GRV_D_inv: A graphical user interface for 3D forward and inverse modeling of gravity data

Authors

  • L.T. Pham University of Science, Vietnam National University, Viet Nam
  • E. Oksum Süleyman Demirel University, Department of Geophysical Engineering, Turkey
  • M.N. Dolmaz Süleyman Demirel University, Department of Geophysical Engineering, Turkey

DOI:

https://doi.org/10.24028/gzh.0203-3100.v43i1.2021.225546

Abstract

This paper presents a new gravity inversion tool GRV_D_inv, specifically a GUI-based Matlab code developed to determine the three-dimensional depth structure of a density interface. The algorithm used performs iteratively in the frequency-domain based on a relationship between the Fourier transforms of the gravity data and the sum of the Fourier transforms of the powers of the depth to the interface. In this context, the proposed code is time-efficient in computations, and thus, it is capable of handling large arrays of data. The GUI-enabled interactive control functions of the code enable the user with easy control in setting the parameters for the inversion strategy prior the operation, and allow optional choice for displaying and recording of the outputs data without requiring coding expertise. We validated the code by applying it to both noise-free and noisy synthetic gravity data produced by a density interface; we obtained good correlation between the calculated ones and the actual relief even in the presence of noise. We also applied the code to a real gravity data from Brittany (France) for determining the 3D Moho interface as a practical example. The recovered depths from the code compare well with the published Moho structures of this study area.

References

Altinoğlu, F.F., Sari, M., & Aydin, A. (2018) Shallow crust structure of the Büyük Menderes graben through an analysis of gravity data. Turkish Journal of Earth Sciences, 27, 421—431.

Babu, H.V.R. (1997). Average crustal density of the Indian Lithosphere — An inference from gravity anomalies and deep seismic soundings. Journal of Geodynamics, 23(1), 14. https://doi.org/10.1016/S0264-3707(96)00025-7.

Barbosa, V.C.F., Silva, J.B.C., & Medeiros, W.E. (1997). Gravity inversion of basement relief using approximate equality constraints on depths. Geophysics, 62(6), 1745—1757. https://doi.org/10.1190/1.1444275.

Barbosa, V.C.F., Silva, J.B.C., & Medeiros, W.E. (1999). Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth. Geophysics, 64(5), 1429—1437. https://doi.org/10.1190/1.1444647.

Bott, M.H.P. (1960). The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins. Geophysical Journal International, 3(1), 63—67. https://doi.org/10.1111/j.1365-246X.1960.tb00065.x.

Cordell, L., & Henderson, R.G. (1968). Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics, 33(4), 596—601. https://doi.org/10.1190/1.1439955.

Dyrelius, D., & Vogel, A. (1972). Improvement of convergency in iterative gravity interpretation. Geophysical Journal International, 27(2), 195—205. https://doi.org/10.1111/j.1365-246X.1972.tb05771.x.

Hsieh, H.H., Yen, H.Y., & Shih, M.H. (2010). Moho depth derived from gravity data in the Taiwan Strait Area. Terrestrial, Atmospheric and Oceanic Sciences, 21(2), 235—241. https://doi.org/10.3319/TAO.2009.03.05.01(T).

Gao, G., Kang, G., Li, G., Bai, C., & Wu, Y. (2016). An analysis of crustal magnetic anomaly and Curie surface in west Himalayan syntaxis and adjacent area. Acta Geodaetica et Geophysica, 52(3), 407—420. https://doi.org/10.1007/s40328-016-0179-z.

Gao, X., & Sun, S. (2019). Comment on «3DINVER.M: A MATLAB program to invert the gravity anomaly over a 3D horizontal density interface by Parker-Oldenburg’s algo¬rithm». Computers & Geosciences, 127, 133—137. https://doi.org/10.1016/j.cageo.2019.01.013

Gomez-Ortiz, D., & Agarwal, B.N.P. (2005). 3DINVER.M: a MATLAB program to invert gravity anomaly over a 3-D horizontal density interface by Parker-Oldenburg’s algorithm. Computers & Geosciences, 31(4), 513—520. https://doi.org/10.1016/j.cageo.2004.11.004.

Guspí, F. (1992). Three-dimensional Fourier gravity inversion with arbitrary density contrast. Geophysics, 57(1), 131—135. https://doi.org/10.1190/1.1443176.

Granser, H. (1986). Convergence of iterative gravity inversion. Geophysics, 51(5), 1146—1147. https://doi.org/10.1190/1.1442169.

