RECURSION FILTERS FOR DIGITAL PROCESSING OF POTENTIAL FIELD DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 712-726 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Vertical Gradient ◽  
Two Dimensional ◽  
Single Variable ◽  
Potential Field Data ◽  
Recursive Filter ◽  
Rational Expression

Zero‐phase two‐dimensional recursive filters, with a specified frequency domain response, have been designed for processing potential field data. In the case of second vertical derivative filters, it is possible to use the rational approximation of symmetrical functions of a single variable for the design of a short recursive filter. The filter so designed has an excellent response in the frequency domain. For vertical gradient and continuation filters, a method is developed for obtaining, by the least‐squares method, a rational expression for a two‐dimensional symmetrical function. In order to ensure the stability of the recursive filter, the denominator of the rational expression is approximated by a product of two factors, each being a function of a single variable. Finally, to keep the error of the filter response as small as possible, an iterative procedure is used for adjusting the zeros of the denominator and then determining the coefficients of the numerator of the rational expression.

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

DESIGN OF SMALL OPERATORS FOR THE CONTINUATION OF POTENTIAL FIELD DATA

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 488-506 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Grid Point ◽  
Frequency Characteristics ◽  
Potential Fields ◽  
Two Dimensional ◽  
Potential Field Data ◽  
Computational Work ◽  
Considerable Loss ◽  
Equivalent Operators

Two‐dimensional continuation of potential fields is commonly achieved by employing a continuation operator which consists of a number of coefficients operating upon uniformly gridded field data. To obtain accurate results, the size of the operator has to be quite large. This not only requires a lot of computational work, but also causes a considerable loss of information due to the reduced size of the field obtained after continuation. Small‐size “equivalent” operators were designed which are free from these drawbacks but yield accurate results. In order to demonstrate the efficiency of these operators, a potential field was continued upward by using 31×31 Tsuboi coefficients. This required 961 multiplications for computing the continued field at each grid point. When procedure was repeated using the equivalent operator, the number of multiplications required for each grid point was reduced to 15, the size of the resulting map was much larger, but the results in both cases were practically identical in accuracy. Frequency characteristics of the equivalent operators and the continuation of data very close to the boundary of the field map are discussed.

ADDITIONAL COMMENTS ON THE ANALYTIC SIGNAL OF TWO‐DIMENSIONAL MAGNETIC BODIES WITH POLYGONAL CROSS‐SECTION

Geophysics ◽  
1974 ◽  
Vol 39 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Cross Section ◽  
Potential Field ◽  
Input Data ◽  
Field Data ◽  
Field Component ◽  
Analytic Signal ◽  
Two Dimensional ◽  
Field Profile ◽  
Total Field ◽  
Potential Field Data

In a previous paper (Nabighian, 1972), the concept of analytic signal of bodies of polygonal cross‐section was introduced and its applications to the interpretation of potential field data were discussed. The input data for the proposed treatment are the horizontal derivative T(x) of the field profile, whether horizontal, vertical, or total field component. As it is known, this derivative curve can be thought of as being due to thin magnetized sheets surrounding the causative bodies.

scholarly journals Backus-Gilbert inversion of potential field data in the frequency domain and its application to real and synthetic data

1994 ◽  
Vol 33 (4) ◽  
pp. 531-539
Author(s):  
Uwe Koppelt ◽  
Javier Rojas
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
Synthetic Data ◽  
Potential Field Data

Se presenta un algoritmo para la inversión de datos del campo potencial en el dominio de las frecuencias utilizando la transformación de Backus-Gilbert. Se describe uno de los problemas fundamentales en todo proceso de interpretación geofísica como es la solución del problema directo y del problema inverso. La comparación de los resultados en el domino del espacio y de las frecuencias muestra las ventajas del algoritmo aquí presentado. Se demuestra la efectividad del algoritmo solucionado tareas de geofísica ambiental como la detección de depósitos antiguos de desechos industriales. Esta técnica interpretativa es aplicable también a la interpretación de investigaciones geofísicas en sitios arqueológicos.

DESIGN OF SPATIAL FILTERS AND THEIR APPLICATION TO HIGH‐RESOLUTION AEROMAGNETIC DATA

Geophysics ◽  
1972 ◽  
Vol 37 (1) ◽  
pp. 68-91 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
High Resolution ◽  
Field Data ◽  
Vertical Gradient ◽  
Double Fourier Series ◽  
Two Dimensional ◽  
Total Field ◽  
Spatial Filters ◽  
Aeromagnetic Survey ◽  
Potential Field Data ◽  
High Frequency Response

Methods for the design of spatial filters are discussed in this paper. For a given response of a one‐dimensional filter, the weighting coefficients are calculated by solving a set of simultaneous equations with a simple matrix inversion procedure. In the case of a two‐dimensional filter, the method for obtaining the coefficients of a double Fourier series representing a set of given values is used to design the spatial operator. The problems connected with the length of the operator and the choice of a suitable decay in the high‐frequency response are discussed in detail. In order to show the usefulness of these methods, the paper presents several examples of operators designed for computing the vertical gradient, the second vertical derivative, and downward continuation of potential field data. A two‐dimensional vertical gradient filter is applied to the total field data obtained during a high‐resolution aeromagnetic survey over an area in the Precambrian Shield of Northeastern Ontario. The calculated gradient maps are compared with maps showing measured gradient values. The quality of the calculated maps in defining trends, patterns, and detailed features of anomalies shows the feasibility of obtaining very accurate vertical gradient maps from observed total field data.

Stable Computation of the Vertical Gradient of Potential Field Data Based on Incorporating the Smoothing Filters

2018 ◽  
Vol 175 (8) ◽  
pp. 2785-2806 ◽  
Author(s):  
Jamaledin Baniamerian ◽  
Shuang Liu ◽  
Mahmoud Ahmed Abbas
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Vertical Gradient ◽  
Potential Field Data ◽  
Stable Computation

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

An improved approach for detecting the locations of the maxima in interpreting potential field data

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Luan Thanh Pham ◽  
Ozkan Kafadar ◽  
Erdinc Oksum ◽  
Ahmed M. Eldosouky
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Potential Field Data
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