gravity data, the discrepancies between EGM2008 geoid undulations and independent GPS/Leveling values are on the order of 5 to 10cm(Pavlis,., 2013). As a result, it has made great progress both in terms of accuracy and resolution.

3.2 Methods

3.2.1 Calculation of the gravity geoid and the residual geoid

Since the study area is located in the ocean,we can not obtain the GPS/leveling data for calibration. Howeverthe previous research results (Pavlis., 2013) showed that the error of earth gravity field model EGM2008 is <10cm in the study area. The precision reaches to centimeter level. Therefore, the geoid of the study area was calculated according to EGM2008 at order 2190. The long wave- length geoid anomalies are determined by deep structures generally. In order to study the effect of a certain layer, the long wavelength components should be subtractedfrom the geoid. Theremaining information is called residual geoid (Kenzie., 1980).

First, we removed model gravity anomalies (∆g) in certain wavelengthsfrom gravity anomalies (∆) to get the residual gravity anomalies:

Then, we calculated model gravity anomalies (∆g) in certain wavelengths by using geopotential coefficients:

, (2)

Finally, we applied the residual gravity anomalies to Stokes integral formula to get the residual geoid ano- malies (N).

whereis normal gravity of the calculated point.

Besides, according to Bowin’s (1986) equivalent point quality source computational formula, we can express the relationship among the field source depthZ, the wave- length, the radius of the earthand the order number of gravity potentialby the following formula:

3.2.2 Calculation of interlayer geoid anomalies

Stokes integral formula for computing the gravity ano- maly geoid can be expressed as:

The difference between two order residual geoids can be expressed by the difference of two order residual gra- vity anomalies:

Therefore, we use the spectrum separation method to filter out the short wavelength components from the re- sidual geoid, and extract the geoid anomalies within the scope of a certain wavelength, which reflects the vertical stratification information in the earth’s interior.

4 Results

According to the above method and principle, we have compiled the corresponding program and formed the software module. The software module has been used to calculate the geoids, residual geoids and interlayer geoids.

4.1 Morphological Characteristics of Geoid

The highest value of the geoid anomalies is 32m in the southwest of the Philippines and Celebes Sea in the study area, while the lowest value is about −27 m in the south of the Mariana Trench (Fig.2). The difference between the highest and lowest value is approximately 60m. In the west of the study area, the geoid shows a ladder-like shape near the coast of China. The geoid gradually rises from −15m to 15m from west to east. The positive values occur in the Japan Sea-the Nankai Trough-the Shikoku Basin, and the Pacific Ocean in the outside of the Izu- Bonin-Japan Trench and the Sulu-Celebes Sea. The geoids in the west Philippines Sea Basin, Parece Vela Sea Basin and the outside of Mariana Trench are slightly lower than the average sea level. In addition, the geoids of the trenches have the same features, which are all negative.

Fig.2 The geoid undulation map in the East Asian margin. The geoid has some differences in different tectonic units. Red and yellow areas represent the uplift zone of geoid. Blue areas represent the depressed zone of geoid. Other plot legends are the same as in Fig.1.

4.2 The Residual Geoid

In order to discuss the role and significance of the residual geoid in researching the shape of the subducting plate, we extract the residual geoid anomalieswith 20km, 30km, 100km, 300km, 500km, 700km, correspnding to the model’s order windows 320, 213, 65, 22, 14 and 10 respectively (Figs.3a–f).

The distribution of residual geoid anomalies shown in Figs.3a and 3b are similar. The variation of the residual geoid anomalies is small, ranging between −1.3 to 1.4m and−3.2 to 2.8m respectively. In most regions,the values of residual geoid anomalies are close to 0m. The contour lines of subduction zone are distributed in beads. Com- pared with Figs.3a and 3b, the residual geoid anomalies varies obviously in Fig.3c, with the range of −12m to 15 m. The outlines of the subduction zone and island arc are gradually clear. On the two sides of the subduction zone are discontinuous positive and negative anomalies. Com- pared with Fig.3c, the variation of anomalies in Fig.3d become more prominent. The distribution area with irre- gular anomalies reduces obviously. Most of the study area has a high value of anomalies. While in the Japan Sea and the west Philippines Basin, the anomalies are low like the residual geoid anomalies in trenches near subduction zones, which are low negative values. The variation of the re- sidual geoid anomalies reaches 34m, from −20m to 14 m (Fig.3e). Positive high anomalies are distributed in shape of long stripalong the island arc within the subduction zone. The values in the region of the Japan-Izu-Bonin- Mariana island arc, the southern part ofthe Okinawa Trough and the Taiwan-PhilippinesIslands are very high. The abnormal values in the peripheral zone, including China’s offshore, are significantly lower than those in Fig.3d. The anomalies of the whole western Philippines Basin are about 0m. The variations of ano- malies expand, ranging from −22m to 22m (Fig.3f). The positive ano- malies in this region is further cutdown. The value of amomalies is reduced to 0m in the Okinawa Trough. The anomalies over the most of Philippines Sea are about 0m except that in the west Philippine Basin they are slightly lower than 0m. The high values in the Japan-Izu-Bonin- Mariana island arc shrink to one side of the trench. Besides, a large range of negative low value anomalies appears in the South China Sea.

