GRATICULE SPACING VERSUS DEPTH DISCRIMINATION IN GRAVITY INTERPRETATION

Geophysics ◽  
1977 ◽  
Vol 42 (1) ◽  
pp. 60-65 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Gravity Anomalies ◽  
Second Derivative ◽  
Practical Procedure ◽  
Depth Discrimination ◽  
Local Gravity ◽  
Gravity Interpretation ◽  
Local Anomalies ◽  
Residual Maps

Very serious distortions in both magnitude and extension of local gravity anomalies result from the still widely used 9-point “residual” and 17-point “second derivative” graticules. Although these types of residual maps are very useful for recognizing and pinpointing the existence of interesting local anomalies, the distorted results cannot be used to derive geologic interpretations of significant reliability. A practical procedure based on changes in anomaly magnitudes from two (or more) different grid spacings, effectively overcomes shortcomings of previous interpretation methods.

Gravity interpretation using Fourier transforms and simple geometrical models with exponential density contrast

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1074-1083 ◽  
Author(s):  
D. Bhaskara Rao ◽  
M. J. Prakash ◽  
N. Ramesh Babu
Keyword(s):  
Los Angeles ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Model Parameters ◽  
Exponential Density ◽  
Exponential Density Contrast ◽  
Gravity Interpretation

The decrease of density contrast in sedimentary basins can often be approximated by an exponential function. Theoretical Fourier transforms are derived for symmetric trapezoidal, vertical fault, vertical prism, syncline, and anticline models. This is desirable because there are no equivalent closed form solutions in the space domain for these models combined with an exponential density contrast. These transforms exhibit characteristic minima, maxima, and zero values, and hence graphical methods have been developed for interpretation of model parameters. After applying end corrections to improve the discrete transforms of observed gravity data, the transforms are interpreted for model parameters. This method is first tested on two synthetic models, then applied to gravity anomalies over the San Jacinto graben and Los Angeles basin.

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.

A COMPREHENSIVE SYSTEM OF AUTOMATIC COMPUTATION IN MAGNETIC AND GRAVITY INTERPRETATION

Geophysics ◽  
1960 ◽  
Vol 25 (3) ◽  
pp. 569-585 ◽  
Author(s):  
Roland G. Henderson
Keyword(s):  
Effective Means ◽  
Gravity Anomalies ◽  
Comprehensive System ◽  
Diagnostic Features ◽  
Special Cases ◽  
Desk Calculator ◽  
Concentric Circles ◽  
Gravity Interpretation ◽  
Magnetic And Gravity Anomalies ◽  
Derivatives Of

In the interpretation of magnetic and gravity anomalies, downward continuation of fields and calculation of first and second vertical derivatives of fields have been recognized as effective means for bringing into focus the latent diagnostic features of the data. A comprehensive system has been devised for the calculation of any or all of these derived fields on modern electronic digital computing equipment. The integral for analytic continuation above the plane is used with a Lagrange extrapolation polynomial to derive a general determinantal expression from which the field at depth and the various derivatives on the surface and at depth can be obtained. It is shown that the general formula includes as special cases some of the formulas appearing in the literature. The process involves a “once for all depths” summing of grid values on a system of concentric circles about each point followed by application of the appropriate one or more of the 19 sets of coefficients derived for the purpose. Theoretical and observed multilevel data are used to illustrate the processes and to discuss the errors. The coefficients can be used for less extensive computations on a desk calculator.

BOUGUER GRAVITY CORRECTIONS USING A VARIABLE DENSITY

Geophysics ◽  
1962 ◽  
Vol 27 (5) ◽  
pp. 616-626 ◽  
Author(s):  
F. S. Grant ◽  
A. F. Elsaharty
Keyword(s):  
Least Squares ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Variable Density ◽  
Bouguer Gravity ◽  
Method Of Least Squares ◽  
Surface Conditions ◽  
Worked Example ◽  
Local Gravity

The principle of density profiling as a means of determining Bouguer densities is studied with a view to extending it to include all of the data in a survey. It is regarded as an endeavor to minimize the correlation between local gravity anomalies and topography, and as such it can be handled mathematically by the method of least squares. In the general case this leads to a variable Bouguer density which can be mapped and contoured. In a worked example, the correspondence between this function and the known geology appears to be good, and indicates that Bouguer density variations due to changing surface conditions can be used routinely in the reduction of gravity data.

