Exploration Geophysics Exploration Geophysics Society
Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

A new inversion algorithm for estimating the best fitting parameters of some geometrically simple body to measured self-potential anomalies

Khalid Essa 1 Salah Mehanee 1 2 4 Paul D. Smith 3
+ Author Affiliations
- Author Affiliations

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

2 Present address: Department of Mathematics, Division of Information and Communication Sciences, Macquarie University, NSW 2109, Australia.

3 Department of Mathematics, Division of Information and Communication Sciences, Macquarie University, NSW 2109, Australia.

4 Corresponding author. Email: smehanee@ics.mq.edu.au

Exploration Geophysics 39(3) 155-163 https://doi.org/10.1071/EG08017
Submitted: 4 December 2006  Published: 22 September 2008

Abstract

We have developed a new least-squares inversion approach to determine successively the depth (z), polarization angle, and electric dipole moment of a buried structure from the self-potential (SP) anomaly data measured along a profile. This inverse algorithm makes it possible to use all the observed data when determining each of these three parameters. The problem of the depth determination has been parameterised from the forward modelling operator, and transformed into a nonlinear equation in the form ξ(z) = 0 by minimising an objective functional in the least-squares sense. Using the estimated depth and applying the least-squares method, the polarization angle is then determined from the entire observed data by a linear formula. Finally, knowing the depth and polarization angle, the dipole moment is expressed by a linear equation and is computed using the whole measured data. This technique is applicable for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The method is tested and verified on numerical examples with and without random noise. It is also successfully applied to two real datasets from mineral exploration in Germany and Turkey, and we have found that the estimated depths and the other SP model parameters are in good agreement with the known actual values.

Key words: least-squares inversion, self-potential anomalies, self-potential parameters.


Acknowledgments

We wish to thank Dr Lindsay Thomas, Dr John Bishop and an anonymous reviewer who provided very useful comments, thorough reviews, and improvements to this paper.


References

Abdelrahman, E. M., and Sharafeldin, S. M., 1997, A least squares approach to depth determination from residual self-potential anomalies caused by horizontal cylinders and spheres: Geophysics 62, 44–48.
CrossRef |

Abdelrahman, E. M., Ammar, A. A., Sharafeldin, S. M., and Hassanein, H. I., 1997a, Shape and depth solutions from numerical horizontal self-potential gradients: Journal of Applied Geophysics 37, 31–43.
CrossRef |

Abdelrahman, E. M., El-Araby, T. M., Ammar, A. A., and Hassanein, H. I., 1997b, A least-squares approach to shape determination from self-potential anomalies: Pure and Applied Geophysics 150, 121–128.
CrossRef |

Abdelrahman, E. M., Ammar, A. A., Hassanein, H. I., and Hafez, M. A., 1998, Derivative analysis of SP anomalies: Geophysics 63, 890–897.
CrossRef |

Abdelrahman, E. M., El-Araby, T. M., El-Araby, H. M., Ammar, A. A., and Hassanein, H. I., 1999, Shape and depth solutions from moving average residual self-potential anomalies: Kuwait Journal of Science & Engineering 26, 321–335.


Abdelrahman, E. M., El-Araby, H. M., Hassanein, A. G., and Hafez, M. A., 2003, New methods for shape and depth determinations from SP data: Geophysics 68, 1202–1210.
CrossRef |

Abdelrahman, E. M., Saber, H. S., Essa, K. S., and Fouda, M. A., 2004, A least-squares approach to depth determination from numerical horizontal self-potential gradients: Pure and Applied Geophysics 161, 399–411.
CrossRef |

Abdelrahman, E. M., Essa, K. S., Abo-Ezz, E. R., Soliman, K. S., and El-Araby, T. M., 2006a, A least-squares depth-horizontal position curves method to interpret residual SP anomaly profiles: Journal of Geophysics and Engineering 3, 252–259.
CrossRef |

Abdelrahman, E. M., Essa, K. S., Abo-Ezz, E. R., and Soliman, K. S., 2006b, Self-potential data interpretation using standard deviations of depths computed from moving-average residual anomalies: Geophysical Prospecting 54, 409–423.
CrossRef |

Asfahani, J., and Tlas, M., 2005, A constrained nonlinear inversion approach to quantitative interpretation of self-potential anomalies caused by cylinders, spheres and sheet-like structures: Pure and Applied Geophysics 162, 609–624.
CrossRef |

