New least-squares algorithm for model parameters estimation using self-potential anomalies

We have developed a new least-squares minimization approach to depth determination from self-potential (SP) data. By defining the anomaly value at the origin and at any two symmetrical points around the origin on the profile, the problem of depth determination from the residual SP anomaly has been transformed into finding a solution to a nonlinear equation of the form f(z)=0. Procedures are also formulated to estimate the polarization angle, amplitude coefficient and the shape of the buried structure (shape factor). The method is simple and can be used as a rapid method to estimate parameters that produced SP anomalies. The method is tested on synthetic data with and without random errors. It is also applied to a field example from Turkey. In all cases, the model parameters obtained are in good agreement with actual ones.

[1]  H. V. Ram Babu,et al.  Quantitative interpretation of self-potential anomalies due to two-dimensional sheet-like bodies , 1983 .

[2]  D. Patella.  Introduction to ground surface self‐potential tomography , 1997 .

[3]  Mrinal Sen,et al.  Interpretation of self-potential anomalies by nonlinear inversion , 1998 .

[4]  El-Sayed M. Abdelrahman,et al.  Derivative analysis of SP anomalies , 1998 .

[5]  B. B. Bhattacharya,et al.  A NOTE ON THE USE OF A NOMOGRAM FOR SELF‐POTENTIAL ANOMALIES* , 1981 .

[6]  Peter Furness,et al.  Modelling spontaneous mineralization potentials with a new integral equation , 1993 .

[7]  El-Sayed M. Abdelrahman,et al.  New methods for shape and depth determinations from SP data , 2003 .

[8]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[9]  J. Asfahani,et al.  A Nonlinear Programming Technique for the Interpretation of Self-potential Anomalies , 2002 .

[10]  R. Corwin,et al.  The self-potential method in geothermal exploration , 1979 .

[11]  John M. Stanley,et al.  SIMPLIFIED MAGNETIC INTERPRETATION OF THE GEOLOGIC CONTACT AND THIN DIKE , 1977 .

[12]  S. Reddy,et al.  Interpretation of self-potential anomalies of some simple geometric bodies , 1970 .

[13]  El-Sayed M. Abdelrahman,et al.  A least-squares approach to depth determination from self-potential anomalies caused by horizontal cylinders and spheres , 1997 .

[14]  R. D. Markiewicz,et al.  The Use of Self-Potential Surveys In Geotechnical Investigations , 1984 .

[15]  M. B. Dobrin.  Introduction to Geophysical Prospecting , 1976 .

[16]  田辺 行人.  J.C.Slater: Quantum Theory of Atomic Structure, Vol.II. Mc Graw-Hill Book Company, Inc., New York, 1960, 439頁, 15×23cm, $ , 1961 .

[17]  Robert F. Corwin.  The Self-Potential Method And Its Engineering Applications: An Overview , 1984 .

[18]  David V. Fitterman,et al.  Inversion of self-potential data from the Cerro Prieto geothermal field, Mexico , 1982 .

[19]  A. A. Ammar,et al.  A Least-squares Approach to Shape Determination from Residual Self-potential Anomalies , 1997 .

[20]  M. K. Paul.  DIRECT INTERPRETATION OF SELF‐POTENTIAL ANOMALIES CAUSED BY INCLINED SHEETS OF INFINITE HORIZONTAL EXTENSIONS , 1965 .

[21]  J. Asfahani,et al.  Fourier Analysis for Quantitative Interpretation of Self-Potential Anomalies Caused byHorizontal Cylinder and Sphere , 2001 .

[22]  P. Meiser,et al.  A METHOD FOR QUANTITATIVE INTERPRETATION OF SELFPOTENTIAL MEASUREMENTS , 1962 .

[23]  H. V. Ram Babu,et al.  Inversion of self-potential anomalies in mineral exploration , 1988 .

[24]  D. Guptasarma.  Effect of surface polarization on resistivity modeling , 1983 .

[25]  B. N. P. Agarwal.  Quantitative Interpretation of Self-potential Anomalies , 1984 .

[26]  L. de Witte.  A new method of interpretation of self-potential field data , 1948 .

[27]  Sulhi Hasan Yungul,et al.  Interpretation of spontaneous polarization anomalies caused by spheroidal ore bodies , 1950 .

[28]  H. El-Araby,et al.  A new method for complete quantitative interpretation of self-potential anomalies , 2004 .

[29]  Lennart A. Anderson.  Self‐potential investigations in the Puhimau thermal area, Kilauea Volcano, Hawaii , 1984 .

[30]  El-Sayed M. Abdelrahman,et al.  Shape and depth solutions from numerical horizontal self-potential gradients , 1997 .

[31]  H. V. Ram Babu,et al.  A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent , 1982 .