Least Squares Residual Anomaly Determination

Agocs, W. B.

doi:10.1190/1.1437720

Cited by 103 publications

(42 citation statements)

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“…The moving average method is an important and simple technique for the separation of gravity anomalies into residual and regional components. The basic theory of the moving average method is described by GRIFFIN (1949) and application of least-squares of the moving average is described by AGOCS (1951).…”

Section: Vol 165 2008mentioning

confidence: 99%

A Least-Squares Standard Deviation Method to Interpret Gravity Data due to Finite Vertical Cylinders and Sheets

Abdelrahman

Abo-Ezz

2008

Pure appl. geophys.

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We have developed a least-squares approach to determine simultaneously the depth to both the top and base of a buried finite vertical cylinder (vertical line element approximation) and a 2-D vertical thin sheet from moving average residual anomaly profiles obtained from gravity data using filters of successive window lengths. The method involves using a relationship between the depth to the top, and base of the source and a combination of windowed observations. The method is based on computing the standard deviation of the depths to the top, determined from all moving average residual anomalies for each value of the depth to the base. The standard deviation may generally be considered a criterion for determining the correct depth to the top and base of the buried structure. When the correct depth to the base value is used, the standard deviation of the depths to the top is less than the standard deviation using incorrect values of the depth to the base. This method can be applied to residuals as well as to the observed gravity data. The method is applied to synthetic examples with and without random errors and tested on two field examples from the USA and Canada.

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Section: Vol 165 2008mentioning

confidence: 99%

A Least-Squares Standard Deviation Method to Interpret Gravity Data due to Finite Vertical Cylinders and Sheets

Abdelrahman

Abo-Ezz

2008

Pure appl. geophys.

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“…The filter operations include for example, the radial weights methods (GRIFFIN, 1949;ELKINS, 1951;ROSENBACH, 1953;RAO et al, 1970;ABDELRAHMAN et al, 1989), the fast Fourier transform methods (BHAT- TACHARYYA, 1965;CLARKE, 1969;BOTEZATU, 1970;MESKO, 1984), the rational approximation techniques (AGARWAL and LAL, 1971), recursion filters (BHAT- TACHARYYA, 1969;INOUE, 1986), and the least-squares method (OLDHAM and SUTHERLAND, 1955;GRANT, 1957;AGOCS, 1951;FAJKLEWICZ, 1959;ABDELRAH-MAN et al, 1985). The determined residual gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Approach to Depth Determination from Residual Gravity Anomaly Due to Two Structures

Abdelrahman

Abo-Ezz

Radwan

1999

Pure and Applied Geophysics

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The residual anomaly expression due to two simple geologic structures can be represented by the sum of fields produced by two known source bodies whose depths are to be determined. For a few fixed characteristic points and distances along the residual anomaly profile, the depth to the upper structure is determined iteratively using a simple formula for each depth of the lower structure.The computed depths to the lower structure are plotted against the depths to the upper structure representing a depth curve. The solution for the depths to both structures is read at the common intersection of the depth curves. Procedures are also formulated to estimate the radii of the two buried structures. The method is a powerful technique for separating the composite residual anomaly into two residual components due to two structures. The method is applied to theoretical data with and without random errors and tested on a field example from U.S.A.

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“…/ sin sin The first moving average (grid) method is an important and very simple technique for separation of potential field data into residual and regional components (Abdelrahman and El-Araby, 1993). The basic theory of the first moving average is described by Griffin (1949) and the application of leastsquares is described by Agocs (1951). However, the use of second moving average method for separation of magnetic anomalies into residual and regional components is yet to be developed.…”

Section: Thin Dikes Horizontal Cylindersmentioning

confidence: 99%

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

Abdurrahman¹,

El-Araby²,

Essa³

2004

ear

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ABSTRACT. We have developed a numerical method to estimate the depth of a buried structure from second moving average residual anomalies obtained from magnetic 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 z = f(z). Formulas have been derived for a dike, horizontal cylinder, geologic contact, and a sphere. The method involves using simple models convolved with the same second moving average filters as applied to the observed magnetic data. As a result, our method can be applied not only to residuals but also to observed magnetic data. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on a field example from Canada. In all cases examined, the depth obtained gives satisfied results with actual depth.

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Least Squares Residual Anomaly Determination

Cited by 103 publications

References 0 publications

A Least-Squares Standard Deviation Method to Interpret Gravity Data due to Finite Vertical Cylinders and Sheets

A Least-Squares Standard Deviation Method to Interpret Gravity Data due to Finite Vertical Cylinders and Sheets

A Numerical Approach to Depth Determination from Residual Gravity Anomaly Due to Two Structures

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

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