Skip to main content
SpringerLink
Log in

Accurate and Efficient Regularized Inversion Approach for the Interpretation of Isolated Gravity Anomalies

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

A very fast and efficient approach for gravity data inversion based on the regularized conjugate gradient method has been developed. This approach simultaneously inverts for the depth (z), and the amplitude coefficient (A) of a buried anomalous body from the gravity data measured along a profile. The developed algorithm fits the observed data by a class of some geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, infinitely long horizontal cylinder, and sphere models using the logarithms of the model parameters [log(z) and log(|A|)] rather than the parameters themselves in its iterative minimization scheme. The presented numerical experiments have shown that the original (non-logarithmed) minimization scheme, which uses the parameters themselves (z and |A|) instead of their logarithms, encountered a variety of convergence problems. The aforementioned transformation of the objective functional subjected to minimization into the space of logarithms of z and |A| overcomes these convergence problems. The reliability and the applicability of the developed algorithm have been demonstrated on several synthetic data sets with and without noise. It is then successfully and carefully applied to seven real data examples with bodies buried in different complex geologic settings and at various depths inside the earth. The method is shown to be highly applicable for mineral exploration, and for both shallow and deep earth imaging, and is of particular value in cases where the observed gravity data is due to an isolated body embedded in the subsurface.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

References

  • Abdelrahman, E. M., Bayoumi, A. I., Abdelhady, Y. E., Gobashy, M. M., and El-araby, H. M., 1989, Gravity interpretation using correlation factors between successive least-squares residual anomalies, Geophysics 54, 1614–1621.

  • Abdelrahman, E. M., Bayoumi, A. I., and El-araby, H. M., 1991, A least-squares minimization approach to invert gravity data, Geophysics, 56, 115–118.

  • Abdelrahman, E. M., and EI-Araby, T. M., 1993, A least-squares minimization approach to depth determination from moving average residual gravity anomalies, Geophysics, 59, 12, 1779–1784.

  • Abdelrahman E.M. and Sharafeldin S.M. 1995a, A least-squares minimization approach to depth determination from numerical horizontal gravity gradients, Geophysics, 60, 1259–1260.

  • Abdelrahman, E. M. and Sharafeldin, S. M., 1995b, A least-squares minimization approach to shape determination from gravity data, Geophysics, 60, 589–590.

  • Abdelrahman, E. M., El-Araby, H. M., El-Araby, T. M., and Abo- Ezz, E. R., 2001, Three-squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data: Geophysics, 66, 1105–1109.

  • Abedi, M., Afshar, A., Ardestani, V. E., Norouzi, G. H., and Lucas, C., 2009, Application of Various Methods for 2D Inverse Modeling of Residual Gravity Anomalies, Acta Geophysica, 58, 2, 317–336, doi:10.2478/s11600-009-0053-2.

  • Asfahani, J., and Tlas, M., 2008, An Automatic Method of Direct Interpretation of Residual Gravity Anomaly Profiles due to Spheres and Cylinders, Pure appl. geophys. 165, 981–994.

  • Asfahani, J., and Tlas, M., 2012, Fair Function Minimization for Direct Interpretation of Residual Gravity Anomaly Profiles Due to Spheres and Cylinders, Pure Appl. Geophys. 169, 157–165.

    Google Scholar 

  • Beck, R. H. and Qureshi, I. R., 1989, Gravity mapping of a subsurface cavity at Marulan, N.S.W, Exploration Geophysics, 20, 481–486.

  • Bowin, C., Scheer, E., and Smith, W., 1986, Depth estimates from ratios of gravity, geoid and gravity gradient anomalies, Geophysics, 51, 123–136.

  • Davis, W. E., Jackson, W. H. and Richter, D. H., 1957, Gravity prospecting for chromite deposits in Camaguey province, Cuba, Geophysics, Vol. XXII, 4, 848–869.

  • Elawadi, E., Salem, A., and Ushijima, K., 2001, Detection of cavities from gravity data using a neural network, Exploration Geophysics, 32, 75–79.

    Google Scholar 

  • Engl, H., Hanke, M., and Neubauer, A., 1996, Regularization of inverse problems, (Dordrecht: Kluwer).

  • Essa, K. S., 2007, Gravity data interpretation using the s-curves method, Journal of Geophysics and Engineering, 4, 2, 204–213.

