Abstract
An automatic 3D spatial domain inversion technique is developed to estimate basement depths of sedimentary basins from observed gravity anomalies using a prescribed exponential mass density contrast. A collage of vertical polygonal cross-sections, each one with unit thickness, in which the density contrast differs exponentially with depth describes the model space. The proposed technique estimates the optimum depth ordinates of the vertices of polygonal cross-sections from a given set of gravity anomalies following predefined convergence criteria. Initial depths to basement interface at plurality of observations are calculated presuming that the density contrast within the Bouguer slab at each observation is also varying exponentially with depth. A previously reported algorithm that make use of both analytic and numeric approaches to compute the gravity response of such 3D model space with exponential mass density contrast is adopted for forward modelling. The proposed inversion is efficient even when the gravity anomalies are available at non-uniform spatial grid intervals. Recovery of basement depths with modest error from a set of gravity anomalies attributable to a synthetic model in the presence of pseudorandom noise and also the fact that the estimated depth structure of the Almazán Basin in NE Spain correlates reasonably well with the information derived from seismic data demonstrates the applicability of the proposed inversion method. The snags associated with other existing density models in the analysis of gravity anomalies are demonstrated on both synthetic and real field anomalies.
Research Highlights
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1.
It is a 3D inversion technique to analyse the gravity anomalies of sedimentary basins.
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2.
Density contrast variation is automatically ascribed by an exponential function in the algorithm.
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The interpretation technique does not require initial model specification to start with.
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4.
The algorithm is fully automatic.
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References
Abdeslem G J 2005 The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial; Geophysics 70(6) J39–J42.
Avseth P, Mukerji T, Mavko G and Tyssekvam J A 2001 Rock physics and AVO analysis for lithofacies and pore fluid prediction in a North Sea oil field; Lead. Edge 20 429–434.
Barbosa V C F, Silva J B C and Medeiros W E 1997 Gravity inversion of basement relief using approximate equality constraints on depths; Geophysics 62 1745–1757.
Bond J 1996 Tectono-sedimentary evolution of the Almazán Basin, NE Spain; In: Tertiary basins of Spain: The stratigraphic record of crustal kinematics (eds) Friend F and Dabro C J, Cambridge University Press, Cambridge, pp. 203–213.
Cai H, Xiong B and Zhu Y 2018 3D Modelling and Inversion of Gravity Data in Exploration Scale. Intech Open Limited, https://www.intechopen.com/books/gravity-geoscience-applications-industrial-technology-and-quantum-aspect/3d-modelling-and-inversion-of-gravity-data-in-exploration-scale.
Chakravarthi V, Mallesh K and Ramamma B 2017 Basement depths estimation from gravity anomalies: Two 2.5D approaches coupled with exponential density contrast model; J. Geophys. Eng. 20 303–315.
Chakravarthi V, Pramod Kumar M, Ramamma B and Sastry Rajeswara 2016 Automatic gravity modelling of sedimentary basins by means of polygonal source geometry and exponential density contrast variation: Two space domain based algorithms; J. Appl. Geophys. 124 54–61.
Chakravarthi V, Rajeswara Sastry S and Ramamma B 2013 MODTOHAFSD – A GUI based JAVA code for gravity analysis of strike limited sedimentary basins by means of growing bodies with exponential density contrast – depth variation: A space domain approach; Comput. Geosci. 56 131–141.
Chakravarthi V 2011 Automatic gravity optimization of 2.5D strike listric fault sources with analytically defined fault planes and depth dependent density; Geophysics 76 I21–I31.
Chakravarthi V and Sundararajan N 2007 3D gravity inversion using depth dependent density; Geophysics 72 I23–I32.
Chakravarthi V and Sundararajan N 2006 Discussion on ‘The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial’ by Juan Garcia-Abdeslem (November–December 2005, Geophysics, pp. j39–j42); Geophysics 71 X17–X19.
Chakravarthi V and Sundararajan N 2004 Automatic 3-D gravity modelling of sedimentary basins with density contrast varying parabolically with depth; Comput. Geosci. 30 601–607.
