A least-squares minimisation approach to depth determination from numerical second horizontal self-potential anomalies

2009 ◽  
Vol 40 (2) ◽  
pp. 214-221 ◽  
Author(s):  
El-Sayed Mohamed Abdelrahman ◽  
Khalid Soliman ◽  
Khalid Sayed Essa ◽  
Eid Ragab Abo-Ezz ◽  
Tarek Mohamed El-Araby
Keyword(s):  
Least Squares ◽  
Depth Determination ◽  
Self Potential

A least‐squares approach to depth determination from self‐potential anomalies caused by horizontal cylinders and spheres

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
El‐Sayed Mohamed Abdelrahman ◽  
Sharafeldin Mahmoud Sharafeldin
Keyword(s):  
Least Squares ◽  
Maximum Error ◽  
Polarization Angle ◽  
Data Errors ◽  
Depth Determination ◽  
Horizontal Cylinders ◽  
Cylinders And Spheres ◽  
Self Potential ◽  
True Values ◽  
Least Squares Approach

We have developed a least‐squares approach to depth determination from self‐potential anomalies caused by horizontal cylinders and spheres. By defining the zero‐anomaly distance and the anomaly value at the origin on the profile, the problem of depth determination from self‐potential data has been transformed into finding a solution to a nonlinear equation. Procedures are also formulated to estimate the electric dipole moment and the polarization angle. The error in the depth parameter estimation introduced by data errors was also studied through imposing 1 to 10% errors in the zero‐anomaly distance and the anomaly value at the origin in one synthetic profile caused by a sphere. When the zero‐anomaly distance and the anomaly value at the origin possess errors of equal magnitude and of the same signs, the results will not differ much from the true values. When errors have opposite signs, the maximum error in depth is 10%. Finally, the validity of the method is tested on a field example from Ergani Copper district, Turkey.

A Least-squares Approach to Depth Determination from Numerical Horizontal Self-potential Gradients

2004 ◽  
Vol 161 (2) ◽  
pp. 399-411 ◽  
Author(s):  
E. M. Abdelrahman ◽  
H. S. Saber ◽  
K. S. Essa ◽  
M. A. Fouda
Keyword(s):  
Least Squares ◽  
Depth Determination ◽  
Potential Gradients ◽  
Self Potential ◽  
Least Squares Approach

A simple method for depth determination from self-potential anomalies due to two superimposed structures

2016 ◽  
Vol 47 (4) ◽  
pp. 308-314 ◽  
Author(s):  
El-Sayed M. Abdelrahman ◽  
Eid R. Abo-Ezz ◽  
Tarek M. El-Araby ◽  
Khalid S. Essa
Keyword(s):  
Simple Method ◽  
Depth Determination ◽  
Self Potential

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

2008 ◽  
Vol 34 (11) ◽  
pp. 1569-1576 ◽  
Author(s):  
El-Sayed M. Abdelrahman ◽  
Khalid S. Essa ◽  
Eid R. Abo-Ezz ◽  
Mohamed Sultan ◽  
William A. Sauck ◽  
...  
Keyword(s):  
Least Squares ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Least Squares Algorithm ◽  
Self Potential

A least‐squares approach to depth determination from gravity data

Geophysics ◽  
1983 ◽  
Vol 48 (3) ◽  
pp. 357-360 ◽  
Author(s):  
O. P. Gupta
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Data ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Random Errors ◽  
Depth Determination ◽  
Vertical Fault ◽  
Horizontal Cylinders ◽  
Least Squares Approach

The present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly. The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form [Formula: see text]. Formulas have been derived for a sphere, vertical and horizontal cylinders, and for a vertical fault (thin plate approximation). The procedure is applied to synthetic data with and without random errors. Finally, a field example is presented in which the depth to a fault is estimated at 3.8 km and verified from drilling results.

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