4.3 Interlayer Geoid

According to the method of spectrum separation, we extract theinterlayer geoid anomalies when the depths of the field sourcesare 20–30km, 30–100km,100–300km, 300–500km, 500–700km respectively. The corresponding model’s order windows are 213-320 order, 65-213 order, 22-65 order, 14-22 order and 10-14 order, respectively (Figs.4a–e). The anomalies are distributed in shape of beads (Fig.4a). The anomalies in the subduction zone are obviously different from the surrounding areas. The outlines of the trench and island arc are gradually clear when the depth of field sources increases (Fig.4b). The anomalies in the regions ofthe Japan-Izu-Bonin-Mariana Trench and the Ryukyu-Manila-Philippine Trench are ne- gatively low value, while a discontinuous high value ano- maliescan be observed in the island arc on the inner side of the trench. The ranges of original low and high value anomalies arc arefurther expanded (Fig.4c). The contour lines of negative low anomalies are broken at the junction of the Izu-Bonin-Mariana Trench. The anomalies of the whole Philippines Sea plate are about 0m. Fig.4d shows that positive high anomalies are observed in the sub- duction zones, while negative sag anomalies appear at the center of the Philippine Sea plate and negativelow anomalies exist in the South China Sea. The distribution of anomalies significantly varies (Fig.4e). A wide range of anomaly traps appears. Two traps with strong positive high value anomalies are observed in the south and north of the study area. A trap with strong negative low ano- malies is located in the southwest of the study area. Anomalies values in the rest of this region are about 0m.

Fig.3 Residual geoid anomalies in different orders. The depths of field source increase gradually in a–f. Red and yellow areas represent the high density zones. Blue areas represent the low density zones. The green areas indicate that the anomalies are at about zero.

Fig.4 Interlayer geoid anomalies in different orders. The depths of field source increase gradually in a–e. Other legends are the same as in Fig.3.

5 Interpretation of Anomalies

5.1 Interpretation of Geoid Anomalies

The geoid (Fig.2) is the integrated resultsat different field source depths, including the influence of submarine topography, the lithosphere, the mantle and the deeper layers of the earth.Generally, long-wavelength infor- mationpredominates in the geoid, while short-wavelength information genarated by the shallow layersmay be covered (Lin., 2012). In China and adjacent areas, 2-6 order geopotential coefficients are usually used to indicate heterohomogeneous distribution of lower mantle materials; 7-60 order geopotential coefficients represent the effects of upper mantle anomalies; 61-720 order geo- potential coefficients show the effects caused by the lithosphere (Fang and Hsu, 2002). The geoid anomalies are related to the density anomalies of the geological bodies. Due to the rise of the mantle plume which is located in the Pacific ocean of the study area, radiating horizontal displacement of the lithosphere and upper mantle are derived (Tong and Tian, 2017). The geoid ano- malies of Japanese Island and Philippines Islands uplift (Fig.2). The geoid anomalies of the trenches are negative, which may be caused by the subduction of the low density plate.

5.2 Interpretation of the Residual Geoid Anomalies

Fig.3a shows the residual geoid anomalies in order 320, corresponding to the depth of gravity field source no more than 20km. Fig.3b shows the order 213, corresponding to the depth of gravity field source shallower than 30km. The residual geoid anomaly contours appear as beads in the two figures. The useful information can not be drawn under the influence of beaded anomaly contours. Lin. (2012) suggests that the phenomenon is caused by the relief of topography which obscures the true abnormal information. There is a strong correlation between the geoid anomalies and the topography in the area around the Japan-Izu-Bonin-Mariana Trench and the Ryukyu-Mani- la-Philippine Trench (Fig.1). We think the residual geoid anomalies at order 320 and order 213 are mainly affected by the terrain. The interlayer geoid anomalies within the range of 20–30km areshown in Fig.4a.Positive ano- malies are alternating with negative anomalies in the area of the Japan-Izu-Bonin-Mariana Trench and the Manila- Philippine Trench. The interlayer geoid anomalies in the Philippines Sea plate are gentle and slightly larger than 0 m, which is different from those at the plate boundary.The distribution of beaded anomalies contours indicates that it is still influenced by the terrain.Due to the limi- tation of the method, the interference of the terrain infor- mationcannot be filtered out completely in the process of the separation and extraction of the interlayer geoid ano- malies. According to previous research results (Teng.,2003; Hu., 2016), the Moho depths of the Izu-Bonin Trench, the Japan Trench and the Yap Trench are all greater than 20km.The Moho depth of Japan Island, the Okinawa Trough and Philippines Archipelago are even up to 30 km. Because the crust of Philippines Sea is oceanic, its Moho depth is between 7–20km and thinner than 10km in most areas. We suggest that the residual geoid ano- malies in Figs.3a and 3b might also be related to the Moho depth. However, because of the serious interference of the terrain, the distribution of Moho depth can not be obtained from Figs.3a and 3b.

