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3D Gravity Analysis in the Spatial Domain: Model Simulation by Multiple Polygonal Cross-Sections Coupled with Exponential Density Contrast

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Abstract

An automatic 3D modeling technique is developed in the spatial domain to analyze the gravity anomalies produced by a concealed density interface with mass density contrast differing exponentially with depth. The sedimentary column above the interface is described with a stack of multiple vertical polygonal sections of unit thickness each. For such a case, the depth ordinates of the vertices of the cross-sections become the unknown parameters to be estimated from gravity data. Forward solution of the model space is realized in the spatial domain by a technique that combines both analytic and numeric approaches. Initial depths to the interface are calculated based on the Bouguer slab approximation and subsequently improved, iteratively, based on the ratio of the product of the observed gravity anomaly and existing depth parameter to the corresponding model gravity response. The iterative process continues until one of the predefined termination criteria is accomplished. Unlike the existing methods, the advantage of the proposed method is that the observed gravity anomalies need not necessarily be sampled/available at regular spatial grid intervals. The applicability of the proposed model is exemplified with a set of noisy gravity anomalies attributable to a synthetic structure before being applied to a real world gravity data. In the case of the synthetic example, the method has yielded a structure that was compatible with the assumed structure even in the presence of random noise. Application of the proposed method to the gravity data set from the Los Angeles Basin, California, using a prescribed exponential density function has yielded a model that concurs reasonably well with the published models.

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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.

    Article  Google Scholar 

  • Bal, O. T., & Kara, I. (2012). 3-D Gravity modeling of basins with vertical prisms: Application to Salt Lake region (Turkey). Journal of the Balkan Geophysical Society, 15(1), 1–6.

    Google Scholar 

  • Banerjee, B., & Das Gupta, S. P. (1977). Short note: Gravitational attraction of a rectangular parallelepiped. Geophysics, 42, 1053–1055.

    Article  Google Scholar 

  • Bhaskara Rao, D., Prakash, M. J., & Ramesh Babu, N. (1990). 3D and 21/2D modelling of gravity anomalies with variable density contrast. Geophysical Prospecting, 38, 411–422.

    Article  Google Scholar 

  • Blakely, R. J. (1996). Potential theory in gravity & magnetic applications. Cambridge: Cambridge University Press.

    Google Scholar 

  • Cai, H., Xiong, B., & Zhu, Y. (2018). 3D Modeling and Inversion of Gravity Data in Exploration Scale. IntechOpen Limited. https://www.intechopen.com/books/gravity-geoscience-applications-industrial-technology-and-quantum-aspect/3d-modeling-and-inversion-of-gravity-data-in-exploration-scale. Accessed 12 Aug 2018.

  • Cai, H., & Zhdanov, M. (2015). Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data. Geophysics, 80, G81–G94.

    Article  Google Scholar 

  • Chai, Y., & Hinze, W. J. (1988). Gravity inversion of an interface above which the density contrast varies exponentially with depth. Geophysics, 53(6), 837–845.

    Article  Google Scholar 

  • 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.

  • Chakravarthi, V. (2009). Automatic gravity inversion for simultaneous estimation of model parameters and regional gravity background: an application to 2D pull-apart basins. Current Science, 96(10), 1349–1360.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chakravarthi, V., Mallesh, K., & Ramamma, B. (2017). Basement depths estimation from gravity anomalies: Two 2.5D approaches coupled with exponential density contrast model. Journal of Geophysics and Engineering, 20, 303–315.

    Article  Google Scholar 

  • Chakravarthi, V., Pramod Kumar, M., Ramamma, B., & Rajeswara Sastry, S. (2016). Automatic gravity modeling of sedimentary basins by means of polygonal source geometry and exponential density contrast variation: Two space domain based algorithms. Journal of Applied Geophysics, 124, 54–61.

    Article  Google Scholar 

  • Chakravarthi, V., Raghuram, H. M., & Singh, S. B. (2002). 3D Forward gravity modeling of density interfaces above which the density contrast varies continuously with depth. Computers & Geosciences, 28, 53–57.

    Article  Google Scholar 

  • Chakravarthi, V., Rajeswara Sastry, S., & 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. Computers & Geosciences, 56, 131–141.

    Article  Google Scholar 

  • Chakravarthi, V., Shankar, G. B. K., Muralidharan, D., Harinarayana, T., & Sundararajan, N. (2007). An integrated geophysical approach for imaging subbasalt sedimentary basins: Case study of Jam River basin, India. Geophysics, 72, B141–B147.

    Article  Google Scholar 

  • Chakravarthi, V., & Sundararajan, N. (2004a). Automatic 3-D gravity modeling of sedimentary basins with density contrast varying parabolically with depth. Computers & Geosciences, 30, 601–607.

