Inversion of Gravity Data by Constrained Nonlinear Optimization based on nonlinear Programming Techniques for Mapping Bedrock Topography

Authors

1 M.Sc. in Geophysics, Department of Geophysics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

2 Associate Professor, Department of Physics, Faculty of science, Arak University, Iran

3 Assistant Professor, Department of physics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran

Abstract

A constrained nonlinear optimization method based on nonlinear programming techniques has been applied to map geometry of bedrock of sedimentary basins by inversion of gravity anomaly data. In the inversion, the applying model is a 2-D model that is composed of a set of juxtaposed prisms whose lower depths have been considered as unknown model parameters. The applied inversion method is a nonlinear one, which minimizes the objective functions by definition of different objective functions and an initial simple model to improve the initial model parameters. In this study, for different cases, sufficient objective functions are defined based on the condition which is encountered in the inverse problem. To control the under- determinacy part of the inverse problem and to prevent unreasonable instability in the resultant model, damping terms are added to the objective function. The act of synthetic inversion for different cases of parameterization has been examined and the results are analyzed. The results have almost depicted the recovery of the model and also fitting of the original and model response data. In addition, the method has been used to invert real gravity data in Aman Abad area. From the inversion results, depths of the basin, features like fractures and uplift in bedrock, along specific profiles have been determined. Thicker parts of sediments in the basin along the profiles have also been recognized, which have the potential for exploring drinking water in this area. 

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References

Abbott, R. E. and Louie, J. N., 2000, Depth to bedrock using gravimetry in the Reno and Carson City, Nevada, area basins. Geophysics, 65(2), 340-350.
Annecchione, M. A., Chouteau, M. and Keating, P., 2001, Gravity interpretation of bedrock topography: the case of the Oak Ridges Moraine, southern Ontario, Canada. Journal of Applied Geophysics, 47(1), 63-81.
Barbosa, V. C., Silva, J. B. and Medeiros, W. E., 1999, Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth. Geophysics, 64(5), 1429-1437.
Bell, R. E., Childers, V. A., Arko, R. A., Blankenship, D. D. and Brozena, J. M., 1999, Airborne gravity and precise positioning for geologic applications. Journal of Geophysical Research: Solid Earth, 104(B7), 15281-15292.
Biggs, M., 1973, Constrained minimisation using recursive quadratic programming: some alternative subproblem formulations: Hatfield Polytechnic. Numerical Optimisation Centre.
Blakely, R. J., 1996, Potential theory in gravity and magnetic applications: Cambridge University Press.
Burkhard, N. and Jackson, D. D., 1976, Application of stabilized linear inverse theory to gravity data. Journal of Geophysical Research, 81(8), 1513-1518.
Chakravarthi, V. and Sundararajan, N., 2007, 3D gravity inversion of basement relief—A depth-dependent density approach. Geophysics, 72(2), I23-I32.
Courtillot, V., Ducruix, J. and Le Mouël, J. L., 1974, A solution of some inverse problems in geomagnetism and gravimetry. Journal of Geophysical Research, 79(32), 4933-4940.
Fletcher, R., 2013, Practical methods of optimization: John Wiley and Sons.
Gill, P. E., Murray, W. and Wright, M. H., 1981, Practical optimization.
Granser, H., 1987, Nonlinear inversion of gravity data using the Schmidt-Lichtenstein approach. Geophysics, 52(1), 88-93.
Guspi, F., 1993, Noniterative nonlinear gravity inversion. Geophysics, 58(7), 935-940.
Han, S.-P., 1977, A globally convergent method for nonlinear programming. Journal of Optimization Theory and Applications, 22(3), 297-309.
Hock, W. and Schittkowski, K., 1983, A comparative performance evaluation of 27 nonlinear programming codes. Computing, 30(4), 335-358.
Kuhn, H. W. and Tucker, A. W., 1951, Nonlinear programming. Paper presented at the 2nd Berkeley Symposium. Berkeley, University of California Press.
Li, X., 2010, Efficient 3D gravity and magnetic modeling. Paper presented at the EGM 2010 International Workshop.
Oldenburg, D. and Pratt, D., 2002, Geophysical inversion for mineral exploration. Geophysical Inversion Facility, 1-53.
Parker, R., 1973, The rapid calculation of potential anomalies. Geophysical Journal International, 31(4), 447-455.
Pedersen, L. B., 1977, Interpretation of Potential Field Data a Generalized Inverse APPROACH*. Geophysical Prospecting, 25(2), 199-230.
Pilkington, M., 2006, Joint inversion of gravity and magnetic data for two-layer models. Geophysics, 71(3), L35-L42.
Pilkington, M. and Crossley, D., 1986, Determination of crustal interface topography from potential fields. Geophysics, 51(6), 1277-1284.
Plouff, D., 1966, Digital terrain corrections based on geographic coordinates. Paper presented at the Geophysics.
Powell, M., 1983, Variable metric methods for constrained optimization Mathematical Programming, The State of the Art, 288-311, Springer.
Powell, M. J., 1978a, The convergence of variable metric methods for non-linearly constrained optimization calculations. Nonlinear Programming, 3.
Powell, M. J., 1978b, A fast algorithm for nonlinearly constrained optimization calculations Numerical analysis, 144-157, Springer.
Richardson, R. M. and MacInnes, S. C., 1989, The inversion of gravity data into three‐dimensional polyhedral models. Journal of Geophysical Research: Solid Earth, 94(B6), 7555-7562.
Sarma D. D. and Selvaraj J. B., 1990, Two dimensional orthonormal trend surfaces for processing. Computer and Geosciences, 16(7), 897-909.
Schaefer, D. H., 1983, Gravity survey of Dixie Valley, west-central Nevada: US Geological Survey.
Schittkowski, K., 1986, NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems. Annals of Operations Research, 5(2), 485-500.
Silva, J. B., Oliveira, A. S. and Barbosa, V. C., 2010, Gravity inversion of 2D basement relief using entropic regularization. Geophysics, 75(3), I29-I35.
Smith, R. A., 1961, A uniqueness theorem concerning gravity fields. Paper presented at the Mathematical Proceedings of the Cambridge Philosophical Society.
Studinger, M., Bell, R. E., Blankenship, D. D., Finn, C. A., Arko, R. A., Morse, D. L., and Joughin, I., 2001, Subglacial sediments: a regional geological template for ice flow in West Antarctica. Geophysical Research Letters, 28(18), 3493-3496.
Zhou, X., 2013, Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods. Geophysical Prospecting, 61(1), 220-234.
Journal of the Earth and Space Physics
Volume 43, Issue 4
January 2018
Pages 27-45

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