Regional‐residual gravity anomaly separation using the minimum‐curvature technique

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 279-283 ◽  
Author(s):  
K. L. Mickus ◽  
C. L. V. Aiken ◽  
W. D. Kennedy
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Bouguer Gravity ◽  
Bouguer Gravity Anomaly ◽  
Residual Gravity ◽  
Residual Gravity Anomaly ◽  
Gravity Interpretation ◽  
Minimum Curvature

One of the most difficult problems in gravity interpretation is the separation of regional and residual gravity anomalies from the Bouguer gravity anomaly. This study discusses the application of the minimum‐curvature method to determine the regional and residual gravity anomalies.

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.

An application of the second derivative as a tool in tectonic analysis in the Qattara Depression area, Egypt

1986 ◽  
Vol 123 (3) ◽  
pp. 307-313
Author(s):  
A. El-Hussaini ◽  
M. Youssef ◽  
H. Ibrahim
Keyword(s):  
Gravity Anomalies ◽  
Horizontal Displacement ◽  
Fault System ◽  
Second Derivative ◽  
Vertical Movements ◽  
Very Old ◽  
First Order ◽  
Basement Structures

AbstractThe second derivative of gravity anomalies of the Qattara area was analysed and statistically studied for determining the tectonic elements. Zones of zero second derivative were considered as the locations of possible faults. The analysis of a constructed tectonic map portrays the predominance of N45°W, N85°E and N45°E fault trends in addition to less pronounced N15°E and N–S faults. The NW–SE faults are very old and inherited from the basement structures. They acted as first order right-lateral wrench faults during the Alpine tectonism. Second and higher orders of faults, developed as a consequence of these movements, are represented by the N85°E and other less abundant trends. Vertical movements along the existing fault system, in addition to the horizontal displacement, is supported by the analysis of the pronounced anomalies of the second derivative map. The subsurface structural picture of the area is composed of uplifted and downfaulted adjoining blocks.

On: “An Automatic Least‐Squares Multimodel Method for Magnetic Interpretation” by Peter H. McGrath and Peter J. Hood (GEOPHYSICS, April 1973, p. 349–358)

Geophysics ◽  
1974 ◽  
Vol 39 (5) ◽  
pp. 692-693 ◽  
Author(s):  
M. Al‐Chalabi
Keyword(s):  
Gravity Anomalies ◽  
Optimization Method ◽  
Optimization Techniques ◽  
General Context ◽  
Complex Method ◽  
Integral Group ◽  
Subsequent Work ◽  
Magnetic Interpretation ◽  
Rotating Coordinates ◽  
Gravity Interpretation

McGrath and Hood present a magnetic interpretation method whereby the search for a solution is carried out in the (hyper) space of n parameters defining the shape and position of an assumed model. The problem is an optimization problem and should be viewed within the general context of nonlinear optimization techniques. McGrath and Hood simply present one optimization method. The usefulness of individual methods is limited. One could similarly propose the use of the method of rotating coordinates (Rosenbrock, 1960), the “complex” method (Box, 1965), Davidon’s methods (Fletcher and Powell, 1963; Stewart, 1967; Davidon, 1969), etc. We currently have a wealth of these methods at our disposal. In fact, the use of these methods for magnetic interpretation has already been presented (Al‐Chalabi, 1970). As this and subsequent work indicated (Al‐Chalabi, 1972), these methods should be used as an integral group for interpreting magnetic and gravity anomalies. The exclusive use of individual methods is inefficient. Studies performed on objective functions used in magnetic and gravity interpretation have shown that the behavior of these functions in the parameter hyperspace is extremely complicated. Consequently, the search for a solution requires different strategies at different stages between the initial estimate and the ultimate solution (Al‐Chalabi, 1970, 1972).

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