Fig.3c shows the residual geoid anomalies at order 65. The corresponding depth of gravity field source is shallower than 100km. The target layer is located on the bottom of lithosphere or the upper mantle asthenosphere. The impact of terrain has been weakened. The values of the anomalies are higher than those in the surrounding area at the spreading center of the Central Basin and the Parece Vela Basin. The spreading of the Central Basin and the Parece Vela Basin are related to slab roll back of the Pacific plate, which belongs to passive expansion- mode (Carlson and Melia, 1984; Honza, 1995). In the early stage of the development of back arc basin, the mantle melts began to pour out and form the spreading center. The upwelling of magma promoted the development of the back arc basin subsequently which became the diver- gence zone of the mantle flow. Therefore, the high value anomalies of the sea basin should be related to the upwelling mantle flow promoting the expansion and development of the basins. Fig.4b shows that the anomalies near the subduction zones appear with intense low values in trenches, low values in back arc basins, intense high values in island arcs and high values in the outside of trenches. The anomalies correspond to the basic cha- racteristics of the small-scale mantle flow stress field in the trench-arc-basin system (Huang and Fu, 1982; Jin and Gao, 2001). The back arc basin is the stress divergence zone, while the island arc is the stress convergence zone. The trench is the stress divergence zone, while the outside of the trench is the stress convergence zone due to the subducting plate blocked by the mantle flow. Therefore, the characteristics of anomalies reflect the intensity of the small-scale mantle convection. In the area of Japan-Izu- Bonin-Mariana Trench, negative anomalies are significantly stronger than those of the Ryukyu Trench. The positive anomalies of the island arc and the outer side of the trench are also stronger than those of the Okinawa Trough. The results show that the intensity and the scale of mantle convection in the Okinawa Trough are relatively weak. Low value anomalies appear as obvious discontinuity in the middle of Mariana Trench, Ryukyu Trench and Manila Trench. Wu and Liu (2004) suggested if the resistance of subducting plate is too strong during the subduction processes, the disturbed depression will be formed in the subduction zone. There will be an extrusion rupture if there is a weak zone. The resistance will increase along with the decrease of the dip angle of the subducting plate. The discontinuity of interlayer geoid anomalies may be caused by the fracture of the subducting slab. The reciprocal extrusion between the Bonin ridge and the island arc lithosphere leads to the increase of the subducting Pacific plate’s resistance, which could cause the break of the subducting slab. It should be the reason for the abnormal fragment of interlayer geoid anomalies at the junction of the Izu-Bonin Trench and Mariana Trench (Fig.4b). The anomalies of Yap Trench have completely disappeared in 30–100km. Previous stu- dies have confirmed that most of the recorded earth- quakes in Yap Trench occurred at depths of <100km (Nagihara., 1989; Fujiwara., 2000). Therefore, it can be inferred that the subduction depth in Yap Trench should be <100km.

Fig.3d shows the residual geoid anomalies at order 22, corresponding to the depth of gravity field source shallower than 300km. The negative anomalies of residual geoid in both the Ryukyu Trench and Manila Trench weaken when compared with the anomalies obtained at 100–300km (Fig.3c). Previous studies show that the sub- duction intensity of the underthrust Philippines Sea plate to Eurasian plate along the Ryukyu Trench increases gradually from northeast to southwest (Huang., 1994; Shang, 2014). The depth of subduction in the southern part of the Ryukyu Trench may be greater than that in the north. It appears a mirror symmetry relationship with the submarine topography. Because the Pacific plate does not influence the Ryukyu Trench directly, the subduction in- tensity of Ryukyu Trench is weaker when compared with the eastern side of the Izu-Bonin-Japan-Mariana Trench. Therefore, the subduction of the Philippines Sea plate along the Ryukyu Trench may have reached the innermost under the Eurasian plate with the subduction depth about 300km in the south, and relatively shallower in the north. In the same way, the subduction depth to the Eurasian plate along the Manila trench for the Philippines Sea plate should be <300km. Zang. (1994) have proved that the depth of subduction in the southern part of Manila Trench reaches 250km while it reaches 150km in the northern part. It is consistent with the speculations based on the 22 order residual geoid anomalies (Fig.3d). In addition, the anomalous values of the back arc basins including the West Philippines Basin, Shikoku Basin, Parece Vela Basin, Japan Islands and the Nankai Trough, the Okinawa Trough and the Philippines Islands are obviously increased. It is found that the distribution of interlayer geoid anomalies in Fig.4c has some small-scale features.Karig (1971) and Gao. (2002) think that the expansion of the back arc basin is closely associated with the mantle convection. Asthenosphere mantle upwells and melts to form magma moving upward which can enhance the mantle convection. The development of the back arc basin is also promoted. The rise and divergence of the upper mantle materials could also have a great influence on the subduction between different plates. The interlayer geoid anomalies in Fig.4c may indicate small mantle flow in the upper mantle. Therefore, we think that the small- scale mantle flow between 100 and 300km has an impor- tant effect on the expansion of the back arc basins and the plate subduction.

