A least‐squares minimization approach to depth determination of a thick vertical fault from gravity data

1983 ◽  
Author(s):  
O. P. Gupta
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Depth Determination ◽  
Vertical Fault ◽  
Minimization Approach ◽  
Least Squares Minimization

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.

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 shape determination from gravity data

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 589-590 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Sharafeldin M. Sharafeldin
Keyword(s):  
Least Squares ◽  
Gravity Anomaly ◽  
Shape Factor ◽  
Gravity Data ◽  
Correlation Factor ◽  
Walsh Transform ◽  
Residual Gravity ◽  
Residual Gravity Anomaly ◽  
Minimization Approach ◽  
Least Squares Minimization

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape (shape‐factor) and depth‐related variables with an amplitude coefficient related to mass (Abdelrahman and El‐Araby, 1993). Few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles. These methods include a Walsh transform approach (Shaw and Agarwal, 1990) and the employment of a correlation factor between successive least‐squares residuals (Abdelrahman and El‐Araby 1993). In the present note, a least‐squares minimization approach to shape‐factor determination from a residual gravity anomaly profile is presented. The problem of the shape‐factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0.

A Least-squares Minimization Approach to Depth Determination from Magnetic Data

2003 ◽  
Vol 160 (7) ◽  
pp. 1259-1271 ◽  
Author(s):  
E. M. Abdelrahman ◽  
H. M. El-Arby ◽  
T. M. El-Arby ◽  
K. S. Essa
Keyword(s):  
Least Squares ◽  
Magnetic Data ◽  
Depth Determination ◽  
Minimization Approach ◽  
Least Squares Minimization

Reply by the author to G. D. Garland.

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1460-1460
Author(s):  
B. A. Sissons
Keyword(s):  
Least Squares ◽  
Standard Error ◽  
Gravitational Constant ◽  
Gravity Data ◽  
Residual Distribution ◽  
Density Measurements ◽  
Least Squares Fit ◽  
Least Squares Adjustment ◽  
Sufficient Precision

Although the Tokaanu experiment does contradict the proposal that the gravitational constant G increases with scale, the result is not significant. The standard error in the least‐squares adjustment is at least 1 percent, which exceeds the predicted variation in G. The uncertainty in mean density is nearer 5 percent. Gravity data with sufficient precision to test for a scale effect in G are obtainable; the main problem appears to be the uncertainty in density determinations. Stacey et al (1981) made a least‐squares determination of G using gravity and density measurements from a mine. However, the pattern of residuals obtained indicated the presence of anomalous masses not adequately accounted for by their density averaging. The method I have used which models the spatial variation in density offers the possibility of obtaining a least‐squares fit for G with a satisfactory residual distribution. However, the problem of the effect on bulk density of joints and voids not sampled in hand specimens remains.

A new least-squares minimization approach to depth and shape determination from magnetic data

2007 ◽  
Vol 55 (3) ◽  
pp. 433-446 ◽  
Author(s):  
El-Sayed M. Abdelrahman ◽  
Eid. R. Abo-Ezz ◽  
Khalid S. Essa ◽  
T.M. El-Araby ◽  
Khaled S. Soliman
Keyword(s):  
Least Squares ◽  
Magnetic Data ◽  
Shape Determination ◽  
Minimization Approach ◽  
Least Squares Minimization

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.

Sign in / Sign up

Export Citation Format

Share Document