    Google Scholar 

  • Essa, K. S., 2011, A new algorithm for gravity or self-potential data interpretation, J. Geophys. Eng. 8, 434–446.

    Google Scholar 

  • Essa, K. S., 2012, A fast interpretation method for inverse modeling of residual gravity anomalies caused by simple geometry, Journal of Geological Research, Volume 2012, Article ID 327037.

  • Essa, K. S., 2013, New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies, Journal of Advanced Research, doi:10.1016/j.jare.2012.11.006.

  • Essa K., Mehanee, S. and Smith, P. D., 2008, A new inversion algorithm for estimating the best fitting parameters of some geometrically simple body to measured self-potential anomalies, Exploration Geophysics. 39 155–63.

  • Fermin, S Viloche Baz, 2008, An Fixed-point iterations in determining the Tikhonov regularization parameter, Inverse Problems 24, 035001 (15pp).

  • Grant, F. S. and West, G. F., 1965, Interpretation Theory in Applied Geophysics. McGraw-Hill Book Co.

  • Gupta, O. P., 1983, A least-squares approach to depth determination from gravity data, Geophysics, 48, 360–375.

  • Hanke, M., 1995, Conjugate gradient type methods for ill posed problems, Longman.

  • Hansen, P. C., 2001, The L-curve and its use in the numerical treatment of inverse problems Computational Inverse Problems in Electrocardiology ed P Johnston (Southampton: WIT Press) pp 119–42 (invited chapter).

  • Hinze, W. J., 1990, The role of gravity and magnetic methods in engineering and environmental studies, Geotechnical and Environmental Geophysics, Vol I: Review and Tutorial, S. H., Ward, ed., Society of Exploration Geophysicists, Tulsa, OK.

  • Hinze, W. J., von Frese, R. R. B., and Saad, A. H., 2013, Gravity and magnetic exploration: Principles, practices and applications, Cambridge University Press, New York, USA.

  • Kilty, T. K., 1983, Werner deconvolution of profile potential field data, Geophysics, 48, 234–237.

  • Kokurin, M. Y., 2006, Stable iteratively regularized gradient method for nonlinear irregular equations under large noise, Inverse Problems 22, 197–207.

    Google Scholar 

  • LaFehr, T. R., and Nabighian, M. N., 2012, Fundamentals of gravity exploration, Society of Exploration Geophysicists, Tulsa, Ok., USA.

  • Long, L. T., and Kaufmann, R. D., 2013, Acquisition and analysis of terrestrial gravity data, Cambridge University Press, New York, USA.

  • Mehanee S., and Zhdanov, M., 2002, Two-dimensional magnetotelluric inversion of blocky geoelectrical structures, Journal of Geophysical Research-Solid Earth, 107(B4), doi:10.1029/2001JB000191.

  • Mehanee S., 2003, Multi-dimensional finite difference electromagnetic modeling and inversion based on the balance method, PhD thesis, The University of Utah, USA.

  • Mehanee, S., 2014, An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters, Ore Geology Reviews 57, 87–115.

    Google Scholar 

  • Mohan, N. L., Anandababu, L., and Seshagiri Rao, S. V., 1986, Gravity interpretation using the Mellin transform, Geophysics, 51, 114–122.

  • Nandi, B. K., Shaw, R. K., and Agarwal, B. N. P., 1997, A short note on: Identification of the shape of simple causative sources from gravity data, Geophysical Prospecting, 45, 513–520.

    Google Scholar 

  • Nettleton, L. L., 1962, Gravity and magnetics for geologists and seismologists, AAPG, 46, 1815–1838.

  • Nettleton, L. L., 1976, Gravity and Magnetics in Oil Prospecting. McGraw-Hill Book Co, 1976.

  • Odegard, M. E., and Berg, J. W., 1965, Gravity interpretation using the Fourier integral, Geophysics 30, 424–438.

  • Ramlau, R., 2005, On the use of fixed point iterations for the regularization of nonlinear ill-posed problems, J. Inv. Ill-Posed Problems, 13, No. 2, 175–200.

    Google Scholar 

  • Reginska, T., 1996, A regularization parameter in discrete ill-posed problems SIAM J. Sci. Comput. 3, 740–9.

