Ilk_inv: a Matlab based algorithm for rapid computation of pseudo-3D density contrast distribution by using Bouguer gravity data

Yıl 2021, Cilt: 166 Sayı: 166, 19 - 31, 15.12.2021

İlkin Özsöz

https://doi.org/10.19111/bulletinofmre.959011

Öz

The new generation Matlab-based algorithm provides a rapid estimation of density contrast distribution. The 3D assumption, which is based on the 1D equation, is used. Therefore, the output is called pseudo-3D instead of 3D. The algorithm uses singular value decomposition and the median filter to produce pseudo-3D results. The success of the method is tested by theoretical and field studies. For synthetic studies,  ingle-source models produce reasonable outputs, compared to the true density contrast value. However, the multiple source model shows slight deviations which are ±0.3 g/cm³, with respect to the true density contrast value. The acceptable results are observed for the Bouguer anomaly of the eastern Mediterranean region. The resolution matrix indicates that the inversion process is biased due to the generalised  inverse. The algorithm provides a quite different qualitative interpretation perspective to the interpreter.

Anahtar Kelimeler

Singular Value Decomposition, Pseudo- 3D Density Map, Gravity Modelling.

Teşekkür

I would like to offer my special thanks to Dr. Chris GREEN for his insightful contributions to the theory of the algorithm. Moreover, I am grateful to anonymous reviewers for their comments.