Fig.3e shows the residual geoid anomalies at order 14. The corresponding depth of gravity field source is lower than 500km.The influence from the deep structures is more obvious. There is a north-south anomalous boundary in the middle of Philippines Sea. Most parts of west Philippines Basin show negative anomalies,while the east Philippines Basin is a positive anomalies gradient zone extending to the Izu-Bonin Mariana island arc. Zhang. (2012) suggest that the subduction of Pacific plate with its slab rollback caused the east-west back arc expansion of the Shikoku basin and the Parece Vela Basin. Subsequently, the Kyushu Palau ridge splits out from the Izu-Bonin-Mariana island arc. During this period, the dehydration of the subduction slab resulted in a large amount of water going into the mantle, whichweakened the original high temperature environment and formed a transition zone between the subduction plate and the surrounding mantle. It also slowed down the abrupt change in density caused by the subduction of slab. The density gradient was formed between Kyushu Palau ridge and the Izu-Bonin-Mariana island arc, which is in accord with the anomalies appearing in Fig.3e. In addition, Fig.3e also shows that the negative anomalies in the northern part of the Philippine Trench are weaker than those in the southern part. Cardwell. (1980) propose that the subduction zone of Philippine Trench can be divided into two parts. The subduction depth of the northern part is shallow, while the subduction depth of the southern part could reach to 600km. The scale of the interlayer geoid anomalies in Fig.4d is larger than that in Fig.4c. Japan Sea-Nankai Trough appears with high value anomalies while the area around the Philippines Islands and Parece Vela Basin appear withhigh value anomaly trap.The appearance of the anomalies is probably related to the contact motion of the plate and the interaction between plate motion and mantle convection (Fu., 2005). Because strong mantle convections can always be found in the plate boundary zones, we inferred that the interlayer geoid anomalies in Fig.4d indicate the rising and spreading characteristics of the upper mantle flow. Fukao. (1992) suggest that the rising and spreading centers of the upper mantle flow basically reflects the characteristics of the mantle upwelling in the basins. The depth of the mantle upwelling source is about 400km, which is consisted with the extracted depth range.There- fore, it is inferred that the interlayer geoid anomalies of Nankai Trough and the Parece Vela Basin are directly related to the expansion of the mantle upwelling (Fig.5).

Fig.3f shows the residual geoid anomalies at order 10. The corresponding depth of gravity field source is not deeper than 700km with the geoid wavelength shorter than 4000km.The variation of the residual geoid anoma- lies is further enlarged, which indicates that the mantle has an increasing influence on the geoid undulation. Com- pared with Fig.3e, a wide range of negative anomalies appears in the Philippines Sea area between Kyushu Palau ridge and Ryukyu Trench. The negative anomalies of the Ryukyu Trench are enhanced obviously. The Pacific plate becomes horizontal at this depth, caused by the rollback of remaining subducting slab (Sun., 2008). Because the layers in the depths are in lack of external heat flux input (Gui and Zhou, 2015), the dehydration of the sub- ducting plate might cause partial melting, as well as the decrease in density. Therefore, the enhancement of nega- tive anomalies in the western Philippines basin and Ryu- kyu Trench are probably related to the dehydration of the subduction slab. In addition, the negative anomalies in the southern part of the Philippine Trench are relatively weak. Cardwell. (1980) indicated that the subduction depth of the southern part can reach 600km, which corresponds to the decline of negative anomalies. According to the interlayer geoid anomalies map in the depth of 500–700km (Fig.4e), negative low value depression occurs in the South China Sea and southeast Asia. By the previous researches about the mantle plume and hot spots beneath and around the Hainan Island and the IndochinaIsland (Richards., 1988; Zeng., 1997; Cai., 2002; Zhu, 2003; Yan and Shi, 2007; Zhao, 2007; Cai., 2010; Xia., 2016), it is known that the formation of the South China Sea may be related to the upwelling of the mantle materials (Fig.5). The upwelling mantle diffu- sion flows could spread out below the plate to form a mushroom head with a diameter about 1000–2000km. It can cause the uplift of the lithosphere. The negative ano- maly trap is thought to be characterized as the upwelling of mantle plume obviously. The negative anomaly trap is also very close to the position of the mantle plume in the western Pacific Ocean. Therefore, we suggest that the negative anomalies (Fig.4e) are related to the mantle plume and hot spots. Besides, two high value anomaly traps are observed in Fig.4e.The high value anomaly trap in the north is located in the east coast of China and Korean Peninsula. The high value anomaly trap in the south is located in the South China Sea and Philippines Peninsula. Jin and Gao (2001) suggested that two large scale mantle convections exist in the north side of Japan Sea and the island of Kalimantan with the characteristics of sinistral and dextral strike-slip, respectively. The locations of the high value anomalies in Fig.4e are in agreement with two large scale mantle convections. Therefore, we suggest that the high value interlayer geoid anomalies in the depth 500–700km could be used to indicate the mantle con- vection.The mantle plume and small-scale mantle con- vection (Fig.4e) begin to diffuse and convert under the influence of large-scale mantle convection(Huang and Fu, 1983; Jin and Gao, 2001). It plays an important role in the expansion of the Japan Sea Basin, South China Sea Basin, Sulu Sea Basin and Celebes Sea Basin. At the same time, the combination of the mantle plume and the upper mantle convection drives the westward expansion and compre- ssion of the Pacific plate.Thus, it leads to the north-south division of the mantle materials in the Eurasian plate and tectonic movement of lithosphere directly,which plays an important role in the global tectonic activities. On the other hand, Richter (1973) and Artyushkov (1973) su- ggested that the mantle convection can not drive the movement of the plates because it can not produce enough stress at the bottom of rigid lithosphere. The pulling force and the viscous force of the decreasing plate are considered as the main driving forces of the plate motion (Backus, 1981). The main driving forces are controversial and many studies (, Ye., 1995; Ye and Zhu, 1996; Fu., 2005) show that it’s impossible to illustrate the main driving forces which need more evidences. The plate and the mantle convection are two aspects of the earth system and interact on each other.

