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 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.

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 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.

Three least‐squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1105-1109 ◽  
Author(s):  
E. M. Abdelrahman ◽  
H. M. El‐Araby ◽  
T. M. El‐Araby ◽  
E. R. Abo‐Ezz
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Least Squares Method ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Anomalies ◽  
Maximum Error ◽  
The United States ◽  
Random Errors ◽  
Amplitude Coefficient

Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.

A least‐squares minimization approach to depth determination from moving average residual gravity anomalies

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1779-1784 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Tarek M. El‐Araby
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Moving Average ◽  
Gravity Anomalies ◽  
The United States ◽  
Random Errors ◽  
Minimization Method ◽  
Residual Gravity ◽  
Average Residual ◽  
Least Squares Minimization

We have developed a least‐squares minimization method to estimate the depth of a buried structure from moving average residual gravity anomalies. The method involves fitting simple models convolved with the same moving average filter as applied to the observed gravity data. As a result, our method can be applied not only to residuals but also to the Bouguer gravity data of a short profile length. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on two field examples from the United States and Senegal.

scholarly journals Depth and shape solutions from residual gravity anomalies due to simple geometric structures using a statistical approach

2017 ◽  
Vol 47 (2) ◽  
pp. 113-132 ◽  
Author(s):  
El-Sayed Abdelrahman ◽  
Mohamed Gobashy
Keyword(s):  
Gravity Data ◽  
Random Noise ◽  
Synthetic Data ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Random Errors ◽  
Residual Gravity ◽  
Characteristic Points ◽  
The Usa

AbstractWe have developed a simple and fast quantitative method for depth and shape determination from residual gravity anomalies due to simple geometrical bodies (semi-infinite vertical cylinder, horizontal cylinder, and sphere). The method is based on defining the anomaly value at two characteristic points and their corresponding distances on the anomaly profile. Using all possible combinations of the two characteristic points and their corresponding distances, a statistical procedure is developed for automated determination of the best shape and depth parameters of the buried structure from gravity data. A least-squares procedure is also formulated to estimate the amplitude coefficient which is related to the radius and density contrast of the buried structure. The method is applied to synthetic data with and without random errors and tested on two field examples from the USA and Germany. In all cases examined, the estimated depths and shapes are found to be in good agreement with actual values. The present method has the capability of minimizing the effect of random noise in data points to enhance the interpretation of results.

scholarly journals A least-squares minimization approach to interpret gravity anomalies caused by a 2D thick, vertically faulted slab

2019 ◽  
Vol 49 (3) ◽  
pp. 229-247
Author(s):  
El-Sayed Abdelrahman ◽  
Mohamed Gobashy
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Central Valley ◽  
Real Data ◽  
Horizontal Gradient ◽  
Vertical Fault ◽  
Independent Observations ◽  
Minimization Approach ◽  
Least Squares Minimization

Abstract We present a least-squares minimization approach to estimate simultaneously the depth to and thickness of a buried 2D thick, vertically faulted slab from gravity data using the sample spacing – curves method or simply s-curves method. The method also provides an estimate for the horizontal location of the fault and a least-squares estimate for the density contrast of the slab relative to the host. The method involves using a 2D thick vertical fault model convolved with the same finite difference second horizontal gradient filter as applied to the gravity data. The synthetic examples (noise-free and noise affected) are presented to illustrate our method. The test on the real data (Central Valley of Chile) and the obtained results were consistent with the available independent observations and the broader geological aspects of this region.

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