Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms

Geophysics ◽  
1982 ◽  
Vol 47 (3) ◽  
pp. 376-387 ◽  
Author(s):  
N. L. Mohan ◽  
N. Sundararajan ◽  
S. V. Seshagiri Rao
Keyword(s):  
Circular Cylinder ◽  
Andhra Pradesh ◽  
Theoretical Models ◽  
Magnetic Anomalies ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
Infinite Depth ◽  
The Hilbert Transform ◽  
Depth Extent ◽  
Horizontal Circular Cylinder

Procedures are formulated using the Hilbert transform for interpreting vertical magnetic anomalies of (1) the sheets (finite and infinite depth extent), (2) the dike, and (3) the horizontal circular cylinder. The applicability of the method is tested on theoretical models. The method is also applied on the well‐known Kursk field anomaly of a sheet (infinite‐depth extent) and the field anomaly of a dike of Karimnagar, Andhra Pradesh, India.

On the short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

On: “Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms, by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri (GEOPHYSICS, 47, 376–387, March, 1982)

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 239-240
Author(s):  
R. Nagendra ◽  
H. V. Ram Babu
Keyword(s):  
Magnetic Anomalies ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
The Subject

We read Mohan et al.’s paper on interpretation of magnetic anomalies using Hilbert transforms and the discussion raised on it by Pauls (1985) and the authors’ reply (Mohan et al., 1985). While critically going through the authors’ reply (Mohan et al., 1985), we noticed a serious error in the subject paper related to the incompatibility of its equations (1) and (2).

On: “Interpretation of two dimensional magnetic bodies using Hilbert transforms,” by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri Rao (March 1982 GEOPHYSICS, 52, p. 376–387)

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 690-691
Author(s):  
B. N. P. Agarwal
Keyword(s):  
Magnetic Field ◽  
Hilbert Transform ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
The Hilbert Transform

While going through some of the publications (Mohan and Babu, 1995), I became interested in the work of Mohan et al. (1982) which proposed a technique for interpretation of magnetic field anomalies over different geometrical sources using the Hilbert transform (HT). Before I put forward my observations, it would be appropriate to look into some important properties of HT (Whalen, 1971, pages 63 and 69.)

Gravity interpretation using the Mellin transform

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 114-122 ◽  
Author(s):  
N. L. Mohan ◽  
L. Anandababu ◽  
S. V. Seshagiri Rao
Keyword(s):  
Circular Cylinder ◽  
Gravity Anomaly ◽  
Mellin Transform ◽  
The Body ◽  
Two Dimensional ◽  
Gravity Effect ◽  
Horizontal Derivative ◽  
Gravity Interpretation ◽  
Body Parameters ◽  
Horizontal Circular Cylinder

The Mellin transform of the gravity effect of a buried sphere and two‐dimensional horizontal circular cylinder, and the first horizontal derivative of the gravity effect of a two‐dimensional thin fault layer are derived. The transformed functions are bounded by two asymptotes. They are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters. The application of the Mellin transform is tested on simulated models as well as on two field examples: (1) the Humble Dome gravity anomaly near Houston, USA; and (2) the Louga gravity anomaly, USA.

On: “A rapid graphical method for the interpretation of the self‐potential anomaly over a two‐dimensional inclined sheet of finite depth extent” by H. V. Ram Babu and D. Atchuta Rao (GEOPHYSICS, 53, 1126–1128, August 1988).

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1215-1216 ◽  
Author(s):  
L. Eskola ◽  
H. Hongisto
Keyword(s):  
Graphical Method ◽  
Theoretical Models ◽  
Finite Depth ◽  
The Self ◽  
Inversion Method ◽  
Two Dimensional ◽  
Depth Extent ◽  
Self Potential ◽  
Graphical Algorithm ◽  
Inclined Sheet

Ram Babu and Atchuta Rao (1988a, b) presented a graphical algorithm for the interpretation of a self‐potential anomaly over a sheet. Ram Babu and Atchuta Rao (1988b) also presented an inversion method based on iterative optimization for the self‐potential anomalies caused by spherical, cylindrical, and sheetlike bodies. The theoretical models on which the algorithms are based are very simple: for the sphere, an electrostatic dipole; for the cylinder, a line dipole; and for the sheet two line poles, the negative one along the upper edge of the sheet and the positive one along its lower edge.

On: “Application of Gauss’s method to magnetic anomalies of dipping dikes” by I. J. Won (GEOPHYSICS, February 1981, p. 211–215).

