Bathymetry Inversion Using Vertical Deections: a Case Study in South China Sea Xiaoyun Wan China University of Geosciences Beijing Bo Liu Qian Xuesen Laboratory of Space and Tecnology Xiaohong Sui ( [email protected] ) Qian Xuesen Labortary of Space and Tecnology https://orcid.org/0000-0002-2376-448X Richar Fii Annan China University of Geosciences Beijing Yijun Min China University of Geosciences Beijing Full paper Keywords: Bathymetry, Vertical Deections, Gravity anomaly, Satellite altimetry Posted Date: February 11th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-185040/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License 1 Bathymetry inversion using vertical deflections: A case study in South China Sea 2 Author #1: Xiaoyun Wan, School of Land Science and Technology, China University of 3 Geosciences (Beijing), Beijing 100083 China, [email protected] 4 Author #2: Bo Liu, Qian Xuesen Laboratory of Space Technology, Beijing 100094 China, 5 [email protected] 6 Author #3: Xiaohong Sui, Qian Xuesen Laboratory of Space Technology, Beijing 100094 7 China, [email protected] 8 Author #4: Richar Fiifi Annan, School of Land Science and Technology, China University 9 of Geosciences (Beijing), Beijing 100083 China, [email protected] 10 Authour #5: Yijun Min, School of Land Science and Technology, China University of 11 Geosciences (Beijing), Beijing 100083 China, [email protected] 12 Correspondence: [email protected] 13 14 1 15 Abstract 16 As an alternative method, an algorithm for bathymetry inversion using vertical 17 deflections is proposed. Firstly, the formulas for the bathymetry inversion from north and 18 east components of vertical deflections are derived and the data processing is introduced. 19 Then a local area in the South China Sea is selected as an example to experiment the 20 method. The bathymetry inversion based on gravity anomaly was also conducted for a 21 comparison. The results show that the bathymetry derived from the north component of 22 the vertical deflections have almost the same accuracy as that derived from gravity 23 anomalies and the results derived from the east component have the poorest accuracy. 24 The experiment’s results also show that accuracy of the derived bathymetry can be 25 improved if the fitting parameters are adjusted according to the water depths. In summary, 26 among the gravity field products used in this study, although the gravity anomaly yielded 27 the best performance in the bathymetry inversion, the vertical defections can still be used 28 as supplements, especially in areas where accurate vertical deflections exist. This is 29 because deriving gravity anomaly from altimetry observations needs additional data and 30 calculation efforts. 2 31 Keywords 32 Bathymetry, Vertical Deflections, Gravity anomaly, Satellite altimetry 33 Introduction 34 Bathymetry information is important for economic, military and Earth science. Many 35 methods are developed for deriving bathymetry information, such as multibeam echo 36 sounding, the derivation based on gravity data (Smith and Sandwell 1997; Hwang 1999; 37 Hisao et al. 2016; Wan et al. 2019, 2020a), detection using laser technology (Kervern et 38 al. 1992), inversion based on imagery (Monteys et al. 2015; Jawak et al. 2015). Among 39 these methods, altimetry derived gravity products have played a great role in global 40 bathymetry inversion. 41 The bathymetry inversion based on altimetry products are mainly based on gravity 42 anomaly. Parks (1972) proposed the spectral method for bathymetry inversion using 43 gravity anomaly. In spectral domain, Smith and Sandwell (1994) proposed an admittance 44 theory and predicted the bathymetry from dense gravity data and sparse shipboard 45 bathymetry for the southern oceans. The spectral method has also been verified in many 46 other areas, such as the South China Sea (Hwang 1999), the western Indian offshore 47 (Bhattachryya and Majumbar 2009), South Atlantic Ocean (Jung and Vogt 1992). In 48 space domain, the so-called gravity geological method (GGM) (Ibrahim and Hinze 1972) 49 is also used widely for bathymetry inversion. For example, GGM was used to enhance 50 the bathymetry of the East Sea by Kim et al. (2010). Hisao et al. (2011) investigated 51 density contrast for bathymetry inversion using GGM and concluded that the predicted 3 52 density contrasts can enhance the accuracy of 3~4 m for GGM. Kim et al. (2011) 53 predicted the bathymetry on the eastern end of the Shackleton Fracture in the Drake 54 Passage. Bathymetry of South China Sea was also predicted using GGM with precision 55 of 76.95 m (Ou yang et al. 2014). Xiang et al. (2017) proposed an adaptive mesh method 56 for modelling long-wavelength gravity in GGM. 57 Recently, gravity