Granser, H. (1987). Nonlinear inversion of gravity data using the Schmidt-Lichtenstein approach. Geophysics, 52(1), 88—93. https://doi.org/10.1190/1.1442243.

Grigoriadis, V.N., Tziavos, I.N., Tsokas, G.N., & Stampolidis, A. (2015). Gravity data inversion for Moho depth modeling in the Hellenic area. Pure and Applied Geophysics, 173(4), 1223—1241. https://doi.org/10.1007/s00024-015-1174-y.

Kaya, C. (2010). Deep crustal structure of northwestern part of Turkey. Tectonophysics, 489(1-4), 227—239. https://doi.org/10.1016/j.tecto.2010.04.019.

Lefort, J.P., & Agarwal, B.N.P. (2000). Gravity and geomorphological evidence for a large crustal bulge cutting across Brittany (France): a tectonic response to the closure of the Bay of Biscay. Tectonophysics, 323(3-4), 149—162. https://doi.org/10.1016/S0040-1951(00)00103-7.

Mendonca, C.A. (2004). Inversion of gravity field inclination to map the basement relief of sedimentary basins. Geophysics, 69(5), 1240—1251. https://doi.org/10.1190/1.1801940.

Mickus, K.L., & Peeples, W.J. (1992). Inversion of gravity and magnetic data for the lower surface of a 2.5 dimensional sedimentary basin1. Geophysical Prospecting, 40(2), 171—193. https://doi.org/10.1111/j.1365-2478.1992.tb00370.x.

Murthy, I.V.R., & Rao, S.J. (1989). A Fortran 77 program for inverting gravity anomalies of two-dimensional basement structures. Computers & Geosciences, 15(7), 1149—1156. https://doi.org/10.1016/0098-3004(89)90126-X.

Murthy, I.V.R., & Rao, P.R. (1993). Inversion of gravity and magnetic anomalies of two-dimensional polygonal cross sections. Computers & Geosciences, 19(9), 1213—1228. https://doi.org/10.1016/0098-3004(93)90026-2.

Nagendra, R., & Prasad, P.V.S., Bhimasanka¬ram, V.L.S. (1996). Forward and inverse computer modeling of gravity field resulting from a density interface using Parker Olden¬burg method. Computers & Geosciences, 22(3), 227—231. https://doi.org/10.1016/0098-3004(95) 00075-5.

Nguiya, S., Lemotio, W., Njandjock, N.P, Pe¬mi, M.M., Tokam, A.P.K., & Ngatchou, E. (2019). 3D Mafic Topography of the Transition Zone between the North-Western Boundary of the Congo Craton and the Kribi-Campo Sedimentary Basin from Gravity Inversion. International Journal of Geophysics, 2019, 7982562. https://doi.org/10.1155/2019/7982562.

Oldenburg, D.W. (1974). The inversion and interpretation of gravity anomalies. Geophysics, 39(4), 526—536. https://doi.org/10.1190/ 1.1440444.

Oruç, B. (2014). Structural interpretation of southern part of western Anatolian using analytic signal of the second order gravity gradients and discrete wavelet transform analysis. Journal of Applied Geophysics, 103, 82—98. https://doi.org/10.1016/j.jappgeo.2014.01.008.

Oruç, B., Gomez-Ortiz, D., & Petit, C. (2017). Lithospheric flexural strength and effective elastic thicknesses of the Eastern Anatolia (Turkey) and surrounding region. Journal of Asian Earth Sciences, 150, 1—13. https://doi.org/10.1016/j.jseaes.2017.09.015.

Oruç, B.,& Sönmez, T. (2017). The rheological structure of the lithosphere in the Eastern Marmara region, Turkey. Journal of Asian Earth Sciences, 139, 183—191. https://doi.org/10.1016/j.jseaes.2017.02.041.

Ouyed, M., Idres, M., Bourmatte, A., Boughacha, M.S., Samai, S., Yelles, A., Haned, A., & Aidi, C. (2010). Attempt to identify seismic sources in the eastern Mitidja basin using gravity data and aftershock sequence of the Boumerdes (May 21, 2003; Algeria) earthquake. Journal of Seismology, 15(2), 173—189. https://doi.org/10.1007/s10950-010-9218-3.

Parker, R.L. (1972). The rapid calculation of potential anomalies. Geophysical Journal International, 31(4), 447—455. https://doi.org/10.1111/j.1365-246X.1973.tb06513.x.

