Measured and Modeled Gravity Anomalies above the Tunnel in Clays – Implication for Errors in 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.

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A LEAST‐SQUARES PROCEDURE FOR GRAVITY INTERPRETATION

Geophysics ◽

10.1190/1.1439560 ◽

1965 ◽

Vol 30 (2) ◽

pp. 228-233 ◽

Cited By ~ 36

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.

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A COMPREHENSIVE SYSTEM OF AUTOMATIC COMPUTATION IN MAGNETIC AND GRAVITY INTERPRETATION

Geophysics ◽

10.1190/1.1438736 ◽

1960 ◽

Vol 25 (3) ◽

pp. 569-585 ◽

Cited By ~ 54

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.

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Observed and calculated gravity anomalies above a tunnel driven in clays – implication for errors in gravity interpretation

Near Surface Geophysics ◽

10.3997/1873-0604.2013032 ◽

2013 ◽

Vol 11 (5) ◽

pp. 569-578 ◽

Cited By ~ 2

Author(s):

Vratislav Blecha ◽

David Mašín

Keyword(s):

Gravity Anomalies ◽

Gravity Interpretation

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

Geophysics ◽

10.1190/1.1443041 ◽

1991 ◽

Vol 56 (2) ◽

pp. 279-283 ◽

Cited By ~ 22

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.

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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 ◽

10.1190/1.1440458 ◽

1974 ◽

Vol 39 (5) ◽

pp. 692-693 ◽

Cited By ~ 1

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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Gravity interpretation of the southern Wind River Mountains, Wyoming

Geophysics ◽

10.1190/1.1441305 ◽

1982 ◽

Vol 47 (11) ◽

pp. 1550-1561 ◽

Cited By ~ 16

Author(s):

Charles A. Hurich ◽

Scott B. Smithson

Keyword(s):

River Basin ◽

Deep Structure ◽

Sedimentary Rocks ◽

Gravity Anomalies ◽

Ductile Deformation ◽

Gravity Modeling ◽

Green River Basin ◽

Green River ◽

Wind River Range ◽

Gravity Interpretation

The Wind River range is the largest Laramide uplift in Wyoming and is cored by Precambrian rocks thrust over sedimentary rocks of the Green River Basin to the southwest. The origin of these uplifts is in dispute; it has been ascribed to horizontal compression along thrusts or vertical movement along high‐angle reverse faults. Therefore, the attitude of the bounding fault is critical to understanding the mechanics of deformation. A gravity study based on 1800 stations has been carried out to attack this question and to complement a COCORP deep crustal reflection study. Smoothed free‐air gravity anomalies are highly positive over the Wind River range and near zero over the adjacent margins. Bouguer gravity anomalies range from −252 and −225 mgal in the Green River basin and Wind River basin, respectively, to −150 mgal in the basement core of the Wind River range. The bulk density of sedimentary rocks in the adjacent basins is the critical parameter for gravity interpretation of the deep structure and ranges from 2.25 to [Formula: see text], based on density logs. Gravity modeling demonstrates that most of the +85 mgal gravity anomaly associated with the uplift is caused by the sediment‐basement density contrast, but about 18 mgal has a deeper source. This can be accounted for by offset of more dense middle crust along a thrust fault dipping at about 40 degrees. Three‐dimensional (3-D) modeling confirms this interpretation along the southern part of the range. No significant offset of the Mohorovicic discontinuity can be present. This suggests that the thrust either flattened out or the lower crust deformed by homogeneous ductile deformation. Gravity interpretation gives information on deep structure not found in the COCORP reflection data and further confirms the compressive nature of this Laramide uplift.

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GRATICULE SPACING VERSUS DEPTH DISCRIMINATION IN GRAVITY INTERPRETATION

Geophysics ◽

10.1190/1.1440714 ◽

1977 ◽

Vol 42 (1) ◽

pp. 60-65 ◽

Cited By ~ 13

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.

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GRAVITY INTERPRETATION USING THE FOURIER INTEGRAL

Geophysics ◽

10.1190/1.1439598 ◽

1965 ◽

Vol 30 (3) ◽

pp. 424-438 ◽

Cited By ~ 72

Author(s):

Mark E. Odegard ◽

Joseph W. Berg

Keyword(s):

Frequency Domain ◽

Fourier Transforms ◽

Gravity Data ◽

Gravity Anomalies ◽

Fourier Integral ◽

Numerical Techniques ◽

Functional Representations ◽

Gravity Interpretation ◽

Mathematical Relations ◽

Gravitational Anomalies

The gravitational anomalies of simple bodies (sphere, cylinder, and fault) were used to develop methods for analyzing gravity data in the frequency domain. The Fourier transforms of the functional representations of the theoretical gravitational anomalies of these bodies were obtained. Mathematical relations were formulated between the transform‐versus‐frequency relationships and the depths and sizes of the bodies. Compound gravity anomalies (multiple cylinders, fault, and cylinder) were analyzed, and the transforms were reduced to transforms of anomalies due to individual simple bodies. These methods of analysis were applied to theoretical anomalies using numerical techniques, and the accuracy of both depth and size determinations was within a few percent in all cases.

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

Geophysics ◽

10.1190/1.1442629 ◽

1989 ◽

Vol 54 (12) ◽

pp. 1614-1621 ◽

Cited By ~ 49

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.

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