We suggest a model (Fig.5) based on the work of Wang. (2013) and some previous studies. By means of the interpretation on geoid anomalies, we obtain some conclusions. Firstly, the anomalies near subduction zones appear in intense low value in trenches, low value in back- arc basins, intense high value in island arcs and high value in the outside of trenches (Fig.4b). The anomalies correspond to the basic characteristics of the small-scale mantle flow stress field in the trench-arc-basin system (Huang and Fu, 1982; Jin and Gao, 2001).Strong mantle flows can always be found in the plate boundary zones. This mantle flow system plays a certain role in driving the plate motion (Fukao., 1992; Ye., 1995; Ye and Zhu, 1996). Secondly, the Parece Vela Basin appears ashigh value anomalies (Fig.4d), which is probably related to the mantle upwelling and is consistent with previous study results (Fukao.,1992; Fu., 2005) that the expansion and development of back arc basins are closely related to the rising and diffusion of mantle flow. Thirdly, according to the interlayer geoid anomalies map in the depth of 500–700km (Fig.4e), the negative low value depressions occur in the South China Sea and Southeast Asia. Based on the previous researches (Richards., 1988; Zeng., 1997; Cai., 2002; Zhu, 2003; Yan and Shi, 2007; Zhao, 2007; Cai., 2010; Xia., 2016), we attribute these depressions to mantle plume and hot spots beneath and around the Hainan Island and the IndochinaIsland. The expansion of the South China Sea is likely to be affected by the upwelling of mantle materials (Huang and Fu, 1983; Jin and Gao, 2001; Lebedev and Nolet, 2003; Lei., 2009). Finally, a wide range of negative anomalies appears in the area between Kyushu Palau ridge and Ryukyu Trench in the Philippines Sea in Fig.4f. It is speculated that the anomalies are related to the horizontal subduction of the Pacific plate, and the subduction depth of the Pacific plate can reach 660km. It is consistent with previous research results (Huang and Zhao, 2006; Zhao, 2007; Sun., 2008), which shows that the subducting slab is horizontal at the depth of 400 km. Because the layers in this depth are in lack of external heat flux input (Gui and Zhou, 2015), the dehydration of the subducting plate might trigger the partial melting of the mantle, as well as the decrease in their densities.

6 Conclusions

By calculating residual and interlayer geoid anomalies in different depths, we depict the spatial distribution of the geoid, and conduct a detailed geophysical interpretation in the East Asian continental margin in combination with other geophysical datasets. The terrain information can disturb the interpretation on the characteristics of the shallow structure described by the geoid undulation. It should be related to the method used in the separation process and the predominance of the long wavelength in the geoid. The residual geoid anomalies can reflect the intensity of small-scale mantle convection in astheno- sphere. The interlayer geoid anomalies can reflect the magmatic activities associated with mantle convection and mantle plume. However, the best model orders for the study of mantle convection in different scales need to be further explored. The analysis of the geoid anomalies can provid some usful information about the subduction position and the shape of some subduction plates in the study area. The diving depths of subducting slabs are consistent with previous researches. Therefore, the geoid anomalies could be effective data for the research of the subduction zone, mantle convection and mantle plume.

Acknowledgements

The research was financially supported by the National Natural Science Foundation of China (No. 41606044) and the Special Fund for Ocean Scientific Research in the Public Interest (No. 201305029-02).

Anny, C., and Kien, D., 1984. Geoid heights over the Louisville Ridge (South Pacific)., 89 (891): 11171-11179.

Artyushkov, E. V., 1973. Stresses in the lithosphere caused by crustal thickness inhomogeneities., 78 (32): 7675-7708, DOI: 10.1029/JB078i032p076 75.

Backus, G., Park, J., and Garbasz, D., 1981. On the relative importance of the driving forces of plate motion., 67 (2): 415-435.

Bhattacharyya, R., and Majumdar, T. J., 2006. Residual geoid and free-air gravity over the Indian offshore from ers-1 high resolution altimeter data., 34 (3): 289-298.

Bowin, C., 1983. Depth of principal mass anomalies contributing to the earth’s geoidalundulations and gravity anomalies., 7 (1): 61-100.

Bowin, C., 1986. Topography at the core-mantle boundary., 13 (13): 1513-1516.

Cai, X. L., Zhu, J. S., Cao, J. M., Yan, Z. Q., Yang, Z. X., and Hong, X. H., 2002. Structure and dynamics of lithosphere and asthenosphere in the gigantic East Asian–West Pacific rift system., 29 (3): 234-245 (in Chinese with English abstract).

Cai, X. L., Zhu, J. S., Cheng, X. Q., and Cao, J. M., 2010. The structure of the composite mushroom-shaped mantle plume in the South China Sea and its mantle dynamics., 37 (2): 268-279 (in Chinese with English abstract).

Campbell, I. H., and O’Neill, H. S. C., 2012. Evidence against a chondritic earth., 483 (7391): 553-558.

Cardwell, R. K., Isacks, B. L., and Karing, D. E., 1980. The spatial distribution of earthquakes, focal mechanism solutions, and subducted lithosphere in the philippine and northeastern Indonesian Islands., 23: 1-35.

Carlson, R. L., and Melia, P. J., 1984. Subduction hinge migra- tion., 102 (1-4): 399-411.

Cornaglia, L. L., Ruiz, F., and Introcaso, A., 2009. Análisis cortical de la Cuenca golfo de san Jorge utilizando anomalías de bouguer y ondulaciones del geoide., 65 (3): 504-515.

