Reply by the authors to N. L. Mohan

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1215-1216 ◽  
Author(s):  
W. R. Roest ◽  
J. Verhoef ◽  
M. Pilkington
Keyword(s):  
Analytic Signal ◽  
Three Dimensions ◽  
Magnetic Interpretation

The purpose of our paper (Roest et al., 1992) was to present the generalization of the analytic signal (Nabighian, 1972) from two to three dimensions and illustrate its use in magnetic interpretation. The comments by Dr. Mohan can be separated into three categories.

Magnetic interpretation using the 3-D analytic signal

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 116-125 ◽  
Author(s):  
Walter R. Roest ◽  
Jacob Verhoef ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Impact Crater ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Eastern Canada ◽  
Magnetic Interpretation ◽  
Absolute Value ◽  
Cape Breton ◽  
Derivatives Of ◽  
The Magnetic Field

A new method for magnetic interpretation has been developed based on the generalization of the analytic signal concept to three dimensions. The absolute value of the analytic signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field. This signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field and source magnetization directions. Locations of these maxima thus determine the outlines of magnetic sources. Under the assumption that the anomalies are caused by vertical contacts, the analytic signal is used to estimate depth using a simple amplitude half‐width rule. Two examples are shown of the application of the method. In the first example, the analytic signal highlights a circular feature beneath Lake Huron that has been identified as a possible impact crater. The second example illustrates the continuation of terranes across the Cabot Strait between Cape Breton and Newfoundland in eastern Canada.

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.

To: “Magnetic interpretation in three dimensions using Euler deconvolution,” by A. B. Reid, J. M. Allsop, H. Granser, A. J. Millett, and I. W. Somerton (GEOPHYSICS, p. 80–91, January 1990)

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 502-502
Keyword(s):  
Three Dimensions ◽  
Euler Deconvolution ◽  
Magnetic Interpretation

Please note that Figures 3 (p. 85) and 5 (p. 87) are not identified. The misplaced captions appear at the bottom of pages 86 and 88, respectively.

Reply by the authors to the discussion by Huang Lin‐ping and Guan Zhi‐ning

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 670-670 ◽  
Keyword(s):  
Analytic Signal ◽  
Magnetic Interpretation

The authors of “Magnetic interpretation using the 3‐D analytic signal” chose not to reply to the discussion by Huang Lin‐ping and Guan Zhi‐ning.

Magnetic interpretation using the 3D analytic signal

1991 ◽  
Author(s):  
W. R. Roest ◽  
M. Pilkington ◽  
J. Verhoef
Keyword(s):  
Analytic Signal ◽  
Magnetic Interpretation

Magnetic interpretation in three dimensions using Euler deconvolution

Geophysics ◽  
1990 ◽  
Vol 55 (1) ◽  
pp. 80-91 ◽  
Author(s):  
A. B. Reid ◽  
J. M. Allsop ◽  
H. Granser ◽  
A. J. Millett ◽  
I. W. Somerton
Keyword(s):  
Calculated Data ◽  
Real Data ◽  
Three Dimensions ◽  
Magnetic Survey ◽  
Good Precision ◽  
Structural Index ◽  
Magnetic Interpretation ◽  
Model Studies ◽  
Index Model ◽  
Using Data

Magnetic‐survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using Euler’s homogeneity relation. The method employs gradients, either measured or calculated. Data need not be pole‐reduced, so that remanence is not an interfering factor. Geologic constraints are imposed by use of a structural index. Model studies show that the method can locate or outline confined sources, vertical pipes, dikes, and contacts with remarkable accuracy. A field example using data from an intensively studied area of onshore Britain shows that the method works well on real data from structurally complex areas and provides a series of depth‐labeled Euler trends which mark magnetic edges, notably faults, with good precision.

Analytic signals of gravity gradient tensor and their application to estimate source location

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. I59-I74 ◽  
Author(s):  
Majid Beiki
Keyword(s):  
Analytic Signal ◽  
Three Dimensions ◽  
Gravity Gradient ◽  
Automatic Identification ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Signal Functions ◽  
First Vertical Derivative ◽  
Tensor Data ◽  
Analytic Signals

The analytic signal concept can be applied to gravity gradient tensor data in three dimensions. Within the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are Hilbert transform pairs. Three analytic signal functions then are introduced along [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. The amplitude of the first vertical derivative of the analytic signals in [Formula: see text]- and [Formula: see text]-directions enhances the edges of causative bodies. The directional analytic signals are homogenous and satisfy Euler’s homogeneity equation. The application of directional analytic signals to Euler deconvolution on generic models demonstrates their ability to locate causative bodies. One of the advantages of this method is that it allows the automatic identification of the structural index from solving three Euler equations derived from the gravity gradient tensor for a collection of data points in a window. The other advantage is a reduction of interference effects from neighboring sources by differentiation of the directional analytic signals in [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-directions. Application of the method is demonstrated on gravity gradient tensor data in the Vredefort impact structure, South Africa.

Attributes of the magnetic field, analytic signal, and monogenic signal for gravity and magnetic interpretation

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. J79-J86 ◽  
Author(s):  
Xiong Li ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Magnetic Anomaly ◽  
Field Vector ◽  
Analytic Signal ◽  
Horizontal Gradient ◽  
Monogenic Signal ◽  
Magnetic Interpretation ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Interpretation ◽  
The Magnetic Field

Many of the transforms and attributes used in gravity and magnetic interpretation can be expressed as a 2D or 3D vector. The horizontal gradient and the 2D analytic signal are 2D vectors. The gravity or magnetic field, the 3D analytic signal, and the monogenic signal are defined by a 3D vector. In practice, we prefer to interpret the amplitude and/or phase of a 2D or 3D vector, but we often forget that a meaningful interpretation requires a magnetic reduction-to-the-pole operation when these techniques are applied to magnetic anomaly data and the source body is 3D. Furthermore, the gravity or magnetic anomaly has an unknown constant level that may affect the amplitude and phase. The horizontal gradient, the analytic signal, and the monogenic signal can be applied to not only the gravity or magnetic anomaly but also any [Formula: see text]th-order derivative or a filtered version of the anomaly. They can be related to each other and to the magnetic field vector. We do not introduce new attributes. Instead, we have explained the relationships among different transforms (or vectors) and addressed precautions and requirements for their practical use.

On: “Magnetic interpretation using the 3-D analytic signal” by W. R. Roest, J. Verhoef, and M. Pilkington (GEOPHYSICS, 1, 116–125, January 1992).

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1214-1214 ◽  
Author(s):  
N. L. Mohan
Keyword(s):  
Magnetic Anomalies ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Magnetic Interpretation ◽  
Vector Addition

It is quite interesting to learn the 3-D analytic signal interpretation of Roest et al. (1992), using the vector addition. However, I am quite skeptical about their objective of determining the depth under the assumption that the magnetic anomalies are caused by vertical contacts from gridded magnetic data which, it appears to me, is nothing but an oversimplification of interpretation.

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