Gravity interpretation using correlation factors between successive least‐squares residual anomalies

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1614-1621 ◽  
Author(s):  
E. M. Abdelrahman ◽  
A. I. Bayoumi ◽  
Y. E. Abdelhady ◽  
M. M. Gobashy ◽  
H. M. El‐Araby
Keyword(s):  
Least Squares ◽  
Bouguer Anomaly ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
The United States ◽  
Horizontal Cylinder ◽  
Regional Component ◽  
Gravity Interpretation ◽  
Regional Gravity ◽  
Correlation Factors

The correlation factors between successive least‐squares residual (or regional) gravity anomalies from a buried sphere, a two‐dimensional (2‐D) horizontal cylinder, and a vertical cylinder and the first horizontal derivative of the gravity from a 2‐D thin faulted layer are computed. Correlation values are used to determine the depth to the center of the buried structure, and the radius of the sphere or the cylinder and the thickness of the fault are estimated. The method can be applied not only to residuals but also to the Bouguer‐anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order. The method is easy to apply and may be automated if desired. It can also be applied to the derivative anomalies of the gravity field. The validity of the method is tested on two field examples from the United States and Denmark.

Shape and depth solutions from gravity data using correlation factors between successive least‐squares residuals

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1785-1791 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Gravity Data ◽  
Bouguer Anomaly ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Amplitude Coefficient ◽  
Regional Component ◽  
Correlation Factors

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape (shape factor) and depth variables with an amplitude coefficient related to the mass. Correlation factors between successive least‐squares residual gravity anomalies from a buried vertical cylinder, horizontal cylinder, and sphere are used to determine the shape and depth of the buried geologic structure. For each shape factor value, the depth is determined automatically from the correlation value. The computed depths are plotted against the shape factor representing a continuous correlation curve. The solution for the shape and depth of the buried structure is read at the common intersection of correlation curves. This method can be applied to a Bouguer anomaly profile consisting of a residual component caused by local structure and a regional component. This is a powerful technique for automatically separating the Bouguer data into residual and regional polynomial components. This method is tested on theoretical examples and a field example. In both cases, the results obtained are in good agreement with drilling results.

A LEAST‐SQUARES PROCEDURE FOR GRAVITY INTERPRETATION

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 228-233 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Least Squares ◽  
High Speed ◽  
Gravity Anomalies ◽  
The Body ◽  
Two Dimensional ◽  
Partial Derivatives ◽  
Dimensional Gravity ◽  
Gravity Interpretation ◽  
Relationship Of ◽  
Derivatives Of

A procedure suitable for use on high‐speed digital computers is presented for interpreting two‐dimensional gravity anomalies. In order to determine the shape of a disturbing mass with known density contrast, an initial model is assumed and gravity anomalies are calculated and compared with observed values at n points, where n is greater than the number of unknown variables (e.g. depths) of the model. Adjustments are then made to the model by a least‐squares approximation which uses the partial derivatives of the anomalies so that the residuals are reduced to a minimum. In comparison with other iterative techniques, convergence is very rapid. A convenient method to use for both the calculation of the anomalies and the adjustments is the two‐dimensional method of Talwani, Worzel, and Landisman, (1959) in which the outline of the body is polygonized and the anomalies and the partial derivatives of the anomaly with respect to the depth of a vertex on the body can be expressed as functions of the coordinates of the vertex. Not only depths but under certain circumstances regional gravity values may be evaluated; however, the relationship of the disturbing body to the gravity information may impose certain limitations on the application of the procedure.

REGIONAL GRAVITY SURVEY IN NORTHEASTERN OKLAHOMA AND SOUTHEASTERN KANSAS

Geophysics ◽  
1956 ◽  
Vol 21 (1) ◽  
pp. 88-106 ◽  
Author(s):  
Kenneth L. Cook
Keyword(s):  
Structural Geology ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Close Correlation ◽  
Geodetic Survey ◽  
Gravity Survey ◽  
Complex Nature ◽  
Gravity Gradients ◽  
Anomaly Map ◽  
Regional Gravity

In 1948 the U. S. Geological Survey, in cooperation with the U. S. Coast and Geodetic Survey, made a regional gravity survey in northeastern Oklahoma and southeastern Kansas in connection with the studies of the deflection of the vertical. About 550 gravity stations were occupied with spacings of 5 to 10 miles in parts of 54 counties, and a Bouguer anomaly map, contoured at intervals of 5 milligals, was drawn. In southeastern Kansas there is a lack of correlation of regional gravity with known regional structural geology. The observed gravity anomalies are apparently caused principally by variations of density in the Precambrian basement and indicate a basement of complex nature, made up of rocks of contrasting properties, with a regional grain striking predominantly west or west‐northwest. In northeastern Oklahoma the several observed regional gravity anomalies indicate different degrees of correlation of regional gravity with regional structural geology. In the Precambrian highland area in Osage, Pawnee, and Creek Counties, there is a lack of correlation, as the gravity anomaly is probably caused chiefly by density contrasts within the basement complex. The anomaly associated with the Hunton arch is probably caused partly by structural relief of the rocks of pre‐Pennsylvanian age and partly by density contrasts within the basement, and thus indicates some correlation. The steep gravity gradients along the outer flanks of the Ozark uplift indicate good correlation with the subsurface geology. The great anomaly over the Arkansas basin, which indicates a close correlation, is probably caused largely—but perhaps not entirely—by downwarping of the basement and pre‐Pennsylvanian rocks.

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.