Ebbing, J., and Olesen, O., 2005. The Northern and Southern Scandes–structural differences revealed by an analysis of gravity anomalies, the geoid and regional isostasy., 411 (1): 73-87.

Fan, J. K., 2013. The seismic tomographic study for the western margin of the Philippine Sea plate. Master thesis. Institute of Oceanography, Graduate University of Chinese Academy of Sciences.

Fang, J., 2006. Isostatic gravity anomaly and its geodynamic characters in China and its adjacent regiona. Master thesis. Institute of Geology, China Earthquake Administration.

Fang, J., and Hsu, H. Z., 2002. A study of the depth of geoid anomaly sources in China and its adjacent regions., 45 (1): 37-43, DOI: 10.1002/cjg2.214 (in Chinese with English abstract).

Featherstone, W. E., 1997. On the use of the geoid in geophysics: A case study over the northwest shelf of Australia., 28: 52-57.

Featherstone, W. E., Kirby, J. F., Kearsley, A. H. W., Gilliland, J. R., Johnston, G. M., Steed, J., Forsherg, R., and Sideris, M. G., 2001. The AUSGeoid98 geoid model of Australia: Data treatment, computations and comparisons with GPS-levelling data., 75 (5): 313-330.

Fu, R. S., Leng, W., and Chang, X. H., 2005. Advancements in the study of mantle convection and the material movements in the deep earth interior., 20 (1): 170- 179 (in Chinese with English abstract).

Fujiwara, T., Tamura, C., Nishizawa, A., Fujioka, K., Kobayashi, K., and Iwabuchi, Y., 2000. Morphology and tectonics of the Yap Trench., 21 (1): 69-86.

Fukao, Y., Obayashi, K., Inoue, H., and Nenbai, M., 1992. Sub- ducting slabs stagnant in the mantle transition zone., 97: 4809-4822.

Gao, J. Y., and Jin, X. L., 2003. Tectonic and geodynamic pattern of marginal seas on the West Pacific inferred from multi- satellite altimetry geoid., 46 (5): 600-609 (in Chinese with English abstract).

Gao, J. Y., Li, J. B., and Lin, C. S., 2002. Probing into litho- spheric tectonic mechanics of Southern Okinawa Trough., 33 (4): 349-357 (in Chinese with English abstract).

Griffiths, R. W., and Campbell, I. H., 1990. Stirring and structure in mantle starting plumes., 99 (1-2): 66-78.

Gui, Y., and Zhou, Y. Z., 2015. Low-velocity anomaly around 410km beneath the Yellow and East China Seas with P wave triplications., 37 (1): 1-14, DOI: 10. 11939/jass.2015.01.001 (in Chinese with English abstract).

Honza, E., 1995. Spreading mode of backarc basins in the western Pacific., 251: 139-152.

Hu, L. T., Hao, T. Y., Xing, J., Hu, W. J., Man-Cheol, S. U. H., and Kwang-Hee, K. I. M., 2016. The Moho depth in the China Sea–West Pacific and its geological implications., 59 (3): 871-883 (in Chinese with English abstract).

Huang, J., and Zhao, D., 2006. High-resolution mantle tomo- graphy of China and surrounding regions., 111 (B9): 4813-4825.

Huang, P. H., and Fu, R. S., 1982.Global stress field of mantle convection currents under lithosphere., 12 (2): 102-108 (in Chinese with English abstract).

Huang, P. H., and Fu, R. S., 1983. Mantle convection pattern under lithosphere of China., 26 (1): 39-47 (in Chinese with English abstract).

Huang, P. H., Su, W. J., and Chen, J. B., 1994. Seismicity and stress field in Okinawa Trough and Ryukyu regions., 7 (4): 513-520.

Jackson, M. G., and Carlson, R. W., 2011. An ancient recipe for flood-basalt genesis., 476 (7360): 316-319.

Jackson, M. G., Carlson, R. W., Kurz, M. D., Kempton, P. D., Francis, D., and Blusztajn, J., 2010. Evidence for the survival of the oldest terrestrial mantle reservoir., 466 (7308): 853-856.

Jin, X. L., and Gao, J. Y., 2001. The satellite altimetry gravity field and the geodynamic feature in the West Pacific., 21 (1): 1-8 (in Chinese with English abstract).

Kamguia, J., Nouayou, R., Tabod, C. T., Tadjou, J. M., Man- guelle-Dicoum, E., and Kande, H. L., 2008. Geophysical signature of geological units inferred from the analysis of geoid maps in Cameroon and its surroundings., 52 (1-2): 1-8.

Karig, D. E., 1971. Origin and development of marginal basins in the western Pacific., 76 (11): 2542-2561.

Ke, X. P., Wang, Y., and Xu, H., 2009. Forward simulation of geoid in middle-short wavelengths in Tibetan Plateau., 29 (2): 19-23 (in Chinese withEnglish abstract).

Kenzie, D. M., Watts, A., Parsons, B., and Roufosse, M., 1980. Planform of mantle convection beneath the Pacific Ocean., 288 (5790): 442-446.

Kodaira, S., Iwasaki, T., Urabe, T., Kanazawa, T., Egloff, F., Makris, J., and Shimamura, H., 1996. Crustal structure across the middle Ryukyu Trench obtained from ocean bottom seismographic data., 263 (1-4): 39-60.

