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.

Balancing images of potential-field data

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. L17-L20 ◽  
Author(s):  
G. R. Cooper
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Large Range ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Aeromagnetic Data ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Total Gradient ◽  
Data Source

Horizontal and vertical gradients, and filters based on them (such as the analytic signal), are used routinely to enhance detail in aeromagnetic data. However, when the data contain anomalies with a large range of amplitudes, the filtered data also will contain large and small amplitude responses, making the latter hard to see. This study suggests balancing the analytic signal amplitude (sometimes called the total gradient) by the use of its orthogonal Hilbert transforms, and shows that the balanced profile curvature can be an effective method of enhancing potential-field data. Source code is available from the author on request.

Direct Analytic Signal Interpretation of Potential Field Data Using 2-D Hilbert Transform

2011 ◽  
Vol 54 (4) ◽  
pp. 551-559 ◽  
Author(s):  
Yao LUO ◽  
Ming WANG ◽  
Feng LUO ◽  
Song TIAN
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Field Data ◽  
Analytic Signal ◽  
Potential Field Data

Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 780-786 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Field Data ◽  
Three Dimensional ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Automatic Interpretation ◽  
The Hilbert Transform

The paper extends to three dimensions (3-D) the two‐dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy‐Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case. Finally, the previously developed concept of analytic signal in 2-D can be extended to 3-D as a first step toward the development of an automatic interpretation technique for potential field data.

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.

EDGE DETECTION OF POTENTIAL FIELD DATA USING AN ENHANCED ANALYTIC SIGNAL TILT ANGLE

2016 ◽  
Vol 59 (4) ◽  
pp. 341-349
Author(s):  
YAN Ting-Jie ◽  
WU Yan-Gang ◽  
YUAN Yuan ◽  
CHEN Ling-Na
Keyword(s):  
Edge Detection ◽  
Tilt Angle ◽  
Potential Field ◽  
Field Data ◽  
Analytic Signal ◽  
Potential Field Data

To: “Automatic 3-D interpretation of potential‐field data using analytic signal derivatives,” by N. Debeglia and J. Corpel (January‐February 1997 GEOPHYSICS, 62, p. 87–96)

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1346-1346
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Analytic Signal ◽  
Potential Field Data ◽  
Computation Algorithms

When we sent the last revision of our paper to Geophysics, we had not yet received the March‐April 1996 issue of Geophysics and read the paper by Hsu et al. Thereby it could not be included in the references used to assess the method and write the paper. We note some convergences between the two approaches despite the fact that the depth computation algorithms are quite different.

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.

THE ANALYTIC SIGNAL OF TWO‐DIMENSIONAL MAGNETIC BODIES WITH POLYGONAL CROSS‐SECTION: ITS PROPERTIES AND USE FOR AUTOMATED ANOMALY INTERPRETATION

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 507-517 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Analytic Function ◽  
Cross Section ◽  
Field Intensity ◽  
Analytic Signal ◽  
Two Dimensional ◽  
Field Profile ◽  
Vertical Derivative ◽  
Horizontal Derivative ◽  
The Hilbert Transform ◽  
Over The Top

This paper presents a procedure to resolve magnetic anomalies due to two‐dimensional structures. The method assumes that all causative bodies have uniform magnetization and a cross‐section which can be represented by a polygon of either finite or infinite depth extent. The horizontal derivative of the field profile transforms the magnetization effect of these bodies of polygonal cross‐section into the equivalent of thin magnetized sheets situated along the perimeter of the causative bodies. A simple transformation in the frequency domain yields an analytic function whose real part is the horizontal derivative of the field profile and whose imaginary part is the vertical derivative of the field profile. The latter can also be recognized as the Hilbert transform of the former. The procedure yields a fast and accurate way of computing the vertical derivative from a, given profile. For the case of a single sheet, the amplitude of the analytic function can be represented by a symmetrical function maximizing exactly over the top of the sheet. For the case of bodies with polygonal cross‐section, such symmetrical amplitude functions can be recognized over each corner of each polygon. Reduction to the pole, if desired, can be accomplished by a simple integration of the analytic function, without any cumbersome transformations. Narrow dikes and thin flat sheets, of thickness less than depth, where the equivalent magnetic sheets are close together, are treated in the same fashion using the field intensity as input data, rather than the horizontal derivative. The method can be adapted straightforwardly for computer treatment.It is also shown that the analytic signal can be interpreted to represent a complex “field intensity,” derivable by differentiation from a complex “potential.” This function has simple poles at each polygon corner. Finally, the Fourier spectrum due to finite or infinite thin sheets and steps is given in the Appendix.

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