Kaynakça

• Al Chalabi, M. A. 1972. Interpretation of gravity anomalies by non-linear optimisation. Geophysical Prospecting 20(1), 1-16.
• Allen, T. I., Cooper, S. A., Cull, J. P. 2001. High definition gravity surveys and density modelling for kimberlite exploration. Exploration Geophysics 32(2), 89-94.
• Arias Castro, E., Donoho, D. L. 2009. Does median filtering truly preserve edges better than linear filtering?. The Annals of Statistics 37(3), 1172- 1206.
• Aster, R. C., Borchers, B., Thurber, C. H. 2018. Parameter Estimation and Inverse Problems. Elsevier.
• Bear, G. W., Al-Shukri, H. J., Rudman, A. J. 1995. Linear inversion of gravity data for 3-D density distributions. Geophysics 60(5), 1354-1364.
• Blakely, R. J. 1996. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press.
• Bonvalot, S., Balmino, G., Briais, A., Kuhn, M., Peyrefitte, A., Vales, N., Biancale, R., Gabalda, G., Reinquin, F. 2012. World Gravity Map: a set of global complete spherical Bouguer and isostatic anomaly maps and grids. International European Geosciences Union General Assembly Conference Abstracts 14, 11091.
• 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.
• Cai,Y. F., Li, C., Saridakis, E. N., Xue, L. Q. 2018. f (T) gravity after GW170817 and GRB170817A. Physical Review 97(10), 103513.
• Church, J. C., Chen, Y., Rice, S. V. 2008. A spatial median filter for noise removal in digital images. Institute of Electrical and Electronics Engineers Southeast Conference, 618-623.
• Clifford, G. D. 2005. Singular value decomposition and independent component analysis for blind source separation. Biomedical, Signal Image Process 44, 489-499.
• Cordell, L., Henderson, R. G. 1968. Iterative three- dimensional solution of gravity anomaly data using a digital computer. Geophysics 33(4), 596- 601.
• Delibasis, N., Ziazia, M., Voulgaris, N., Papadopoulos, T., Stavrakakis, G., Papanastassiou, D., Drakatos, G. 1999. Microseismic activity and seismotectonics of Heraklion area (central Crete Island, Greece). Tectonophysics 308(1-2), 237-248.
• Dilek, Y. 2006. Collision tectonics of the Mediterranean region: causes and consequences. Geological Society of America Special Papers 409, 1.
• Enmark, T. 1981. A versatile interactive computer program for computation and automatic optimization of gravity models. Geoexploration 19(1), 47-66.
• Fedi, M. 1997. Estimation of density, magnetization, and depth to source: a nonlinear and noniterative 3-D potential-field method. Geophysics 62(3), 814- 830.
• Fedi, M., Rapolla, A. 1999. 3-D inversion of gravity and magnetic data with depth resolution. Geophysics 64(2), 452-460.
• Freire, S. L., Ulrych, T. J. 1988. Application of singular value decomposition to vertical seismic profiling. Geophysics 53(6), 778-785.
• Golub, G. H., Van Loan, C. F. 1996. Matrix Computations. Johns Hopkins
• Gönenç, T., Akgün, M., Ergün, M. 2006. Girit yayının sismolojik ve bouguer gravite anomalisi verilerine göre yorumlanması. Geosound 48(1), 51-68.
• Gönenç, T., Akgün, M. 2012. Structure of the Hellenic subduction zone from gravity gradient functions and seismology. Pure and Applied Geophysics 169(7), 1231-1255.
• Grandis, H. 2009. Introduction to Geophysical Inversion Modeling. Indonesia Geophysical Expert Association (HAGI).
• Grandis, H., Dahrin, D. 2014. Constrained two-dimensional inversion of gravity data. Journal of Mathematical and Fundamental Sciences 46(1), 1-13.
• Granser, H. 1987. Nonlinear inversion of gravity data using the Schmidt-Lichtenstein approach. Geophysics 52(1), 88-93.
• Guspi, F. 1992. Three-dimensional Fourier gravity inversion with arbitrary density contrast. Geophysics 57(1), 131-135.
• Hammer, P. T. C., Hildebrand, J. A., Parker, R. L. 1991. Gravity inversion using semi-norm minimization: density modeling of Jasper Seamount. Geophysics 56(1), 68-79.
• Hinze, W. J. 1990. Geotechnical an Environmental Geophysics. SEG, I, 75-126.
• Hinze, W. J., Von Frese, R. R., Saad, A. H. 2013. Gravity and Magnetic Exploration: Principles, Practices, and Applications. Cambridge University Press.
• Huestis, S. P. 1988. Uniform norm minimization for two- signed solutions. Geophysics 53(5), 721-722.
• Justusson, B. I. 1981. Median Filtering: Statistical Properties. In Two-Dimensional Digital Signal Processing II. Springer, Heidelberg, Berlin, 161-196.
• Kahveci, M., Çırmık, A., Doğru, F., Pamukçu, O., Gönenç, T. 2019. Subdividing the tectonic elements of Aegean and Eastern Mediterranean with gravity and GPS data. Acta Geophysica 67(2), 491-500.
• Lanczos, C. 1997. Linear Differential Operators. Society for Industrial and Applied Mathematics, 564.
• Lawson, C. L., Hanson, R. J. 1974. Solving Least Squares Problems. Society for Industrial and Applied Mathematics, U.S., 350.
• Le Pichon, X. 1983. Land-locked oceanic basins and continental collision: the eastern Mediterranean as a case example. Hsu, K. (Ed.) Mountain Building, Academic Press, London, 201-211.
• Le Pichon, X., Angelier, J. 1979. The Hellenic arc and trench system: a key to the neotectonic evolution of the eastern Mediterranean area. Tectonophysics 60(1-2), 1-42.
• Levenberg, K. 1944. A method for the solution of certain nonlinear problems. Quarterly Applied Mathematics 2, 164-168.
• Li, Y., Oldenburg, D. W. 1998. 3-D inversion of gravity data. Geophysics 63(1), 109-119.
• Mareschal, J. C. 1985. Inversion of potential field data in Fourier transform domain. Geophysics 50(4), 685-691.
• Mart, Y., Ryan, W. 2003. The tectonics of Cyprus Arc: a model of complex continental collision. European Geophysical Society - American Geophysical Union - European Union of Geosciences Joint Assembly, 2282.
• McClusky, S., Balassanian, S., Barka, A., Demir, C., Ergintav, S., Georgiev, I., Gürkan, O., Hamburger, M., Hurst, K., Kahle, H., Kastens, K. 2000. Global positioning system constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. Journal of Geophysical Research: Solid Earth 105(B3), 5695-5719.