    Article  Google Scholar 

  • Chakravarthi, V., & Sundararajan, N. (2004b). Ridge regression algorithm for gravity inversion of fault structures with variable density. Geophysics, 69, 1394–1404.

    Article  Google Scholar 

  • Chakravarthi, V., & 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, P. j39–j42). Geophysics, 71, X17–X19.

    Article  Google Scholar 

  • Comacho, A. G., Montesinos, F. G., & Vieira, R. (1997). A three-dimensional gravity inversion applied to Sao Miguel Island Azores. Journal of Geophysical Research B, Solid Earth and Planets, 102, 7717–7730.

    Article  Google Scholar 

  • Cordell, L. (1973). Gravity anomalies using an exponential density-depth function—San Jacinto Graben, California. Geophysics, 38, 684–690.

    Article  Google Scholar 

  • Cordell, L., & Henderson, R. G. (1968). Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics, 33(4), 596–601.

    Article  Google Scholar 

  • Cowie, P. A., & Karner, G. D. (1990). Gravity effect of sediment compaction: examples from the North Sea and Rhine graben. Earth and Planetary Science Letters, 99(1–2), 141–153.

    Article  Google Scholar 

  • Crosby, A. G., McKenzie, D., & Sclater, J. G. (2006). The relationship between depth, age and gravity in the oceans. Geophysical Journal International, 166, 553–573.

    Article  Google Scholar 

  • D’Urso, M. G. (2014a). Analytical computation of gravity effects for polyhedral bodies. Journal of Geodesy, 88, 13–29.

    Article  Google Scholar 

  • D’Urso, M. G. (2014b). Gravity effects of polyhedral bodies with linearly varying density. Celestial Mechanics & Dynamical Astronomy, 120(4), 349–372.

    Article  Google Scholar 

  • Debeglia, N., & Corpell, J. (1997). Automatic 3-D interpretation of potential field data using analytic signal derivatives. Geophysics, 62, 87–96.

    Article  Google Scholar 

  • Feng, J., Zhang, S., & Meng, X. (2016). Constraint 3D density interface inversion from gravity anomalies. Arabian Journal of Geoscience. https://doi.org/10.1007/s12517-015-2213-9.

    Google Scholar 

  • Gallardo-Delgado, L. A., Perez-Flores, M. A., & Gomez-Trevino, E. (2003). A versatile algorithm for joint 3D inversion of gravity and magnetic data. Geophysics, 68(3), 949–959.

    Article  Google Scholar 

  • Gokula, A. P., & Sastry, R. G. (2015). Gravitational attraction of a vertical pyramid model of flat top-and-bottom with depth-wise parabolic density variation. Journal of Earth System Science, 124(8), 1735–1744.

    Article  Google Scholar 

  • Grabowska, T., Bojdys, G., & Dolnicki, J. (1998). Three-dimensional density model of the earth’s crust and the upper mantle for the Area of Poland. Journal of Geodynamics, 25, 5–24.

    Article  Google Scholar 

  • Granser, H. (1987). Three-dimensional interpretation of gravity data from sedimentary basins using an exponential density-depth function. Geophysical Prospecting, 35, 1030–1041.

    Article  Google Scholar 

  • Gu, X., Tenzer, R., & Gladkikh, V. (2014). Empirical models of the ocean-sediment and marine sediment-bedrock density contrasts. Geosciences Journal, 18(4), 439–447.

    Article  Google Scholar 

  • Hansen, R. O. (1999). An analytical expression for the gravity field of a polyhedral body with linearly varying density. Geophysics, 64(1), 75–77.

    Article  Google Scholar 

  • Holstein, H. (2002). Gravimagnetic similarity in anomaly formulas for uniform polyhedral. Geophysics, 67, 1126–1133.

    Article  Google Scholar 

  • Holstein, H. (2003). Gravimagnetic anomaly formulas for polyhedra of spatially linear media. Geophysics, 68(1), 157–167.

    Article  Google Scholar 

  • Isik, M., & Senel, H. (2009). 3D gravity modeling of Buyuk Menderes basin in western Anatolia using parabolic density function. Journal of Asian Earth Sciences, 34(3), 317–325.

    Article  Google Scholar 

  • Kadirov, F. A. (2000). Application of the Hartley transform for interpretation of gravity anomalies in the Shamakhy-Gobustan and Absheron oil- and gas-bearing regions, Azerbaijan. Journal of Applied Geophysics, 45, 49–61.

