On: “A least‐squares approach to depth determination from gravity data” by G. P. Gupta,(GEOPHYSICS, 48, 357‐360, March 1983).

Geophysics ◽  
1985 ◽  
Vol 50 (2) ◽  
pp. 262-262 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Abdel‐Rhim I. Bayoumi ◽  
Yehia A. Amin
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Data ◽  
Depth Estimation ◽  
Numerical Approach ◽  
Point Of View ◽  
Theory And Practice ◽  
Buried Structures ◽  
Depth Determination ◽  
Least Squares Approach

In his paper, Gupta was able to transform the problem of depth estimation of buried structures into a problem of finding a solution of a nonlinear equation in the form of [Formula: see text]. Gupta also indicated that such a numerical approach is found to be capable of determining optimum depths particularly from residual anomaly profiles even if small segments of the gravity profiles are observed. No doubt this numerical approach has its point of view both in theory and practice over any other depth estimation techniques such as those defined by the [Formula: see text] rule (Nettleton, 1940, 1942; Telford et al., 1976). However, Gupta’s technique would be much more effective if applied not to residuals but to derivative anomalies, particularly when the regional field has few extrema in it; this is obviously due to the following.

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.

On: “A least‐squares approach to depth determination from gravity data” by O.P. Gupta (GEOPHYSICS, 48, 357–360, March 1983)

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 376-377 ◽  
Author(s):  
El‐Sayed M. Abdelrahman
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Residual Gravity ◽  
Depth Determination ◽  
Residual Gravity Anomaly ◽  
Least Squares Approach

In the article by Gupta, the problem of depth determination of a buried structure from the residual gravity anomaly has been transformed into a problem of finding the solution of a nonlinear equation of the form f(z) = 0. Gupta begins his formulation of the problem with equation (1) from Mettleton (1942) Eq. (1) [Formula: see text]

A least‐squares minimization approach to depth determination from numerical horizontal gravity gradients

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1259-1260 ◽  
Author(s):  
El‐Sayed Mohamed Abdelrahman ◽  
Sharafeldin Mahmoud Sharafeldin
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Depth Estimation ◽  
Horizontal Cylinder ◽  
Theory And Practice ◽  
Gravity Gradient ◽  
Quantitative Interpretation ◽  
Gravity Gradients

The sphere and the horizontal cylinder models can be very useful in quantitative interpretation of gravity data measured in a small area over buried structures. Several graphical and numerical methods have been developed by many workers for interpreting the residual gravity anomalies caused by these models to find the depth of most geologic structures. Excellent reviews are given in Saxov and Nygaard (1953) and Bowin et al. (1986). The numerical approaches (Odegard and Berg, 1965; Gupta, 1983; Sharma and Geldart, 1968; Lines and Treitel, 1984; and Shaw and Agarwal, 1990) may have advantages in theory and practice over graphical depth estimation techniques (Pick et al., 1973: Nettleton, 1976; Telford et al., 1976). However, effective quantitative interpretation procedures using the least‐squares method based on the analytical expression of simple numerical horizontal gravity gradient anomalies are yet to be developed.

ADAPTIVE LEAST SQUARES ACQUISITION OF HIGH RESOLUTION IMAGES

2005 ◽  
Vol 02 (01) ◽  
pp. 45-53 ◽  
Author(s):  
S. E. EL-KHAMY ◽  
M. M. HADHOUD ◽  
M. I. DESSOUKY ◽  
B. M. SALAM ◽  
F. E. ABD EL-SAMIE
Keyword(s):  
Computational Complexity ◽  
High Resolution ◽  
Least Squares ◽  
Edge Effects ◽  
Estimation Error ◽  
Point Of View ◽  
Suggested Algorithm ◽  
High Resolution Images ◽  
Number Of Iterations ◽  
Least Squares Approach

This paper presents a least squares block by block adaptive approach for the acquisition of high resolution (HR) images from available (LR) images. The suggested algorithm is based on the segmentation of the image to overlapping blocks and the interpolation of each block separately. The purpose of the overlapping of blocks is to avoid edge effects. An adaptive 2D least squares approach, which considers the image acquisition model, is used in the minimization of the estimation error of each block. In this suggested algorithm, a weight matrix of moderate dimensions is estimated in a small number of iterations to interpolate each block. This algorithm avoids the large computational complexity due to the matrices of large dimensions required to interpolate the image as a whole. The performance of the proposed algorithm is studied for different LR images with different SNRs. The performance of the proposed algorithm is also compared to the standard as well as the warped distance cubic O-MOMS image interpolation algorithms from the PSNR point of view.

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 least-squares variance analysis method for shape and depth estimation from gravity data

2006 ◽  
Vol 3 (2) ◽  
pp. 143-153 ◽  
Author(s):  
E M Abdelrahman ◽  
E R Abo-Ezz ◽  
K S Essa ◽  
T M El-Araby ◽  
K S Soliman
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Depth Estimation ◽  
Variance Analysis ◽  
Analysis Method
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