• McKenzie, D. 1972. Active tectonics of the Mediterranean region. Geophysical Journal International 30(2), 109-185.
• Meier, T., Rische, M., Endrun, B., Vafidis, A., Harjes, H.P. 2004. Seismicity of the Hellenic subduction zone in the area of western and central Crete observed by temporary local seismic networks. Tectonophysics 383(3-4), 149-169.
• Menichetti, V., Guillen, A. 1983. Simultaneous interactive magnetic and gravity inversion. Geophysical Prospecting 31(6), 929-944.
• Menke, W. 1984. Geophysical Data Analysis. Discrete Inverse Theory. Academic Press, New York, 312.
• Menke, W. 2018. Geophysical Data Analysis: Discrete Inverse Theory. Academic Press, New York.
• Mercier, J. L., Sorel, D., Vergely, P., Simeakis, K. 1989. Extensional tectonic regimes in the Aegean basins during the Cenozoic. Basin Research 2(1), 49-71.
• Nagihara, S., Hall, S. A. 2001. Three-dimensional gravity inversion using simulated annealing: constraints on the diapiric roots of allochthonous salt structures. Geophysics 66(5), 1438-1449.
• Oldenburg, D. W. 1974. The inversion and interpretation of gravity anomalies. Geophysics 39(4), 526-536.
• Öner, Z., Dilek, Y., Kadıoğlu, Y. K. 2010. Geology and geochemistry of the synextensional salihli granitoid in the Menderes core complex, western Anatolia, Turkey. International Geology Review 52(2-3), 336-368.
• Pamukçu, O. 2016. Geodynamic assessment of eastern Mediterranean region: a joint gravity and seismic b value approach. Arabian Journal of Geosciences 9(5), 360.
• Papazachos, B. C., Karakostas, V. G., Papazachos, C. B., Scordilis, E. M. 2000. The geometry of the Wadati–Benioff zone and lithospheric kinematics in the Hellenic arc. Tectonophysics 319(4), 275- 300.
• Parker, R. L. 1972. The rapid calculation of potential anomalies. Royal Astronomical Society Geophysical Journal, 31.
• Parker, R. L. 1974. Best bounds on density and depth from gravity data. Geophysics 39(5), 644-649.
• Parker, R. L. 1975. The theory of ideal bodies for gravity interpretation. Geophysical Journal International 42(2), 315-334.
• Parker, R. L. 1977. Understanding inverse theory. Annual Review of Earth and Planetary Sciences 5(1), 35- 64.
• Paterson, N. R., Reeves, C. V. 1985. Applications of gravity and magnetic surveys: The state-of-the-art in 1985. Geophysics 50(12), 2558-2594.
• Peacock, R. J. 1992. Cavity detection? an engineering application for gravity. Exploration Geophysics 23(4), 567-570.
• Pedersen, L. B. 1977. Interpretation of potential field data a generalized inverse approach. Geophysical Prospecting 25(2), 199-230.
• Pedersen, L. B. 1979. Constrained inversion of potential field data. Geophysical Prospecting 27(4), 726-748.
• Pilkington, M., Crossley, D. J. 1986. Determination of crustal interface topography from potential fields. Geophysics 51(6), 1277-1284.
• Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B.P. 2007. Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press.
• Reamer, S. K., Ferguson, J. F. 1989. Regularized two- dimensional Fourier gravity inversion method with application to the Silent Canyon caldera, Nevada. Geophysics 54(4), 486-496.
• Roberts, R. L., Hinze, W. J., Leap, D. I., Ward, S. H. 1990. Application of the gravity method to the investigation of a landfill in glaciated midcontinent, USA. Geotechnical and Environmental Geophysics 2, 253-260.
• Roy, A. 1962. Ambiguity in geophysical interpretation. Geophysics 27(1), 90-99.
• Smith, R. A. 1959. Some depth formulae for local magnetic and gravity anomalies. Geophysical Prospecting 7(1), 55-63.
• Smith, R. A. 1960. Some formulae for interpreting local gravity anomalies. Geophysical Prospecting 8(4), 607-613.
• Sorel, D., Mercier, J. L., Keraudren, B., Cushing, M. 1988. Le rôle de la traction de la lithosphère subductée dans l'évolution géodynamique plio-pléistocène de l'arc égéen: mouvements verticaux alternés et variations du régime tectonique. Comptes rendus de l'Académie des sciences. Série 2, Mécanique, Physique, Chimie, Sciences de l'univers, Sciences de la Terre 307(19), 1981-1986.
• Strang, G. 1988. Linear Algebra and Its Applications. Hartcourt Brace Jovanovich College Publishers.
• Tadjou, J. M., Nouayou, R., Kamguia, J., Kande, H. L., Manguelle Dicoum, E. 2009. Gravity analysis of the boundary between the Congo Craton and the Pan-African belt of Cameroon. Austrian Journal of Earth Sciences 102(1).
• Tarantola, A., Valette, B. 1982. Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics 20(2), 219-232.
• Tontini, F. C., Cocchi, L., Carmisciano, C. 2008. Potential- field inversion for a layer with uneven thickness: the Tyrrhenian Sea density model. Physics of the Earth and Planetary Interiors 166(1-2), 105-111.
• Tukey, J. W. 1974. Nonlinear (nonsuperposable) methods for smoothing data. Proceedings of Congress Record EASCOM, 673-681.
• Ulrych,T.J.,Freire,S.,Siston,P.1988.Eigenimageprocessing of seismic sections. International Society of Exploration Geophysicists Technical Program Expanded Abstracts, 1261-1265.
• Vasco, D. W. 1989. Resolution and variance operators of gravity and gravity gradiometry. Geophysics 54(7), 889-899.
• Vrabie, V. D., Mars, J. I., Lacoume, J. L. 2004. Modified singular value decomposition by means of independent component analysis. Signal Processing 84(3), 645-652.
• Xia, J., Sprowl, D. R. 1992. Inversion of potential-field data by iterative forward modelling in the wavenumber domain. Geophysics 57(1), 126-130.
• Zhao, B. B., Chen, Y. Q. 2011. Singular value decomposition (SVD) for extraction of gravity anomaly associated with gold mineralization in Tongshi gold field, Western Shandong Uplifted Block, Eastern China. Nonlinear Processes in Geophysics18(1), 103.