A new approach to semi-infinite thin slab depth determination from second moving average residual gravity anomalies
El-Sayed M. Abdelrahman 1 2 Khalid S. Essa 1
+ Author Affiliations
- Author Affiliations
1 Geophysics Department, Faculty of Science, Cairo University, Giza, 12613, Egypt.
2 Corresponding author. Email: sayed5005@yahoo.com
Exploration Geophysics 44(3) 185-191 https://doi.org/10.1071/EG12045
Submitted: 25 July 2012 Accepted: 30 April 2013 Published: 7 June 2013
Abstract
In this paper, we have developed a new least- squares minimisation approach to determine the depth of a buried faulted structure approximated by a 2D semi-infinite horizontal slab from second moving average residual gravity anomalies. The problem of depth determination has been transformed into a problem of finding the solution to a nonlinear equation of the form z = f(z) .The method can be applied not only to residuals but also to observed data. The method overcomes the problems associated with determining the depth from successive horizontal derivative anomalies obtained from 2D gravity data using filters of successive graticule spacings. The method is applied to theoretical data with and without random errors and is tested on a field example from Egypt. In all cases, the depth solution obtained is in good agreement with the actual depth.
Key words: faults, gravity interpretation, least-squares method, second moving average method.
References
Abdelrahman, E. M., and Bayoumi, A. I., 1989, Nomograms for determining fault parameters from gravity data with application to the Mersa Matruh Basin, Egypt: Journal of African Earth Sciences, 9, 455–459| Nomograms for determining fault parameters from gravity data with application to the Mersa Matruh Basin, Egypt:Crossref | GoogleScholarGoogle Scholar |
Abdelrahman, E. M., and El-Araby, T. M., 1996, Shape and depth solutions from moving average residual gravity anomalies: Journal of Applied Geophysics, 36, 89–95
| Shape and depth solutions from moving average residual gravity anomalies:Crossref | GoogleScholarGoogle Scholar |
Abdelrahman, E. M., Riad, S., Refai, E., and Amin, Y., 1985, On the least-squares residual anomaly determination: Geophysics, 50, 473–480
| On the least-squares residual anomaly determination:Crossref | GoogleScholarGoogle Scholar |
Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., and Abo-Ezz, E. R., 2001, A new method for shape and depth determinations from gravity data: Geophysics, 66, 1774–1780
| A new method for shape and depth determinations from gravity data:Crossref | GoogleScholarGoogle Scholar |
Abdelrahman, E. M., El-Araby, H. M., El-Araby, T. M., and Abo-Ezz, E. R., 2003, A least-squares derivatives analysis of gravity anomalies due to faulted thin slabs: Geophysics, 68, 535–543
| A least-squares derivatives analysis of gravity anomalies due to faulted thin slabs:Crossref | GoogleScholarGoogle Scholar |
Agocs, W. B., 1951, Least-squares residual anomaly determination: Geophysics, 16, 686–696
| Least-squares residual anomaly determination:Crossref | GoogleScholarGoogle Scholar |
Barakat, M. G., and Darwish, M., 1984, Contribution to the litho-stratigraphy of the Lower Cretaceous Sequence in Mersa Matruh area, North Western Desert, Egypt: Paper presented at Egyptian Petroluem Exploration Society, Cairo.
Dobrin, M. B., 1976, Introduction to geophysical prospecting (3rd edition): McGraw Hill Book Co.
Fedi, M., and Quarta, T., 1998, Wavelet analysis for the regional-residual separation of potential field anomalies: Geophysical Prospecting, 46, 507–525
| Wavelet analysis for the regional-residual separation of potential field anomalies:Crossref | GoogleScholarGoogle Scholar |
Griffin, W. R., 1949, Residual gravity in theory and practice: Geophysics, 14, 39–56
| Residual gravity in theory and practice:Crossref | GoogleScholarGoogle Scholar |
Gupta, O. P., 1983, A least-squares approach to depth determination from gravity data: Geophysics, 48, 357–360
| A least-squares approach to depth determination from gravity data:Crossref | GoogleScholarGoogle Scholar |
Hammer, S., 1977, Graticule spacing versus depth discrimination in gravity interpretation: Geophysics, 42, 60–65
| Graticule spacing versus depth discrimination in gravity interpretation:Crossref | GoogleScholarGoogle Scholar |
Hinze, W. J., von Frese, R. R. B., and Saad, A. H., 2013, Gravity and magnetic exploration – principles, practices, and applications: Cambridge University Press.
Kilty, K. T., 1983, Werner deconvolution of profile potential field data: Geophysics, 48, 234–237
| Werner deconvolution of profile potential field data:Crossref | GoogleScholarGoogle Scholar |
Li, Y., and Oldenburg, D. W., 1998, Separation of regional and residual magnetic field data: Geophysics, 63, 431–439
| Separation of regional and residual magnetic field data:Crossref | GoogleScholarGoogle Scholar |
Lines, N. L., and Treitel, S., 1984, A review of least-squares inversion and its application to geophysical problems: Geophysical Prospecting, 32, 159–186
| A review of least-squares inversion and its application to geophysical problems:Crossref | GoogleScholarGoogle Scholar |
Martelet, G., Sailhac, P., Moreau, F., and Diament, M., 2001, Characterization of geological boundaries as 1-D wavelet transforms on gravity data: theory and application to the Himalayas: Geophysics, 66, 1116–1129
| Characterization of geological boundaries as 1-D wavelet transforms on gravity data: theory and application to the Himalayas:Crossref | GoogleScholarGoogle Scholar |
McGrath, P. H., 1991, Dip and depth extent of density boundaries using horizontal derivatives of upward continued gravity data: Geophysics, 56, 1533–1542
| Dip and depth extent of density boundaries using horizontal derivatives of upward continued gravity data:Crossref | GoogleScholarGoogle Scholar |
Nettleton, L. L., 1976, Gravity and magnetics in oil prospecting: McGraw Hill Book Co.
Oldham, C. H. G., and Sutherland, D. B., 1955, Orthogonal polynomials: their use in estimating the regional effect: Geophysics, 20, 295–306
| Orthogonal polynomials: their use in estimating the regional effect:Crossref | GoogleScholarGoogle Scholar |
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 2007, Numerical recipes: the art of scientific computing (3rd edition): Cambridge University Press.
Said, R., 1962, The geology of Egypt: Elsevier Publishing Co.
Stanley, J. M., 1977, Simplified gravity and magnetic interpretation of contact and dyke-like structures: Bulletin of the Australian Society of Exploration Geophysics, 8, 60–64
| Simplified gravity and magnetic interpretation of contact and dyke-like structures:Crossref | GoogleScholarGoogle Scholar |
Telford, W. M., Geldart, L. P., and Sheriff, R. E., 1990, Applied geophysics (2nd edition): Cambridge University Press.