Koppers, A. A. P., Morgan, J. P., Morgan, J. W., and Staudigel, H., 2001. Testing the fixed hotspot hypothesis using40Ar/39Ar age progressions along seamount trails., 185 (3-4): 237-252.

Kubo, A., and Fukuyama, E., 2003. Stress field along the Ryukyu arc and the Okinawa Trough inferred from moment tensors of shallow earthquakes., 210: 305-316.

Lazarewicz, A. P., and Schwank, D. C., 1982. Detection of uncharted seamounts using satellite altimetry., 9 (4): 385-388.

Lebedev, S., and Nolet, G., 2003. Upper mantle beneath south- east Asia from S-velocity tomography., 108 (B1): 2048, DOI: 10.1029/2000JB 000073.

Lee, C. T., Luffi, P., Höink, T., Li, J., Dasgupta, R., and Hernlund, J., 2010. Upside-down differentiation and generation of a ‘primordial’ lower mantle., 463 (7283): 930-933, DOI: 10.1038/nature08824.

Lei, J., Zhao, D. P., Steinberger, B., Wu, B., Shen, F. L., and Li, Z. X., 2009. New seismic constraints on the upper mantle structure of the Hainan plume., 173 (1-2): 33-50.

Li, C. Z., Li, N. S., and Lin, M. H., 2000. Terrain features of the Philippine Sea., 24 (6): 47-51 (in Chinese with English abstract).

Li, C., Hilst, R. D. V. D., Engdahl, E. R., and Burdick, S., 2008. A new global model for P wave speed variations in earth’s mantle., 9 (5): 1-21, DOI: 10.1029/2007GC001806.

Li, S. Z., Yu, S., Zhao, S. J., Liu, X., Gong, S. Y., Suo, Y. H., Dai, L. M., Ma, Y., Xu, L. Q., Cao, X. Z., Wang, P. C., Sun, W. J., Yang, C., and Zhu, J. J., 2013. Tectonic transition and plate reconstructions of the East Asian continental margin., 33 (3): 65-94 (in Chinese with English abstract).

Lin, M., Zhu, J. J., Tian, Y. M., and Tao, X. J., 2012. On the use of the geoid anomalies for geophysical interpretation over the area of Hunan., 55 (2): 472- 483 (in Chinese with English abstract).

Lu, Y., 2002. High-resolution geoid and topographic features in South China Sea., 12 (7): 767- 770, DOI: 10.3321/j.issn:1002-008X.2002.07.019 (in Chinese with English abstract).

Mcadoo, D. C., 1981. Geoid anomalies in the vicinity of sub- duction zones., 86 (B7): 6073-6090.

Montelli, R., Nolet, G., Dahlen, F. A., and Masters, G., 2006. A catalogue of deep mantle plumes: New results from finite- frequency tomography., 7 (11): 335-360, DOI: 10.1029/2006GC001248.

Nagihara, S., Kinoshita, M., Fujimoto, H., Katao, H., Kinoshita, H., and Tomoda, Y., 1989. Geophysical observation arround the northern Yap Trench: Seismicity, gravity and heat flow., 163 (1): 93-104.

Pavlis, N. K., Holmes, S. A., Kenyon, S. C., and Factor, J. K., 2013. The development and evaluation of the Earth Gra- vitational Model 2008 (EGM2008)., 117: B04406,DOI: 10.1029/2011JB008916.

Richards, M. A., Hager, B. H., and Sleep, N. H., 1988. Dyna- mically supported geoid highs over hotspots: Observation and theory., 93 (B7): 7690-7708, DOI: 10.1029/JB093iB07p07690.

Richter, F. M., 1973. Convection and the large-scale circulation of the mantle., 78 (35): 8735- 8745, DOI: 10.1029/JB078i035p08735.

Safonova, I., Kotlyarov, A., Krivonogov, S., and Xiao, W., 2017. Intra-oceanic arcs of the paleo-Asian Ocean., 8 (3): 547-550.

Sdrolias, M., Roest, W. R., and Müller, R. D., 2004. An ex- pression of Philippine Sea plate rotation: The Parece Vela and Shikoku Basins., 394 (1-2): 69-86, DOI: https: //doi.org/10.1016/j.tecto.2004.07.061.

Shang, L. N., 2014. Tectonics and evolution of the Okinawa Trough. Master thesis. Ocean University of China.

Sharp, W. D., and Clague, D. A., 2006. 50-Ma initiation of Ha- waiian-Emperor bend records major change in Pacific plate motion., 313 (5791): 1281-1284.

Sreejith, K. M., Rajesh, S., Majumdar, T. J., Rao, G. S., Rad- hakrishna, M., Krishna, K. S., and Rajawat, A. S., 2013. High-resolution residual geoid and gravity anomaly data of the northern Indian Ocean–An input to geological under- standing., 62: 616-626, DOI: https://doi.org/10.1016/j-jseaes.2012.11.010.

Sun, W. D., Ling, M. X., Wang, F. Y., Ding, X., Hu, Y. H., Zhou, J. B., and Yang, X. Y., 2008. Pacific plate subduction and Mesozoic geological event in eastern China., 27 (3): 218-225, DOI: 10.3969/j.issn.1007-2802 (in Chinese with English abstract).

