A Comparative Performance of Least-Square Method and Very Fast Simulated Annealing Global Optimization Method for Interpretation of Self-Potential Anomaly over 2-D Inclined Sheet Type Structure

Authors

  • Arkoprovo Biswas
     Department of Earth and Environmental Sciences, Indian Institute of Science Education and Research (IISER), Bhopal, Bhopal - 462 066

DOI:

https://doi.org/10.1007/s12594-016-0512-8

Keywords:

Self Potential Anomaly, 2D Inclined Sheet, least Square, VFSA.

Abstract

Inversion of self-potential anomaly for 2-D inclined sheets of infinite horizontal extent has been studied. Least-square inversion and very fast simulated annealing global optimization has been used to model the five parameters of self potential anomaly. The method of least square and very fast simulated annealing global optimization method is compared and analyzed. Very fast simulated annealing can model the noisy and field data of self potential anomaly very precisely than linear inversion technique. However, time taken by very fast simulated annealing inversion is larger than linearized inversion. The comparative analysis has been done on synthetic data (noise free and noisy) and two field data from Bavarian woods anomaly, Germany and Surda anomaly, India to show the efficacy of both the methods. The estimated parameters were compared with those from previous studies using various global optimization algorithms, mainly neural network, genetic algorithm and particle swarm optimization on the same field data sets. It can be concluded that the global optimization algorithms considered in this study were able to yield compatible solutions with those from least-square methods. The present global optimization method is in good agreement with the other global optimization methods in terms of results and computation time.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Issue

Volume 88, Issue 4, October 2016 Pages (399-532)

Section

Research Articles

Downloads

Published

2016-10-01

How to Cite

Biswas, A. (2016). A Comparative Performance of Least-Square Method and Very Fast Simulated Annealing Global Optimization Method for Interpretation of Self-Potential Anomaly over 2-D Inclined Sheet Type Structure. Journal of Geological Society of India, 88(4), 493–502. https://doi.org/10.1007/s12594-016-0512-8
Crossref
Scopus
Google Scholar
Europe PMC

References

ABDELRAHMAN, E.M., EL-ARABY, H.M., EL-ARABY, T.M., HASSANEEN, A.G. and HAFEZ, M. A. (2003) New methods for shape and depth determinations from SP data. Geophys., v.68, pp.1202-1210.

ABDELRAHMAN, E.M., ESSA, K.S., ABO-EZZ, E.R., SULTAN, M., SAUCK, W.A. And Gharieb, A.G. (2008) New least-square algorithm for model parameters estimation using self- potential anomalies. Computers and Geosciences, v.34, pp.1569-1576.

ABDELRAHMAN, E.M., EL-ARABY, T.M. and ESSA, K.S. (2009) Shape and depth determinations from second moving average residual self-potential anomalies. Jour. Geophys. Engg., v.6, pp.43-52.

AL-GARANI, M.A. (2010) Interpretation of Spontaneous Potential Anomalies from Some Simple Geometrically Shaped Bodies Using Neural Network Inversion. Acta Geophysica, v.58, pp.143-162.

ASFAHANI, J. and TLAS, M. (2005) A Constrained Nonlinear Inversion Approach to Quantitative Interpretation of Selfpotential Anomalies Caused by Cylinders, Spheres and Sheetlike Structures. Pure Appld. Geophys., v.162, pp.609-624.

BACKUS, G. and GILBERT, F. (1967) Numerical applications of formalism for geophysical inversion problems. Geophys. Jour. Royal Astron. Soc., v.13, pp.247-276.

BACKUS, G. and GILBERT, F. (1970) Uniqueness in the inversion of inaccurate gross earth data. Phil. Trans. Royal Soc. A, v.266, pp.123-192.

BISWAS, A. (2016) Interpretation of gravity and magnetic anomaly over thin sheet-type structure using very fast simulated annealing global optimization technique. Modeling Earth Systems and Environment, v.2(1), pp.30.

BISWAS, A. and SHARMA, S.P. (2016a) Interpretation of Self-potential anomaly over 2-D inclined thick sheet structures and analysis of uncertainty using very fast simulated annealing global optimization. Acta Geodaetica et Geophysica, (DOI: 10.1007/ s40328-016-0176-2).

BISWAS, A. and SHARMA, S.P. (2016b) Integrated geophysical studies to elicit the structure associated with Uranium mineralization around South Purulia Shear Zone, India: A Review. Ore Geol. Rev., v.72, pp.1307-1326 (DOI: 10.1016/j.oregeorev.2014.12.015).

BISWAS, A. (2015) Interpretation of residual gravity anomaly caused by a simple shaped body using very fast simulated annealing global optimization. Geoscience Frontiers, (DOI: 10.1016/ j.gsf.2015.03.001).