On the least‐squares residual anomaly determination

Geophysics ◽  
1985 ◽  
Vol 50 (3) ◽  
pp. 473-480 ◽  
Author(s):  
E. M. Abdelrahman ◽  
S. Riad ◽  
E. Refai ◽  
Y. Amin
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Vertical Cylinder ◽  
Correlation Factor ◽  
Western Desert ◽  
Bouguer Gravity ◽  
Residual Component ◽  
Optimum Order ◽  
Gravity Interpretation ◽  
Residual Maps

This paper discusses an approach to determine the least‐squares optimum order of the regional surface which, when subtracted from the Bouguer gravity anomaly data, minimizes distortion of the residual component of the field. The least‐squares method was applied to theoretical composite gravity fields each consisting of a constant residual component (sphere or vertical cylinder) and a regional component of different order using successively increasing orders of polynomial regionals for residual determination. The overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables. Similarity between residual maps of the lowest orders, verified by good correlation, may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component. The residual map of the lower order in this well‐correlated doublet is considered the most plausible one and may be used for gravity interpretation. This approach was successfully applied to the Bouguer gravity of Abu Roash dome, located west of Cairo in the Western Desert of Egypt.

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.

THE USE OF CRACOVIAN COMPUTATION IN ESTIMATING THE REGIONAL GRAVITY

Geophysics ◽  
1959 ◽  
Vol 24 (3) ◽  
pp. 465-478 ◽  
Author(s):  
Zbigniew Fajklewicz
Keyword(s):  
Least Squares ◽  
Gravity Field ◽  
Gravity Anomalies ◽  
Second Order ◽  
Method Of Least Squares ◽  
Electronic Computers ◽  
Regional Gravity ◽  
Work Done ◽  
Very High ◽  
Digital Computers

The author uses the method of least squares in cracovian form and second order polynomials for estimating the regional gravity field. Expressions yielding the regional field are obtained very rapidly by using the inverse cracovians of the coefficients as given in the present paper, and there is no need of electronic digital computers for the computation. The equivalent of the entire work done by a computer of this kind in constructing the formula of the regional field, when effected by this method, takes no more than 20 minutes. The method is exemplified by the treatment of two gravity anomalies from the territory of Poland. The author stresses the fact that electronic computers adapted to the use of cracovians and characterized by a very high versatility may be applied in the method.

scholarly journals Marquardt inverse modeling of the residual gravity anomalies due to simple geometric structures: A case study of chromite deposit

2019 ◽  
Vol 49 (2) ◽  
pp. 153-180 ◽  
Author(s):  
Ata Eshaghzadeh ◽  
Alireza Dehghanpour ◽  
Sanaz Seyedi Sahebari
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Synthetic Data ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Inversion Method ◽  
Chromite Deposit ◽  
Different Shapes

Abstract In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. According to the interpreted parameters, the best shape that can imagine for the gravity anomaly source is the vertical cylinder with a depth to top of 7.4 m and a radius of 11.7 m.

REGIONAL GRAVITY SURVEY OF PARTS OF TOOELE, JUAB, AND MILLARD COUNTIES, UTAH

Geophysics ◽  
1957 ◽  
Vol 22 (1) ◽  
pp. 48-61 ◽  
Author(s):  
J. Burlin Johnson ◽  
Kenneth L. Cook
Keyword(s):  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Basin And Range ◽  
Fault Zones ◽  
Gravity Survey ◽  
Gravity Gradients ◽  
Northern Margin ◽  
Eastern Margin ◽  
Vertical Displacements ◽  
Regional Gravity

In the summer of 1955 a regional gravity survey was made in parts of Tooele, Juab, and Millard Counties, Utah. A total of 455 gravity stations were occupied in an area of about 1,700 square miles. A Bouguer anomaly map was compiled with a contour interval of 2 milligals. Steep gravity gradients indicate major Basin and Range fault zones along the eastern margin of the Cedar Mountains, the southwestern margin of Davis Mountain and its associated outcrops, the northeastern margins of Camels Back Ridge and Simpson Buttes, the eastern margin of Granite Mountain, and the northern margin of the Dugway Range. The principal trend of these fault zones is northwesterly; and they were instrumental in partly outlining several of the mountain ranges in the surveyed area. Great graben with probable vertical displacements of at least several thousand feet were found east of Granite Mountain and northeast of Camels Back Ridge. The highest gravity values, which lie just northwest of Granite Mountain, are about 40 milligals higher than the surrounding surveyed region. Gravity anomalies transecting the Dugway and Thomas Ranges probably indicate pre‐Basin and Range faulting.

A least‐squares derivatives analysis of gravity anomalies due to faulted thin slabs

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 535-543 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby ◽  
Tarek M. El‐Araby ◽  
Eid Ragab Abo‐Ezz
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Gravity Data ◽  
Bouguer Anomaly ◽  
Theoretical Data ◽  
Gravity Anomalies ◽  
Random Errors ◽  
Fault Structure ◽  
Amplitude Coefficient ◽  
Buried Fault

This paper presents two different least‐squares approaches for determining the depth and amplitude coefficient (related to the density contrast and the thickness of a buried faulted thin slab from numerical first‐, second‐, third‐, and fourth‐horizontal derivative anomalies obtained from 2D gravity data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z) = 0. Knowing the depth and applying the least‐squares method, the amplitude coefficient is determined using a simple linear equation. In this way, the depth and amplitude coefficient are determined individually from all observed gravity data. The depths and the amplitude coefficients obtained from the first‐, second‐, third‐, and fourth‐ derivative anomaly values can be used to determine simultaneously the actual depth and amplitude coefficient of the buried fault structure and the optimum order of the regional gravity field along the profile. The method can be applied not only to residuals but also to the Bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local fault structure (shallow or deep) and a regional component represented by a polynomial of any order. The method is applied to theoretical data with and without random errors and is tested on a field example from Egypt.

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