Chakravarthi V 2003 Digitally implemented method for automatic optimization of gravity fields obtained from three-dimensional density interfaces using depth dependent density; US Patent #6,615,139.
Chávez R E, Lazaro-Mancilla O, Campos-Enríquez J O and Flores-Márquez E L 1999 Basement topography of the Mexicali Valley from spectral and ideal body analysis of gravity data; J. South Am. Earth Sci. 12 579–587.
Chen C, Ren Z, Pan K, Tang J, Kalscheuer T, Maurer H, Sun Y and Li Y 2018 Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders; Geophys. J. Int. 214 2115–2132.
Cordell L and Henderson R G 1968 Iterative three-dimensional solution of gravity anomaly data using a digital computer; Geophysics 33(4) 596–601.
Cordell L 1973 Gravity anomalies using an exponential density-depth function – San Jacinto Graben, California; Geophysics 38 684–690.
D’Urso M G and Trotta S 2017 Gravity anomaly of polyhedral bodies having a polynomial density contrast; Surv. Geophys. 38(4) 781–832.
Fukushima T 2018 Recursive computation of gravitational field of a right rectangular parallelepiped with density varying vertically by following an arbitrary degree polynomial; Geophys. J. Int. 215(2) 864–879.
Granser H 1987 Three-dimensional interpretation of gravity data from sedimentary basins using an exponential density–depth function; Geophys. Prospect. 35 1030–1041.
Gerard A and Debeglia N 1975 Automatic three-dimensional modelling for the interpretation of gravity or magnetic anomalies; Geophysics 40(6) 1014–1034.
Gómez-Ortiz D, Tejero-lópez R, Babón-Vich R and Rivas-Ponce A 2005 Crustal density structure in the Spanish Central System derived from gravity data analysis (Central Spain); Tectonophys. 403 131–149.
Gu X, Tenzer R and Gladkikh V 2014 Empirical models of the ocean-sediment and marine sediment-bedrock density contrasts; Geosci. J. 18(4) 439–447.
Hamayun Prutkin I and Tenzer R 2009 The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution; J. Geodesy. 83 1163–1170.
Hansen R O 1999 An analytical expression for the gravity field of a polyhedral body with linearly varying density; Geophysics 64 75–77.
Hansen R O and Suciu L 2002 Multiple-source Euler deconvolution; Geophysics 67(2) 525–535.
Han D H and Batzle M 2002 Fizz water and low gas-saturated reservoirs; Lead. Edge 21(4) 395–398.
Hartmann R R, Teskey D and Friedberg I 1971 A system for rapid digital aeromagnetic interpretation; Geophysics 36 891–918.
Holstein H 2003 Gravimagnetic anomaly formulas for polyhedra of spatially linear media; Geophysics 68(1) 157–167.
ITGE 1990 Documentacin sobre la geología del subsuelo de España. Tomo V (Duero - Almazán); Internal report number 29040, Madrid.
Jiang L, Zhang J and Feng Z 2017a A versatile solution for the gravity anomaly of 3D prism-meshed bodies with depth-dependent density contrast; Geophysics 82(4) G77–G86.
Jiang L, Liu J, Zhang J and Feng Z 2017b Analytic Expressions for the Gravity Gradient Tensor of 3D Prisms with Depth-Dependent Density; Surv. Geophys. 39(3) 337–363.
Kilty K T 1983 Werner deconvolution of profile potential field data; Geophysics 48(2) 234–237.
LaFehr T R and Nabighian M N 2012 Fundamentals of gravity exploration; Society of Exploration Geophysics.
Li X 2001 Vertical resolution: Gravity versus vertical gravity gradient; Lead. Edge 20 901–904.
Liu J, Zhang J, Jiang L, Lin Q and Wan L 2019 Polynomial-based density inversion of gravity anomalies for concealed iron-deposit exploration in North China; Geophysics 84(5) B325–B334.
Luo X, Wang Y, Zhang J, Deng J, Wu Z and Chen S N 2018 Applicability analysis and application of Euler deconvolution method in potential field; Comput. Techn. Geophys. Geochem. Explor. 40(6) 789–796.
Marquardt D W 1970 Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation; Technometrics 12 591–612.