Geophysics ◽  
1982 ◽  
Vol 47 (2) ◽  
pp. 266-267
Author(s):  
K. Kunaratnam
Keyword(s):  
Magnetic Anomaly ◽  
Magnetic Anomalies ◽  
Transverse Component ◽  
The Other ◽  
Infinite Depth ◽  
Dip Angle ◽  
Depth Extent ◽  
Permanent Magnetization

In a recent paper, Won discussed the application of Gauss’s method for obtaining the parameters of a dipping dike from its magnetic anomaly. He assumed the magnetization to be entirely induced and did not consider the effect of the presence of any permanent magnetism. In view of the reported agreement of the calculated dip angles with drilled results, the assumption seems to be valid in this particular case. If permanent magnetization in an unknown direction is present, neither the dip angle of the dike nor the susceptibility can be determined, although the other parameters of the dike (i.e., depth to the top, horizontal location, and thickness) can be deduced from the magnetic anomaly. The dip angle of the dike and the angle made by the transverse component of the resultant intensity of magnetization combine to form a single angle which alone can be determined uniquely from the magnetic anomaly. If the transverse component of the resultant intensity of magnetization is J and it dips at an angle α below the horizontal, then using the other notations given by Won it can be shown that [Formula: see text] and [Formula: see text] (Bruckshaw and Kunaratnam, 1963). For this reason, the magnetic anomaly due to an inclined dike of infinite depth extent and horizontal top surface is the same as that due to a vertical dike having the same top surface but for a modified direction and intensity of magnetization. The inclined dike anomalies can, therefore, be analyzed using the vertical prism models as well. If the magnetization is entirely induced, the dip angle of the inclined dike can be deduced from the direction of magnetization of the equivalent vertical dike.

scholarly journals Spectral Analysis of Magnetic Anomalies Due to a 2-D Horizontal Circular Cylinder: A Hartley Transforms Technique

2011 ◽  
Vol 16 ◽  
pp. 45 ◽  
Author(s):  
Mansour A. Al-Garni
Keyword(s):  
Spectral Analysis ◽  
Circular Cylinder ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Horizontal Cylinder ◽  
Hartley Transform ◽  
Alternative Approach ◽  
Hartley Transforms ◽  
High Level ◽  
Horizontal Circular Cylinder

The spectral analysis of the vertical effect of magnetic anomalies due to a 2-D horizontal circular cylinder is presented using Hartley transform. Hartley transform is an alternative approach to the famous complex Fourier transform. The depth to the center of the horizontal cylinder can be computed by a simple equation as a function of frequency. A synthetic example has been used to illustrate this technique and the validity of this approach has been proved by applying it to real data of a narrow band of quartz-magnetite in Mangampalli near Karimnagar town, India. The noise analyses were tested on the technique and showed a high level of confidence. The results of the field example are in good agreement with the ones published in the literature.  

MAGNETIC ANOMALIES OF THIN SHEETS AND THEIR INTERPRETATIONS

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 963-974 ◽  
Author(s):  
Buddhadeb Banerjee
Keyword(s):  
Iterative Process ◽  
Thin Sheet ◽  
Theoretical Models ◽  
Magnetic Anomalies ◽  
Graphic Method ◽  
Thin Sheets ◽  
Unknown Parameters ◽  
Actual Field ◽  
Depth Extent

A method of quantitative interpretation of the vertical magnetic anomaly (ΔZ) caused by a thin sheet infinite in horizontal extent but limited in depth extent is developed. The determination of the position of the point on the profile above the dike plays an important role in the analysis and is done either by a graphic method or with the help of a rapidly convergent iterative process. When the depth extent of the sheet, either vertical or inclined, becomes infinite, the mathematical steps become simpler, and evaluation of different unknown parameters of the causative body is possible without any prior knowledge of the positions of the cartesian axes. The proposed methods are applied both on theoretical models and on actual field cases.

STANDARD CURVES FOR MAGNETIC ANOMALIES OVER LONG HORIZONTAL CYLINDERS

Geophysics ◽  
1965 ◽  
Vol 30 (5) ◽  
pp. 818-828 ◽  
Author(s):  
S. Parker Gay
Keyword(s):  
Circular Cylinder ◽  
Magnetic Anomalies ◽  
Curve Matching ◽  
Profile Curve ◽  
Complete Family ◽  
Family Of Curves ◽  
Isolated Points ◽  
Horizontal Cylinders ◽  
Magnetizing Field ◽  
Horizontal Circular Cylinder

The magnetic anomalies in Z, H, and [Formula: see text] for the long horizontal circular cylinder are shown to belong to a single mathematical family of curves for all values of strike and all values of inclination of the magnetizing field, a characteristic that was previously shown to hold for long tabular bodies, or dikes (Gay, 1963). The complete family of standard curves has been constructed and is incorporated into an interpretational scheme based on superposition with observed magnetic profiles. Comparison of cylinder anomalies with dike anomalies shows only slight differences in the two types of curves, which would be very difficult, if not impossible, to detect using interpretational methods based on a few isolated points of a profile curve, such as half‐width, distance between maximum and minimum, etc. Curve‐matching, or superposition, appears to be mandatory for reliable quantitative interpretations.

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