BISWAS, A. and SHARMA, S.P. (2015b) Interpretation of self-potential anomaly over idealized body and analysis of ambiguity using very fast simulated annealing global optimization. Near Surface Geophysics, v.13(2), pp.179-195.

BISWAS, A., MANDAL, A., SHARMA, S.P. and MOHANTY, W.K. (2014) Delineation of subsurface structure using self-potential, gravity and resistivity surveys from South Purulia Shear Zone, India: Implication to uranium mineralization. Interpretation, v.2(2), pp.T103–T110.

BISWAS, A. and SHARMA, S.P. (2014a) Optimization of Self-Potential interpretation of 2-D inclined sheet-type structures based on Very Fast Simulated Annealing and analysis of ambiguity. Jour. Appld. Geophys., v.105, pp.235-247.

BISWAS, A. and SHARMA, S.P. (2014b) Resolution of multiple sheettype structures in self-potential measurement. Jour. Earth System Sci., v.123(4), pp.809-825.

BISWAS, A. (2013) Identification and Resolution of Ambiguities in Interpretation of Self-Potential data: Analysis and integrated study around South Purulia Shear Zone, India. Ph.D Thesis, Department of Geology and Geophysics, Indian Institute of Technology Kharagpur, 199pp, DOI: http://www.idr.iitkgp. ac.in/xmlui/handle/123456789/3247

CAGLAR, I. (2000) Visual interpretation of superposed self-potential anomalies in mineral exploration. Computers and Geosciences, v. 26, pp.847-852.

CORWIN, R.F. And HOOVER, D.B. (1979) The self-potential method in geothermal exploration. Geophys., v.44, pp.226-245.

CORRY, C.E. (1985) Spontaneous potential associated with porphyry sulphide mineralization. Geophys., v.50, pp.10201034.

DOSSO, S.E. and OLDENBURG, D.W. (1991) Magnetotelluric appraisal using simulated annealing. Geophys. Jour. Internat., v.106, pp.370-385.

EL-ARABY, H.M. (2004) A new method for complete quantitative interpretation of self-potential anomalies. Journal of Applied Geophysics, v. 55, pp.211-224.

EL-KALIOUBY, H.M. And AL-GARANI, M.A. (2009) Inversion of selfpotential anomalies caused by 2D inclined sheets using neural networks. Jour. Geophys. Engg., v.6, pp.29-34.

FITTERMAN, D. V. and CORWIN, R.F. (1982) Inversion of selfpotential data from the Cerro-Prieto geothermal field Mexico. Geophysics, v.47, pp.938- 945.

GOKTURKLER, G. and BALKAYA, C. (2012) Inversion of self-potential anomalies caused by simple-geometry bodies using global optimization algorithms. Jour. Geophys. Engg., v.9, pp.498507.

JARDANI, A., REVIL, A. BOLEVE, A. and DUPONT, J.P. (2008) Threedimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields. Jour. Geophys. Res., Solid Earth, v.113, pp.B09204.

JUAN, L.F.M., ESPERANZA, G.G., JOSí‰, P.F.í., HEIDI, A.K. and Cí‰SAR, O.M.P. (2010) PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case. Jour. Appld. Geophys., v.71, pp.13-25.

MARQUARDT, D.W. (1970) Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation. Technometrics, v.12, pp.591-612.

MARQUARDT, D.W. (1963) An algorithm for least-squares optimization of non-linear parameters. Jour. Soc. Industrial Appld. Mathematics, v. 11, pp. 431-441.

MEISER, P. (1962) A method of quantitative interpretation of selfpotential measurements. Geophys. Prospect., v.10, pp.203-218.

MENDONCA, C.A. (2008) Forward and inverse self-potential modeling in mineral exploration. Geophys., v.73, pp.F33-43.

MONTEIRO SANTOS, F. A., ALMEIDA, E. P., CASTRO, R., NOLASCO, M. and MENDES-VICTOR, L. (2002) A hydrogeological investigation using EM34 and SP surveys. Earth Planets and Space, v.54, pp.655-662.

MONTEIRO SANTOS, F. A. (2010) Inversion of Self-potential of Idealized bodies anomalies using particle swarm optimization. Computers and Geosciences, v.36, pp.1185-1190.

MOSEGAARD, K. and TARANTOLA, A. (1995) Monte Carlo sampling of solutions to inverse problems. Jour. Geophys. Res., v.100 (B7), pp.12431-12447.

MURTHY, B.V.S. and HARICHARAN, P. (1984) Self-potential anomaly over double line of poles-interpretation through log curves. Proc. Indian Acad. Sci. (Earth Planet. Sci.), v.93, pp.437-445.