Mallesh K, Chakravarthi V and Ramamma B 2019 3D Gravity analysis in spatial domain: Model simulation by multiple polygonal cross-sections coupled with exponential density contrast; Pure Appl. Geophys. 176(6) 2497–2511.
Maxant J 1980 Variation of density with rock type, depth, and formation in the Western Canada basin from density logs; Geophysics 45(6) 1061–1076.
Mooney W D and Kaban M K 2010 The North American upper mantle: Density, composition, and evolution; J. Geophys. Res. 115 B12424.
Murthy I V R, Rama Rao P and Rao S J 1990 The density difference and generalized programs for two-and three-dimensional gravity modelling; Comput. Geosci. 16(3) 277–287.
Murthy I V R, Swamy K V and Rama Rao P 2000 Use and abuse of Werner deconvolution technique; J. Indian Geophys. Union 4(2) 97–102.
Panzner M, Ebbing J and Jordan M 2011 3D gravity inversion constrained by stereotomography, SEG Technical Program Expanded Abstracts.
Pham L T, Oksu E and Do T D 2018 GCH_gravinv: A MATLAB-based program for inverting gravity anomalies over sedimentary basins; Comput. Geosci. 120 40–47.
Pohanka V 1988 Optimum expression for computation of the gravity field of a polyhedral body with linearly varying density; Geophys. Prospect. 46 391–404.
Rao D B, Prakash M J and Babu N R 1990 3D and 2.5D modelling of gravity anomalies with variable density contrast; Geophys. Prospect. 38 411–422.
Rao P R, Swamy K V and Murthy I V R 1999 Inversion of gravity anomalies of three-dimensional density interfaces; Comput. Geosci. 25 887–896.
Ren Z, Zhong Y, Chen C, Tang J and Pan K 2017 Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts up to cubic order; Geophysics 83(1) G1–G13.
Schön J 1996 Physical properties of rocks: Fundamentals and principles of petrophysics; In: Handbook Geophys. Explor. (eds) Helbig K and Teitel S, Sect. 1, 18.
SHELL 1983 Informe del sondeo Baides-1; Internal report.
Tenzer R and Gladkikh V 2014 Assessment of Density Variations of Marine Sediments with Ocean and Sediment Depths; The Scientific World Journal, https://www.hindawi.com/journals/tswj/2014/823296/.
Thompson D T 1982 EULDPH: A new technique for making computer-assisted depth estimates from magnetic data; Geophysics 47(1) 31–37.
Toushmalani R and Hemati M 2013 Euler deconvolution of 3D gravity data interpretation: New approach; J. Appl. Sci. Agric. 8(5) 696–700.
Werner S 1953 Interpretation of magnetic anomalies at sheet like bodies; Sver. Geol. Undersok. Serv C. Arsbok. 43 6.
Wu L and Chen L 2016 Fourier forward modelling of vector and tensor gravity fields due to prismatic bodies with variable density contrast; Geophysics 81(1) G13–G26.
Zhang J Z and Jiang L 2017 Analytical expressions for the gravitational vector field of a 3-D rectangular prism with density varying as an arbitrary-order polynomial function; Geophys. J. Int. 210 1176–1190.
Zhdanov M S and Cai H 2013 Inversion of gravity and gravity gradiometry data for density contrast surfaces using Cauchy-type integrals; SEG Expanded Abstracts, https://doi.org/10.1190/segam2013-0429.1.
Acknowledgements
We sincerely thank anonymous reviewers and the associate editor for their critical reviews and making suggestions to improve the quality of the manuscript as presented. Ramamma Batta acknowledges DST, Government of India for granting Women Scientist Scheme.
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Ramamma has developed the inversion methodology. Mallesh has tested the algorithm on data sets, prepared illustrations and tables and Chakravarthi has written the manuscript.
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Communicated by Munukutla Radhakrishna
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Ramamma, B., Mallesh, K. & Chakravarthi, V. 3D spatial domain gravity inversion with growing multiple polygonal cross-sections and exponential mass density contrast. J Earth Syst Sci 130, 73 (2021). https://doi.org/10.1007/s12040-021-01576-4
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DOI: https://doi.org/10.1007/s12040-021-01576-4