    Google Scholar 

  • Reynolds, J. M., 1997, An introduction to applied and environmental geophysics, John Wiley & Sons, pp. 796, New York.

  • Ritz, M., and Bellion, Y., 1989, Geologic sections across the onshore Senegal - Mauritania basin derived from geoelectric studies, Can. J. Earth Sci. 26, 65–73.

    Google Scholar 

  • Ritz, M., and Vassal, J., 1986, Geoelectrical structure of the northern part of the Senegal Basin from joint interpretation of magnetotelluric and geomagnetic data, Journal of Geophysical Research, 91, b10, 443–10,456, September 10.

  • Robinson, E.S., Coruh, C., 1988, Basic Exploration Geophysics. Wiley, New York, NY.

  • Roussel, J. and Liger, J. L., 1983, A review of deep structure and ocean-continent transition in the Senegal basin (West Africa), Tectonophysics, 91, 183–211.

  • Roy, A., 1966, The method of continuation in mining geophysical interpretation, Geoexploration, 4, 65–83, 1966.

  • Roy, L., Agarwal, B. N. P., and Shaw, R. K., 2000, A new concept in Euler deconvolution of isolated gravity anomalies, Geophysical Prospecting, 48, 559–575.

    Google Scholar 

  • Roy, L., 2001, Short note: source geometry identification by simultaneous use of structural index and shape factor, Geophysical Prospecting, 49, 159–164.

    Google Scholar 

  • Salem, A., Elawadib, E., Ushijima, K., 2003, Depth determination from residual gravity anomaly data using a simple formula, Computers & Geosciences 29, 801–804.

    Google Scholar 

  • Salem, A., Ravat, D., Mushayandebvu, M. F. , and Ushijima, K., 2004, Linearized least-squares method for interpretation of potential-field data from sources of simple geometry, Geophysics, 69, 3, 783–788.

  • Shaw, R. K. and Agarwal, B. N. P., 1990, The application of Walsh transforms to interpret gravity anomalies due to some simple geometrically shaped causative sources: A feasibility study, Geophysics, 55, 843–850.

  • Siegel, H. O., Winkler, H. A. and Boniwell, J. B., 1957, Discovery of the Mobrun Copper Ltd. sulphide deposit, Noranda Mining District, Quebec. In methods and case histories in mining geophysics. Commonwealth Mining Met. Congr., 6th, Vancouver, 1957, pp.237–245 (1957).

  • Skeels, D. C., 1963, An approximate solution of the problem of maximum depth in gravity interpretation, Geophysics, 28 (5), 724–735.

  • Tarantola, A., 1987, Inverse problem theory, Elsevier, New York, 613 pp.

  • Tarantola, A., 2005, Inverse problem theory and methods for model parameters estimation, the Society for Industrial and Applied Mathematics.

  • Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of ill-posed problems: John Wiley and Sons.

  • Tikhonov, A. N., Leonov, A. S., and Yagola, A. G., 1998, Nonlinear Ill-Posed Problems Vols 1 and 2, London: Chapman and Hall.

  • Tlas, M., Asfahani, J., and Karmeh, H., 2005, A versatile nonlinear inversion to interpret gravity anomaly caused by a simple geometrical structure, Pure and Applied Geophysics, 162, 2557–2571.

    Google Scholar 

  • van den Doel, K., Ascher, U. M., and Haber, E., 2013, The lost honour of l2-based regularization, in “Large Scale Inverse Problems”, M. Cullen, M. Freitag, S. Kindernmann and R. Scheichl (Eds.), de Gryter, 181–203.

  • Zhdanov, M. S., 2002, Geophysical inversion theory and regularization problems, Elsevier.

Download references

Acknowledgment

I wish to thank Dr. José Fernández, Editor, for the time he dedicated for this paper. I also wish to thank two anonymous expert reviewers for their constructive comments which improved the paper.

Author information

Authors and Affiliations

  1. Department of Geophysics, Faculty of Science, Cairo University, Giza, Egypt

    Salah A. Mehanee

Authors
  1. Salah A. Mehanee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salah A. Mehanee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mehanee, S.A. Accurate and Efficient Regularized Inversion Approach for the Interpretation of Isolated Gravity Anomalies. Pure Appl. Geophys. 171, 1897–1937 (2014). https://doi.org/10.1007/s00024-013-0761-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-013-0761-z

keywords

Search

Navigation