MURTHY, B.V.S. and HARICHARAN, P. (1985) Nomograms for the complete interpretation of spontaneous potential profiles over sheet like and cylindrical 2D structures. Geophys., v.50, pp.1127-1135.

MURTHY, I.V.R., SUDHAKAR, K.S. and RAO, P.R. (2005) A new method of interpreting self- potential anomalies of twodimensional inclined sheets. Computers and Geosciences, v.31, pp.661-665.

PAUL, M. K., (1965) Direct interpretation of self-potential anomalies caused by inclined sheets of infinite extension. Geophys., v.30, pp.418-423.

PAUL, M.K., DATA, S. and BANERJEE, B. (1965) Interpretation of SP anomalies due to localized causative bodies. Pure Appld. Geophys., v.61, pp.95-100.

RAO, B.S.R., MURTHY, I.V.R. and REDDY, S.J. (1970) Interpretation of self-potential anomalies of some simple geometrical bodies. Pure Appld. Geophys., v.78, pp.60-77.

ROTHMAN, D.H. (1985) Nonlinear inversion, statistical mechanics and residual statics estimation. Geophys., v.50, pp.2784-2796.

ROTHMAN, D.H. (1986) Automatic estimation of large residual statics correction. Geophys., v.51, pp.337-346.

ROY, S.V.S. and Mohan, N.L. (1984) Spectral interpretation of self potential anomalies of some simple geometric bodies. Pure Appld. Geophys., v.78, pp.66-77.

SATO, M. and MOONEY, H.M. (1960) The electrochemical mechanism of sulfide self-potentials. Geophys., v.25, pp.226249.

SEN, M.K., BHATTACHARYA, B.B. and STOFFA, P.L. (1993) Nonlinear inversion of resistivity sounding data. Geophys., v.58, pp.496507.

SEN, M.K. and STOFFA, P.L. (1995) Global Optimization Methods in Geophysical Inversion Elsevier Amsterdam 277p.

SINGH, A. and BISWAS, A. (2016) Application of global particle swarm optimization for inversion of residual gravity anomalies over geological bodies with idealized geometries. Natural Resources Res., v.25(3), pp.297-314.

SHARMA, S.P. and BISWAS, A. (2011) Global nonlinear optimization for the estimation of static shift and interpretation of 1-D Magnetotelluric sounding data. Annals Geophys., v.54(3), pp.249-264.

SHARMA, S.P. and BISWAS, A. (2013a) Interpretation of self-potential anomaly over 2D inclined structure using very fast simulated annealing global optimization-An insight about ambiguity. Geophysics, v.78(3), pp.WB3-15.

SHARMA, S.P. and BISWAS, A. (2013b). A practical solution in delineating thin conducting structures and suppression problem in direct current resistivity sounding. Jour. Earth System Sci., 122 (4), 1065–1080.

SHARMA, S. P., BISWAS, A. and MITTAL, S. (2014). Delineation of extension of uranium mineralization zone using resistivity and Very low frequency electromagnetic surveys around South Purulia Shear Zone, India. Jour. Geol. Soc. India, v.84(6), pp.645–656.

SHARMA, S.P. and KAIKKONEN, P. (1998) Two-dimensional nonlinear inversion of VLF-R data using simulated annealing. Geophys. Jour. Internat., v.133, pp.649-668.

SHARMA, S.P. and KAIKKONEN, P. (1999) Appraisal of equivalence and suppression problems in 1-D EM and DC measurements using global optimization and joint inversion. Geophys. Prospect., v.47, pp.219-249.

SHARMA, S.P. (2012) VFSARES- A very fast simulated annealing FORTRAN program for interpretation of 1-D DC resistivity sounding data from various electrode array. Computers and Geosciences, v.42, pp.177-188.

SUNDARARAJAN, N, ARUN KUMAR, I., MOHAN, N.L., and SESHAGIRI RAO, S.V. (1990) Use of Hilbert transform to interpret self potential anomalies due to two dimensional inclined sheets. Pure Applied Geophysics, v.133, pp. 117-126.

SUNDARARAJAN, N., SRINIVASA RAO, P. and SUNITHA, V. (1998) An analytical method to interpret self-potential anomalies caused by 2D inclined sheets. Geophys., v.63, pp.1551-1555.

ZHAO, L. S., SEN, M. K., STOFFA, P. and FROHLICH, C. (1996) Application of Very Fast Simulated Annealing to the Determination of the Crustal Structure beneath Tibet. Geophys. Jour. Internat., v.125, pp.355-370.

ZLOTNICKI, J. and NISHIDA, Y. (2003) Review on morphological insights of Self-Potential anomalies on volcanoes. Surv. Geophysics, v.24, pp.291-338.