    Article  Google Scholar 

  • Li, Y., & Oldenburg, D. W. (1998). 3-D inversion of gravity data. Geophysics, 63(1), 109–119.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • McCulloh. J. H. (1960). Gravity variation and the geology of the Los Angeles basin of California. U.S.G.S. Prof. Paper 400B, B320–B325.

  • Murthy, I. V. R., Rama Rao, P., & Rao, S. J. (1990). The density difference and generalized programs for two-and three-dimensional gravity modeling. Computers & Geosciences, 16(3), 277–287.

    Article  Google Scholar 

  • Nagy, D. (1966). The gravitational attraction of a right rectangular prism. Geophysics, 30, 362–371.

    Article  Google Scholar 

  • Nasuti, A., & Ardestani, E. V. (2007). 3-D Forward gravity modeling of basement interfaces with quadratic density contrast. EGM 2007 International Workshop. http://www.eageseg.org/data/egm2007/Sessione%20B/Poster%20papers/B_PP_07.pdf. Accessed 12 Aug 2018.

  • Nelson, T. H., & Fairchild, L. (1989). Emplacement and evolution of salt sills in the northern Gulf of Mexico. Houston Geological Society Bulletin, 32(1), 6–7.

    Google Scholar 

  • Okabe, M. (1979). Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translation into magnetic anomalies. Geophysics, 44, 730–741.

    Article  Google Scholar 

  • Papp, G., & Kalmar, J. (1995). Investigation of sediment compaction in the Pannonian basin using 3D gravity modelling. Physics of the Earth and Planetary Interiors, 88, 89–100.

    Article  Google Scholar 

  • Paul, M. K. (1974). The gravity effect of a homogeneous polyhedron for three-dimensional interpretation. Pure and Applied Geophysics, 112, 553–561.

    Article  Google Scholar 

  • Pham, L. T., Oksum, E., & Do, T. D. (2018). GCH_gravinv: a MATLAB-based program for inverting gravity anomalies over sedimentary basins. Computers & Geosciences (in press). https://www.sciencedirect.com/science/article/pii/S0098300418301730. Accessed 13 Aug 2018.

  • Pilkington, M., & Crossley, D. J. (1986). Determination of crustal interface topography from potential fields. Geophysics, 51, 1277–1284.

    Article  Google Scholar 

  • Pohanka, V. (1988). Optimum expression for computation of the gravity field of a homogeneous polyhedral body. Geophysical Prospecting, 36, 733–751.

    Article  Google Scholar 

  • Rao, P. R., Swamy, K. V., & Murthy, I. V. R. (1999). Inversion of gravity anomalies of three-dimensional density interfaces. Computers & Geosciences, 25, 887–896.

    Article  Google Scholar 

  • Rezaie, M., Moradzadeh, A., & Kalate, A. N. (2017). 3D gravity data-space inversion with sparseness and bound constraints. Journal of Mining & Environment, 8(2), 227–235.

    Google Scholar 

  • Talwani, M., & Ewing, M. (1960). Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape. Geophysics, 25(1), 203–225.

    Article  Google Scholar 

  • Tenzer, R., & 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/. Accessed 08 Aug 2018.

  • Tsoulis, D. (2000). A note on the gravitational field of the right rectangular prism. Bollettino di Geodesia e Scienze Affini, 1, 21–35.

    Google Scholar 

  • Wu, L., & Chen, L. (2016). Fourier forward modeling of vector and tensor gravity fields due to prismatic bodies with variable density contrast. Geophysics, 81(1), G13–G26.

    Article  Google Scholar 

  • Yerkes, R.F., McCulloh, T. H., Schoellhamer, J. E., & Vedder, J. G. (1965). Geology of the Eastern Los Angeles Basin, California—an Introduction, Geological Survey Professional Paper 420-A, United States Government Printing Office. https://pubs.usgs.gov/pp/0420a/report.pdf. Accessed 10 Aug 2018.

  • Zhdanov, M. S., & 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. Accessed 08 Aug 2018.

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Acknowledgements

The authors sincerely thank the reviewers Drs. H Holstein in particular and Coşkun SARI and the Editor Hans-Jürgen Götze for their very useful comments/suggestions and feed back to improve the manuscript as presented.

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  1. Centre for Earth, Ocean and Atmospheric Sciences, University of Hyderabad, Gachibowli, Hyderabad, 500046, India

    K. Mallesh, V. Chakravarthi & B. Ramamma

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  1. K. Mallesh
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Mallesh, K., Chakravarthi, V. & Ramamma, B. 3D Gravity Analysis in the Spatial Domain: Model Simulation by Multiple Polygonal Cross-Sections Coupled with Exponential Density Contrast. Pure Appl. Geophys. 176, 2497–2511 (2019). https://doi.org/10.1007/s00024-019-02103-9

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