Babu, R. H. V., and Rao, A. D., 1988, A rapid graphical method for the interpretation of the self-potential anomaly over a two-dimensional inclined sheet of finite depth extent: Geophysics 53, 1126–1128.
CrossRef |

Banerjee, B., 1971, Quantitative interpretation of self-potential anomalies of some specific geometric bodies: Pure and Applied Geophysics 90, 138–152.
CrossRef |

Bhattacharya, B. B., and Roy, N., 1981, A note on the use of nomograms for self-potential anomalies: Geophysical Prospecting 29, 102–107.
CrossRef |

Castermant, J., Mendonca, C. A., Revil, A., Trolard, F., Bourrié, G., and Linde, N., 2008, Redox potential distribution inferred from self-potential measurements associated with the corrosion of a burden metallic body: Geophysical Prospecting 56, 269–282.
CrossRef |

Colangelo, G., Lapenna, V., Perrone, A., Piscitelli, S., and Telesca, L., 2006, 2D Self-Potential tomographies for studying groundwater flows in the Varco d’Izzo landslide (Basilicata, southern Italy): Engineering Geology 88, 274–286.
CrossRef |

De Witte, L., 1948, A new method of interpretation of self-potential field data: Geophysics 13, 600–608.
CrossRef |

El-Araby, H. M., 2004, A new method for complete quantitative interpretation of self-potential anomalies: Journal of Applied Geophysics 55, 211–224.
CrossRef |

Essa K. , and Mehanee S. , 2007, A rapid algorithm for self-potential data inversion with application to mineral exploration: Presented at the 19th International Geophysical Conference and Exhibition, Australian Society of Exploration Geophysicists, 18–22 November, Perth, Australia.

Fitterman, D. V., 1979, Calculations of self-potential anomalies near vertical contacts: Geophysics 44, 195–205.
CrossRef |

Furness, P., 1992, Modeling spontaneous mineralization potentials with a new integral equation: Journal of Applied Geophysics 29, 143–155.
CrossRef |

Goldie, M., 2002, Self-potentials associated with the Yanacocha high-sulphidation gold deposit in Peru: Geophysics 67, 684–689.
CrossRef |

Heiland C. A. , 1940, Geophysical exploration: Hanfner Publ. Co.

Hämmann, M., Maurer, H. R., Green, A. G., and Horstmeyer, H., 1997, Self-potential image reconstruction: capabilities and limitations: Journal of Environmental & Engineering Geophysics 2, 21–35.


Jardani, A., Dupont, J. P., and Revil, A., 2006, Self-potential signals associated with preferential groundwater flow pathways in sinkholes: Journal of Geophysical Research 111, B09204.
CrossRef |

Meiser, P., 1962, A method of quantitative interpretation of self-potential measurement: Geophysical Prospecting 10, 203–218.
CrossRef |

Minsley, B. J., Sogade, J., and Morgan, F. D., 2007, Three-dimensional self-potential inversion for subsurface DNAPL contaminant detection at the Savannah River Site, South Carolina: Water Resources Research 43, W04429.
CrossRef |

Murty, B. V. S., and Haricharan, P., 1985, Nomogram for the spontaneous potential profile over sheet-like and cylindrical two-dimensional sources: Geophysics 50, 1127–1135.
CrossRef |

Press W. H. , Flannery B. P. , Teukolsky S. A. , and Vetterling W. T. , 1986, Numerical Recipes, The Art of Scientific Computing: Cambridge University Press.

Rao, A. D., and Babu, R. H. V., 1983, Quantitative interpretation of self potential anomalies due to two-dimensional sheet-like bodies: Geophysics 48, 1659–1664.
CrossRef |

Shi W. , and Morgan F. D. , 1996, Non-uniqueness in self-potential inversion: 66th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 950–953.

Stanley, J. M., 1977, Simplified magnetic interpretation of the geologic contact and thin dike: Geophysics 42, 1236–1240.
CrossRef |

Tarantola A. , 2005, Inverse problem theory and methods for model parameter estimation: Society of Industrial and Applied Mathematics (SIAM).

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

Yungul, S., 1950, Interpretation of spontaneous polarization anomalies caused by spherical ore bodies: Geophysics 15, 237–246.
CrossRef |

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



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