Świeczak, M., Kozlovskaya, E., Majdański, M., and Grad, M., 2009. Interpretation of geoid anomalies in the contact zone between the East European Craton and the Palaeozoic platform–II: Modelling of density in the lithosphericmantle., 177 (2): 334-346.

Teng, J. W., Zeng, R. S., Yan, Y. F., and Zhang, H., 2003. Depth distribution of Moho and tectonic framework in eastern Asian continent and its adjacent ocean areas., 46 (5): 428-446.

Tong, H. S., and Tian, J. J., 2017. The polarized super mantle plume in Pacific Rim and its mineralization response., 33 (1): 1-8 (in Chinese with English abstract).

Wang, C. Y., and Huang, J. L., 2012. Mantle transition zone structure around Hainan by receiver function analysis., 55 (4): 1161-1167 (in Chinese with English abstract).

Wang, X. C., Li, Z. X., Li, X. H., Li, J., Xu, Y. G., and Li, X. H., 2013. Identification of an ancient mantle reservoir and young recycled materials in the source region of a young mantle plume: Implications for potential linkages between plume and plate tectonics., 377-378 (5): 248-259, DOI: 10.1016/j.epsl.2013.07.003.

Wang, X. S., and Fang, J., 2014. Effect of geoid undulation on inversion of density structures of the earth., 34 (2): 10-13, DOI: 10.14075/j.jgg. 2014.02.016 (in Chinese with English abstract).

Wu, S. G., and Liu, W. C., 2004. Tectonics of subduction zone in the East Asia continental margin.,11 (3): 15-22, DOI: 10.3321/j.issn:1005-2321.2004.03.003 (in Chinese with English abstract).

Xia, S. H., Zhao, D. P., Sun, J. L., and Huang, H. B., 2016. Teleseismic imaging of the mantle beneath southernmost China: New insights into the Hainan plume., 36: 46-56, DOI: http://dx.doi.org/10.1016/j.gr.2016. 05.003.

Yan, Q. S., and Shi, X. F., 2007. Hainan mantle plume and the formation and evolution of the South China Sea., 13 (2): 311-322. DOI: 10.39 69/j.issn.1006-7493.2007.02.0.14 (in Chinese with English abstract).

Ye, Z. R., and Zhu, R. X., 1996. Coupling between mantle circulation and lithospheric plates: (II) the mantle’s mixed convection model and its application to explanation of plate velocity field., 39 (1): 47-57 (in Chinese with English abstract).

Ye, Z. R., Teng, C. K., and Zhang, X. W., 1995. Coupling between mantle circulation and lithospheric plates–(I) thermal free convection in a spherical shell., 38 (2): 174-181 (in Chinese with English abstract).

Yin, A., 2010. Cenozoic tectonic evolution of Asia: A pre- liminary synthesis., 488 (1-4): 293-325, DOI: https://doi.org/10.1016/j.tecto.2009.06.002.

Zang, S. X., and Ning, J. Y., 1996. Study on the subduction zone in Western Pacific and its implication for the geo- dynamics., 39 (2): 188-202 (in Chinese with English abstract).

Zang, S. X., Chen, Q. Z., and Huan, J. S., 1994. Distribution of earthquakes, stress state and interaction of the plates in the southern Taiwan-Philippines area., 16 (1): 29-37 (in Chinese with English abstract).

Zang, S., and Ning, J., 2002. Interaction between the Philippine Sea plate and the Eurasia plate and its influence on the tectonics of eastern Asia., 45 (2): 184-194 (in Chinese with English abstract).

Zeng, W. J., Li, Z. W., Wu, N. Y., Chen, Y. Z., Du, D. L., Wen, X. W., and Li, G. S., 1997. The upper mantle activation in South China Sea and the Indosinian mantle plume., 9: 1-19 (in Chinese with English abstract).

Zhang, B., Li, G. X., and Huang, J. F., 2014. The tectonic geomorphology of the Philippine Sea., 34 (2): 79-88, DOI: 10.3724/SP.J.1140. 2014.02079 (in Chinese with English abstract).

Zhang, G. H., and Zhang, J. P., 2015. A discussion on the tectonic inversion and its genetic mechanism in the East China Sea shelf basin., 22 (1): 260- 270, DOI: 10.13745/j.esf.2015.01.022 (in Chinese with Eng- lish abstract).

Zhang, J., Li, J. B., and Ding, W. W., 2012. Reviews of the study on crustal structure and evolution of the Kyushu-Palau Ridge., 30 (4): 595-607, DOI: 10. 3969/j.issn.1671-6647.2012.04.016 (in Chinese with English abstract).

Zhang, Q., Wang, Y. L., Jin, W. J., and Li, C. D., 2008. Eastern China plateau during the late Mesozoic: Evidence, problems and implication., 27 (9): 1404- 1430, DOI: 10.3969/j.issn.1671-2552.2008.09.004 (in Chinese with English abstract).

Zhao, D. P., 2007. Seismic images under 60 hotspots: Search for mantle plumes., 12 (4): 335-355, DOI: https://doi.org/10.1016/j.gr.2007.03.001.

Zhu, T., 2003. Progress in mantle dynamics–mantle convection., 18 (1): 65-73, DOI: 10.3969/j.issn. 1004-2903.2003.01.011 (in Chinese with English abstract).

(Edited by Chen Wenwen)

(Received June29, 2017; revised September 17, 2017; accepted October9, 2017)

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