An Expression for Gravity Generated by an Anomalous Geological Body and Its Application in Bathymetry Inversion

doi:10.11947/j.JGGS.2021.0405

Journal of Geodesy and Geoinformation Science ›› 2021, Vol. 4 ›› Issue (4): 63-73.doi: 10.11947/j.JGGS.2021.0405

Previous Articles Next Articles

An Expression for Gravity Generated by an Anomalous Geological Body and Its Application in Bathymetry Inversion

Huan XU¹(),Jinhai YU¹(),Xiaoyun WAN²,Lei LIANG³

1. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
2. School of Land Science and Technology, China University of Geosciences (Beijing), Beijing 100083, China
3. Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China

Received:2021-02-28 Accepted:2021-08-30 Online:2021-12-20 Published:2021-12-30
Contact: Jinhai YU E-mail:xuhuan@ucas.edu.cn;yujinhai@ucas.edu.cn
About author:Huan XU(1993—), male, PhD, engaged in the scientific research of satellite altimetry gravity.E-mail: xuhuan@ucas.edu.cn
Supported by:
Major Research Plan of China(2016YFB0501702);National Nature Science Funds of China(41774089)

Abstract

Abstract:

The gravity anomaly and vertical gravity gradient due to anomalous geological bodies are mainly computed by numerical methods, so it is difficult and time-consuming to use the gravity-geological method to invert seafloor topography. This paper addresses this issue by deriving an expression for gravity generated by a cylinder based on a series expansion. The choice of number for terms in the series is estimated by comparing with the numerical method, especially when the depth H=4000m, the accuracy of 1mGal(1Gal=10^-2m/s²) can be achieved when the series are 9. The expressions can be used to establish the relationships between the shape of an anomalous body and the generated vertical gravity and vertical gravity gradient, respectively. Finally, the potential applications of the expressions in inverting seafloor topography are illustrated by synthetic examples.

Key words: gravity-geological method; anomalous geological body; vertical gravity anomaly; vertical gravity gradient anomaly

Huan XU,Jinhai YU,Xiaoyun WAN,Lei LIANG. An Expression for Gravity Generated by an Anomalous Geological Body and Its Application in Bathymetry Inversion[J]. Journal of Geodesy and Geoinformation Science, 2021, 4(4): 63-73.

Figures/Tables 11

Fig.1

Fig.2

Tab.1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Tab.2

Fig.9

References 18

[1]	DETRICK R S, WATTS A B. An analysis of isostasy in the world’s oceans: 3. Aseismic ridges[J]. Journal of Geophysical Research: Solid Earth, 1979, 84(B7):3637-3653.
[2]	HUBBERT M K. A line-integral method of computing the gravimetric effects of two-dimensional masses[J]. Geophysics, 1948, 13(2):215-225. doi: 10.1190/1.1437395
[3]	HU Minzhang, LI Jiancheng, LI Hui, et al. Bathymetry predicted from vertical gravity gradient anomalies and ship soundings[J]. Geodesy and Geodynamics, 2014, 5(1):41-46.
[4]	HSIAO Y S, KIM J W, KIM K B, et al. Bathymetry estimation using the gravity-geologic method: an investigation of density contrast predicted by the downward continuation method[J]. Terrestrial, Atmospheric and Oceanic Sciences, 2011, 22(3):347-358. doi: 10.3319/TAO.2010.10.13.01(Oc)
[5]	HSIAO Y S, HWANG C, CHENG Y S, et al. High-resolution depth and coastline over major atolls of South China Sea from satellite altimetry and imagery[J]. Remote Sensing of Environment, 2016, 176:69-83. doi: 10.1016/j.rse.2016.01.016
[6]	IBRAHIM A, HINZE W J. Mapping buried bedrock topography with gravity[J]. Groundwater, 1972, 10(3):18-23. DOI: 10.1111/j.1745-6584.1972.tb02921.x. doi: 10.1111/j.1745-6584.1972.tb02921.x
[7]	KIM J W, VON FRESE R R B, LEE B Y, et al. Altimetry-derived gravity predictions of bathymetry by the gravity-geologic method[J]. Pure and Applied Geophysics, 2011, 168(5):815-826. doi: 10.1007/s00024-010-0170-5
[8]	KIM K B, YUN H S. Satellite-derived bathymetry prediction in shallow waters using the gravity-geologic method: a case study in the west sea of Korea[J]. KSCE Journal of Civil Engineering, 2018, 22(7):2560-2568. doi: 10.1007/s12205-017-0487-z
[9]	KIM S S, WESSEL P. New analytic solutions for modeling vertical gravity gradient anomalies[J]. Geochemistry, Geophysics, Geosystems, 2016, 17(5):1915-1924. DOI: 10.1002/2016GC006263. doi: 10.1002/2016GC006263
[10]	OUYANG Mingda, SUN Zhongmiao, ZHAI Zhenhe. Predicting bathymetry in South China Sea using the gravity-geologic method[J]. Chinese Journal of Geophysics, 2014, 57(9):2756-2765.
[11]	PAVLIS N K, HOLMES S A, KENYON S C, et al. An earth gravitational model to degree 2160: EGM2008[C]// Proceedings of the 2008 General Assembly of the European Geosciences Union. Vienna, Austria: EGU, 2008.
[12]	SMITH W H F, SANDWELL D T. Bathymetric prediction from dense satellite altimetry and sparse shipboard bathymetry[J]. Journal of Geophysical Research: Solid Earth, 1994, 99(B11):21803-21824. DOI: 10.1029/94JB00988. doi: 10.1029/94JB00988
[13]	SMITH W H F, SANDWELL D T. Global sea floor topography from satellite altimetry and ship depth soundings[J]. Science, 1997, 277(5334):1956-1962. doi: 10.1126/science.277.5334.1956
[14]	TALWANI M, EWING W M. Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape[J]. Geophysics, 1960, 25(1):203-225. doi: 10.1190/1.1438687
[15]	TALWANI M, WORZEL J L, LANDISMAN M. Rapid gravity computations for two-dimensional bodies with application to the mendocino submarine fracture zone[J]. Journal of Geophysical Research, 1959, 64(1):49-59. doi: 10.1029/JZ064i001p00049
[16]	WANG Yanming. Predicting bathymetry from the Earth’s gravity gradient anomalies[J]. Marine Geodesy, 2000, 23(4):251-258. doi: 10.1080/01490410050210508
[17]	WAN Xiaoyun, RAN Jiangjun, JIN Shuanggen. Sensitivity analysis of gravity anomalies and vertical gravity gradient data for bathymetry inversion[J]. Marine Geophysical Research, 2019, 40:87-96. DOI: 10.1007/s11001-018-9361-8. doi: 10.1007/s11001-018-9361-8
[18]	YANG Junjun, JEKELI C, LIU Lintao. Seafloor topography estimation from gravity gradients using simulated annealing[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(8):6958-6975. DOI: 10.1029/2018JB015883. doi: 10.1029/2018JB015883

H/km Terms [H-h]/km	1	2	3	4
0.4	9	9	9	9
0.8	7	6	5	5
1.2	-	4	4	3
1.6	-	4	3	3

	Max	Max Error	RMS
VG anomaly/mGal	3.76	0.20	0.16
VG Height/m	1000	100	63.17
VGG anomaly/E	40.73	2.86	2.58
VGG Height/m	1000	100	66.51

An Expression for Gravity Generated by an Anomalous Geological Body and Its Application in Bathymetry Inversion

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 11

References 18

Related Articles 0

Recommended Articles

Metrics

Comments