MAGNETIC ANOMALIES DUE TO PRISM‐SHAPED BODIES WITH ARBITRARY POLARIZATION

Geophysics ◽  
1964 ◽  
Vol 29 (4) ◽  
pp. 517-531 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Polarization Vector ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
The Body ◽  
Simple Extension ◽  
Second Derivative ◽  
Positive Anomaly ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Dip Angle

A study is made of magnetic anomalies due to prism‐shaped bodies with arbitrary polarization. Expressions of the total field and its first and second derivatives are derived on the assumption of uniform magnetization through out the body. Formulas for all possible cases in connection with a rectangular prism with vertical sides can be obtained either directly from this paper or by simple extension of the formulas given here. Using the exact expressions given in this paper, the total field and its derivatives are evaluated conveniently and rapidly with the aid of a digital computer. The effect of the dip angle anti declination of the polarization vector on the size and shape of the magnetic anomaly is then studied for the case when the earth’s normal total field vector has a dip angle of 60° and declination of 0°. With an increase in the dip angle of the polarization vector, the negative anomaly occurring on the north of the causative body diminishes in magnitude, whereas the positive and second derivative anomalies increase to maximum values and then decrease. With an increase in declination, this latter trend is repeated with the positive anomaly but the negative and second‐derivative anomalies decrease systematically. Both the positive and second‐derivative anomalies become more and more symmetrical with respect to the prismatic body with increase in either the inclination or declination of the polarization vector.

END CORRECTIONS IN MAGNETIC PROFILE INTERPRETATION

Geophysics ◽  
1973 ◽  
Vol 38 (3) ◽  
pp. 507-512 ◽  
Author(s):  
R. T. Shuey ◽  
A. S. Pasquale
Keyword(s):  
Magnetic Anomalies ◽  
The Body ◽  
Two Dimensional ◽  
Total Field ◽  
Magnetic Profile ◽  
Arbitrary Magnetization ◽  
End Corrections

Simple expressions are presented for the vertical and total field magnetic anomalies due to a polygonal body of finite strike length and arbitrary magnetization. These formulas incorporate end corrections into the well‐known Talwani‐Heirtzler (1964) formulas for two‐dimensional polygonal bodies and reduce to the latter for large strike length. Because of their simplicity, the formulas with end corrections lend themselves to rapid use in digital interpretation. Analysis of the formulas shows that interpretation with end corrections gives a body which is deeper and has a larger magnetization and different shape than the body inferred without end corrections.

A rapid method for three‐dimensional modeling of magnetic anomalies

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1729-1737 ◽  
Author(s):  
D. Bhaskara Rao ◽  
N. Ramesh Babu
Keyword(s):  
Computing Time ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Three Dimensional Modeling ◽  
Prismatic Bodies ◽  
Forward Calculation ◽  
Approximate Equations

A computer program has been developed for three‐dimensional analysis of total field magnetic anomalies due to arbitrary polarization suitable for present‐day personal computers. A vertical sided prism with arbitrary polarization is used as a basic model. A nonlinear optimization technique based on Marquardt’s algorithm is used to estimate all parameters of the model. A combination of prisms is used to analyze more complex magnetic fields. Analytical methods are used to estimate the derivatives required in the simultaneous solutions of the normal equations. Methods have been developed to minimize the computing time in forward calculation as well as in inversion. Approximate equations have been derived for rapid calculation of magnetic anomalies and partial derivatives of anomalies of prismatic bodies, which are valid beyond short distances from the sources. The algorithm has been developed in such a way that the use of the exact and approximate equations may be efficiently monitored as a trade‐off between accuracy and speed. The method is applied to analyze a synthetic anomaly contour map and the total field aeromagnetic anomalies in the offshore region of Mahanadi basin, Orissa, India.

A DIRECT COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES CAUSED BY 2- AND 3-DIMENSIONAL BODIES OF ARBITRARY SHAPE AND ARBITRARY MAGNETIC POLARIZATION BY EQUIVALENT‐POINT METHOD AND A SIMPLIFIED CUBIC SPLINE

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 610-622 ◽  
Author(s):  
Chao C. Ku
Keyword(s):  
Arbitrary Shape ◽  
Gaussian Quadrature ◽  
Magnetic Anomalies ◽  
Cubic Spline ◽  
The Body ◽  
Point Method ◽  
Magnetic Polarization ◽  
3 Dimensional ◽  
Equivalent Point ◽  
Gravity And Magnetic

