1887
Volume 39, Issue 3
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Abstract

We have developed a new least-squares inversion approach to determine successively the depth (), 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 () = 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.

Loading

Article metrics loading...

/content/journals/10.1071/EG08017
2008-09-01
2026-01-19
Loading full text...

Full text loading...

References

  1. Abdelrahman E. M. 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 doi:10.1190/1.1444143
    [Google Scholar]
  2. Abdelrahman E. M. Ammar A. A. Sharafeldin S. M. Hassanein H. I. 1997 a Shape and depth solutions from numerical horizontal self-potential gradients: Journal of Applied Geophysics 37 31 43 doi:10.1016/S0926-9851(96)00058-4
    [Google Scholar]
  3. Abdelrahman E. M. El-Araby T. M. Ammar A. A. Hassanein H. I. 1997 b A least-squares approach to shape determination from self-potential anomalies: Pure and Applied Geophysics 150 121 128 doi:10.1007/s000240050067
    [Google Scholar]
  4. Abdelrahman E. M. Ammar A. A. Hassanein H. I. Hafez M. A. 1998 Derivative analysis of SP anomalies: Geophysics 63 890 897 doi:10.1190/1.1444399
    [Google Scholar]
  5. Abdelrahman E. M. El-Araby T. M. El-Araby H. M. Ammar A. A. Hassanein H. I. 1999 Shape and depth solutions from moving average residual self-potential anomalies: Kuwait Journal of Science & Engineering 26 321 335
    [Google Scholar]
  6. Abdelrahman E. M. El-Araby H. M. Hassanein A. G. Hafez M. A. 2003 New methods for shape and depth determinations from SP data: Geophysics 68 1202 1210 doi:10.1190/1.1598112
    [Google Scholar]
  7. Abdelrahman E. M. Saber H. S. Essa K. S. Fouda M. A. 2004 A least-squares approach to depth determination from numerical horizontal self-potential gradients: Pure and Applied Geophysics 161 399 411 doi:10.1007/s00024-003-2446-5
    [Google Scholar]
  8. Abdelrahman E. M. Essa K. S. Abo-Ezz E. R. Soliman K. S. El-Araby T. M. 2006 a A least-squares depth-horizontal position curves method to interpret residual SP anomaly profiles: Journal of Geophysics and Engineering 3 252 259 doi:10.1088/1742-2132/3/3/007
    [Google Scholar]
  9. Abdelrahman E. M. Essa K. S. Abo-Ezz E. R. Soliman K. S. 2006 b Self-potential data interpretation using standard deviations of depths computed from moving-average residual anomalies: Geophysical Prospecting 54 409 423 doi:10.1111/j.1365-2478.2006.00541.x
    [Google Scholar]
  10. Asfahani J. 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 doi:10.1007/s00024-004/2624-0
    [Google Scholar]
  11. Babu R. H. V. 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 doi:10.1190/1.1442551
    [Google Scholar]
  12. Banerjee B. 1971 Quantitative interpretation of self-potential anomalies of some specific geometric bodies: Pure and Applied Geophysics 90 138 152 doi:10.1007/BF00000875518
    [Google Scholar]
  13. Bhattacharya B. B. Roy N. 1981 A note on the use of nomograms for self-potential anomalies: Geophysical Prospecting 29 102 107 doi:10.1111/j.1365-2478.1981.tb01013.x
    [Google Scholar]
  14. Castermant J. Mendonca C. A. Revil A. Trolard F. Bourrié G. 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 doi:10.1111/j.1365-2478.2007.00675.x
    [Google Scholar]
  15. Colangelo G. Lapenna V. Perrone A. Piscitelli S. 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 doi:10.1016/j.enggeo.2006.09.014
    [Google Scholar]
  16. De Witte L. 1948 A new method of interpretation of self-potential field data: Geophysics 13 600 608 doi:10.1190/1.1437436
    [Google Scholar]
  17. El-Araby H. M. 2004 A new method for complete quantitative interpretation of self-potential anomalies: Journal of Applied Geophysics 55 211 224 doi:10.1016/j.jappgeo.2003.11.002
    [Google Scholar]
  18. 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.
  19. Fitterman D. V. 1979 Calculations of self-potential anomalies near vertical contacts: Geophysics 44 195 205 doi:10.1190/1.1440961
    [Google Scholar]
  20. Furness P. 1992 Modeling spontaneous mineralization potentials with a new integral equation: Journal of Applied Geophysics 29 143 155 doi:10.1016/0926-9851(92)90005-6
    [Google Scholar]
  21. Goldie M. 2002 Self-potentials associated with the Yanacocha high-sulphidation gold deposit in Peru: Geophysics 67 684 689 doi:10.1190/1.1484511
    [Google Scholar]
  22. Heiland C. A. 1940, Geophysical exploration: Hanfner Publ. Co.
  23. Hämmann M. Maurer H. R. Green A. G. Horstmeyer H. 1997 Self-potential image reconstruction: capabilities and limitations: Journal of Environmental & Engineering Geophysics 2 21 35
    [Google Scholar]
  24. Jardani A. Dupont J. P. Revil A. 2006 Self-potential signals associated with preferential groundwater flow pathways in sinkholes: Journal of Geophysical Research 111 B09204 doi:10.1029/2005JB004231
    [Google Scholar]
  25. Meiser P. 1962 A method of quantitative interpretation of self-potential measurement: Geophysical Prospecting 10 203 218 doi:10.1111/j.1365-2478.1962.tb02009.x
    [Google Scholar]
  26. Minsley B. J. Sogade J. 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 doi:10.1029/2005WR003996
    [Google Scholar]
  27. Murty B. V. S. Haricharan P. 1985 Nomogram for the spontaneous potential profile over sheet-like and cylindrical two-dimensional sources: Geophysics 50 1127 1135 doi:10.1190/1.1441986
    [Google Scholar]
  28. Press W. H. , Flannery B. P. , Teukolsky S. A. , and Vetterling W. T. 1986, Numerical Recipes, The Art of Scientific Computing: Cambridge University Press.
  29. Rao A. D. Babu R. H. V. 1983 Quantitative interpretation of self potential anomalies due to two-dimensional sheet-like bodies: Geophysics 48 1659 1664 doi:10.1190/1.1441446
    [Google Scholar]
  30. 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.
  31. Stanley J. M. 1977 Simplified magnetic interpretation of the geologic contact and thin dike: Geophysics 42 1236 1240 doi:10.1190/1.1440788
    [Google Scholar]
  32. Tarantola A. 2005, Inverse problem theory and methods for model parameter estimation: Society of Industrial and Applied Mathematics (SIAM).
  33. Tikhonov A. N. , and Arsenin V. Y. 1977, Solutions of ill-posed problems: John Wiley and Sons.
  34. Yungul S. 1950 Interpretation of spontaneous polarization anomalies caused by spherical ore bodies: Geophysics 15 237 246 doi:10.1190/1.1437597
    [Google Scholar]
  35. Zhdanov M. S. 2002, Geophysical inversion theory and regularization problems: Elsevier.
/content/journals/10.1071/EG08017
Loading
/content/journals/10.1071/EG08017
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error