Pallero, J.L.G., Fernandez-Martinez, J.L., Bonvalot, S., & Fudym, O. (2015), Gravity inversion and uncertainty assessment of basement relief via particle swarm optimization. Journal of Applied Geophysics, 116, 180—191. https://doi.org/10.1016/j.jappgeo.2015.03.008.

Pham, L.T., & Do, T.D. (2017). Estimation of sedimentary basin depth using the hybrid technique for gravity data. VNU Journal of Science: Mathematics-Physics, 33(2), 48—52. https://doi.org/10.25073/2588-1124/vnumap.4203.

Pham, L.T., Oksum, E., & Do, T.D. (2018). GCH_gravinv: A MATLAB-based program for inverting gravity anomalies over sedimentary basins. Computers & Geosciences, 120, 40—47. https://doi.org/10.1016/j.cageo.2018.07.009.

Pham, L.T., Do, T.D., Oksum, E., & Le, S.T. (2019). Estimation of Curie point depths in the Southern Vietnam continental shelf using magnetic data. Vietnam Journal of Earth Sciences, 41(3), 216—228.

Pham, L.T., Oksum, E., Gómez-Ortiz, D., & Do, T.D. (2020). MagB_inv: A high performance Matlab program for estimating the magnetic basement relief by inverting magnetic anomalies. Computers & Geosciences, 134, 104347. https://doi.org/10.1016/j.cageo.2019.104347.

Pilkington, M. (2006). Joint inversion of gravity and magnetic data for two-layer models. Geophysics, 71, L35—L42. https://doi.org/10.1190/1.2194514.

Reamer, S.K., & Ferguson, J.F. (1989). Regularized two-dimensional Fourier gravity inversion method with application to the Silent Canyon caldera, Nevada. Geophysics, 54, 486—496. https://doi.org/10.1190/1.1442675.

Shin, Y.H., Choi, K.S., & Xu, H. (2006). Three-dimensional forward and inverse models for gravity fields based on the Fast Fourier Transform. Computers & Geosciences, 32(6), 727—738. https://doi.org/10.1016/j.cageo.2005.10.002.

Starostenko, V.I., & Legostaeva, O.V. (1998). Calculations of the gravity field from an inhomogeneous, arbitrary truncated vertical rectangular prism. Izvestiya, Physics of the Solid Earth, 34(12), 991—1003.

Švancara, J. (1983). Approximate method for direct interpretation of gravity anomalies caused by surface three-dimensional geologic structures. Geophysics, 48(3), 361—366. https://doi.org/10.1190/1.1441474.

Talwani, M,,Worzel, J., &Ladisman, M. (1959). Rapid gravity computations for two dimensional bodies with application to the Mendocino submarine fracture zone. Journal of Geophysical Research, 64(1), 49—59. https://doi.org/10.1029/JZ064i001p00049.

Talwani, M., & Ewing, M. (1960). Rapid computation of gravitational attraction of three-dimen¬sio¬nal bodies of arbitrary shape. Geo¬phy¬sics, 25(1), 203—225. https://doi.org/10.1190/1.1438687.

Tsuboi, C. (1983). Gravity. London: George Allen & Unwin Ltd, 254 p.

Tugume, F., Nyblade, A., Julià, J., & van der Meijde, M. (2013). Precambrian crustal structure in Africa and Arabia: Evidence lacking for secular variation. Tectonophysics, 609, 250—266. https://doi.org/10.1016/j.tecto.2013.04.027.

Van der Meijde, M., Julià, J., & Assumpção, M. (2013). Gravity derived Moho for South America. Tectonophysics, 609, 456—467. https://doi.org/10.1016/j.tecto.2013.03.023.

Wu, L., & Lin, Q. (2017). Improved Parker’s method for topographic models using Chebyshev series and low rank approximation. Geophysical Journal International, 209(2), 1296—1325. https://doi.org/10.1093/gji/ggx093.

Zhang, C., Huang, D., Wu, G., Ma, G., Yuan, Y., & Yu, P. (2015). Calculation of Moho depth by gravity anomalies in Qinghai—Tibet Plateau based on an improved iteration of Parker—Oldenburg Inversion. Pure and Applied Geophysics, 172(10), 2657—2668. https://doi.org/10.1007/s00024-015-1039-4.

Downloads

Published

2021-03-13

How to Cite

Pham, L. ., Oksum, E. ., & Dolmaz, M. . (2021). GRV_D_inv: A graphical user interface for 3D forward and inverse modeling of gravity data. Geofizičeskij žurnal, 43(1), 181–193. https://doi.org/10.24028/gzh.0203-3100.v43i1.2021.225546

Issue

Section

Articles