gradients were used to predict bathymetry in some areas. Wang 58 (2000) proposed a least-square method for bathymetry inversion using vertical gravity 59 gradients. However, it has not been experimented using actual gravity gradient data. Hu 60 et al. (2015) used vertical gravity gradients to predict the bathymetry over a part of the 61 North Pacific and the accuracy can be improved by combing gravity gradients and gravity 62 anomalies, compared to the bathymetry inversion only based on gravity anomalies. Fan 63 et al. (2021) proposed a nonlinear iterative least square method for seafloor topography 64 by combining gravity anomalies and gravity gradients. The feasibility of seafloor 65 topography estimation from airborne gravity gradients was discussed using real data 66 (Yang et al. 2020). All these studies indicate that the gravity gradients can play a great 67 role in bathymetry inversion, especially with the accuracy improvement of marine gravity 68 gradients. 69 As mentioned above, gravity anomaly and vertical gravity gradients are the most 70 commonly used gravity field products for bathymetry inversion. However, vertical 71 deflections, as another type of important products, are seldomly used. Indeed, the vertical 72 deflections can be derived with high accuracy using altimetry observations and are often 73 used further to derive gravity anomaly (Hwang et al. 1998; Sandwell and Smith 1997; 4 74 Wan et al. 2020b). Since the gravity anomalies derived from vertical deflections have 75 high accuracy, the vertical deflections certainly contain abundant gravity information, 76 including those generated from the bathymetry. Hence, in theory it is feasible to use 77 vertical deflections to inverse bathymetry. 78 This study investigates how to derive bathymetry using vertical deflections as well as 79 its performance. Section 2 proposes the inversion method based on vertical deflections. 80 Data used and study area are introduced in Section 3. Section 4 presents the inversion 81 results, and some discussions are given in Section 5. Conclusions are made in Section 6. 82 Method 83 The relationship between vertical deflections and bathymetry 84 According to Parks (1972), the disturbing gravitational potential at the ocean surface 85 (Figure 1) has the following relationship with ocean water depths, 1 86 F T 2 G e kz0 F h (1) k 87 where T is the disturbing potential created by the seafloor topography, h is the 88 2 2 seafloor topography relative to the mean water depth, k kxy, k , kx , ky , x y 89 G is the gravitational constant, represents the density contrast between the ocean 90 3 water and seafloor crust, often setting as 1670 kg/m , Z0 denotes the mean water depths 91 in the observation area and F means fast Fourier transform computation. And then, the 92 gravity anomaly, g , caused by the seafloor topography can be represented as: kz 93 F g k F T =2 G e0 F h (2) 5 94 And thus, the bathymetry can be derived as Equation (3). 1 1 kz0 95 h F e F g (3) 2G 96 This is the formula which has been used widely for bathymetry inversion in the spectral 97 domain (Hu et al. 2014). Indeed, according to Equation (1), we also have kz0 kx F Txx ik F T i2 G e F h k 98 （4） k F T ik FTF i2 G e k z0 y h yy k 99 According to Heiskanen and Moritz (1967), 12iG kz0 kx F F Tx e F h k 100 (5) 12iG k F F T e k z0 y F h y k 101 where is the normal gravity. Finally, the formulas for bathymetry inversion can be 102 constructed as follows: 1 kz k h= F e0 F i2 G kx 103 (6) 1 kz k h= F e0 F i2 G k y 104 According to Equations (3) and (6), is an important parameter for the inversion. 105 According to the previous studies, its theoretical value does not always lead to the best 106 inversion results (Annan et al. 2020). Instead, it can be derived by linear regression 107 between the water depths at the control points and gravity anomaly after downward 108 continuation (Smith and Sandwell 1994; Hu et al. 2014). This method is often used in 109 bathymetry inversion with spectral methods. The advantage is that the we do not need to 110 know an accurate density contrast. Similar technique is also adopted for the vertical 6 111 deflections in this study. The issue is that the ocean depths do not have a linear 112 relationship with the vertical deflections even after downward continued processing. In 113 order to solve this issue, two new values are defined. Fk '1=F kiy 114 (7) '1 Fk F kix 115 We call this preprocessing a scale factor correction in this study. Then we have ' kz0 F 2 G e F h 116 (8) ' kz0 F 2 G e F h 117 Equation (8) has the same functional relationship as Equation (2). Therefore, the 118 algorithm of bathymetry inversion based on gravity anomaly can all adopted for that 119 based on ' and ' .