A computational method, which combines the Gaussian quadrature formula for numerical integration and a cubic spline for interpolation in evaluating the limits of integration, is employed to compute directly the gravity and magnetic anomalies caused by 2-dimensional and 3-dimensional bodies of arbitrary shape and arbitrary magnetic polarization. The mathematics involved in this method is indeed old and well known. Furthermore, the physical concept of the Gaussian quadrature integration leads us back to the old concept of equivalent point masses or equivalent magnetic point dipoles: namely, the gravity or magnetic anomaly due to a body can be evaluated simply by a number of equivalent points which are distributed in the “Gaussian way” within the body. As an illustration, explicit formulas are given for dikes and prisms using 2 × 2 and 2 × 2 × 2 point Gaussian quadrature formulas. The basic limitation in the equivalent‐point method is that the distance between the point of observation and the equivalent points must be larger than the distance between the equivalent points within the body. By using a reasonable number of equivalent points or dividing the body into a number of smaller subbodies, the method might provide a useful alternative for computing in gravity and magnetic methods. The use of a simplified cubic spline enables us to compute the gravity and magnetic anomalies due to bodies of arbitrary shape and arbitrary magnetic polarization with ease and a certain degree of accuracy. This method also appears to be quite attractive for terrain corrections in gravity and possibly in magnetic surveys.

Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1549-1553 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Data ◽  
Dipole Source ◽  
Point Dipole ◽  
Main Subject ◽  
Depth Extent ◽  
Dipole Sources

The concept of point‐pole and point‐dipole in interpretation of magnetic data is often employed in the analysis of magnetic anomalies (or their derivatives) caused by geologic bodies whose geometric shapes approach those of (1) narrow prisms of infinite depth extent aligned, more or less, in the direction of the inducing earth’s magnetic field, and (2) spheres, respectively. The two geologic bodies are assumed to be magnetically polarized in the direction of the Earth’s total magnetic field vector (Figure 1). One problem that perhaps is not realized when interpretations are carried out on such anomalies, especially in regions of high magnetic latitudes (45–90 degrees), is that of being unable to differentiate an anomaly due to a point‐pole from that due to a point‐dipole source. The two anomalies look more or less alike at those latitudes (Figure 2). Hood (1971) presented a graphical procedure of determining depth to the top/center of the point pole/dipole in which he assumed prior knowledge of the anomaly type. While it is essential and mandatory to make an assumption such as this, it is very important to go a step further and carry out a test on the anomaly to check whether the assumption made is correct. The procedure to do this is the main subject of this note. I start off by first using some method that does not involve Euler’s differential equation to determine depth to the top/center of the suspected causative body. Then I employ the determined depth to identify the causative body from the graphical diagram of Hood (1971, Figure 26).

Electroreception in Gymnotus carapo: pre-receptor processing and the distribution of electroreceptor types

2000 ◽  
Vol 203 (21) ◽  
pp. 3279-3287 ◽  
Author(s):  
M.E. Castello ◽  
P.A. Aguilera ◽  
O. Trujillo-Cenoz ◽  
A.A. Caputi
Keyword(s):  
Electric Fields ◽  
Electric Fish ◽  
Fish Tissue ◽  
Field Vector ◽  
The Body ◽  
Type I ◽  
Type Ii ◽  
Field Patterns ◽  
Different Types ◽  
Very High

This paper describes the peripheral mechanisms involved in signal processing of self- and conspecific-generated electric fields by the electric fish Gymnotus carapo. The distribution of the different types of tuberous electroreceptor and the occurrence of particular electric field patterns close to the body of the fish were studied. The density of tuberous electroreceptors was found to be maximal on the jaw (foveal region) and very high on the dorsal region of the snout (parafoveal region), decaying caudally. Tuberous type II electroreceptors were much more abundant than type I electroreceptors. Type I electroreceptors occurred exclusively on the head and rostral trunk regions, while type II electroreceptors were found along as much as 90 % of the fish. Electrophysiological data indicated that conspecific- and self-generated electric currents are ‘funnelled’ by the high conductivity and geometry of the body of the fish. These currents are concentrated at the peri-oral zone, where most electroreceptors are located. Moreover, within this region, field vector directions were collimated, constituting the most efficient stimulus for electroreceptors. It can be concluded that the passive properties of the fish tissue represent a pre-receptor device that enhances exafferent and reafferent electrical signals at the fovea-parafoveal region.

A comparative study of the relation figures of magnetic anomalies due to two‐dimensional dike and vertical step models

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 926-931 ◽  
Author(s):  
H. V. Ram Babu ◽  
A. S. Subrahmanyam ◽  
D. Atchuta Rao
Keyword(s):  
Comparative Study ◽  
Major Axis ◽  
Magnetic Anomalies ◽  
The Body ◽  
Two Dimensional ◽  
Depth Ratio ◽  
Characteristic Points ◽  
Vertical Step ◽  
Bottom To Top ◽  
Body Parameters

Magnetic anomalies in vertical and horizontal components, when plotted one against the other in polar form, result in a curve called the relation figure (Werner, 1953). In this paper, a comparative study of the relation figures of magnetic anomalies due to two‐dimensional (2-D) dike and vertical step models is made. The relation figures for these two models are found to be ellipses with different properties. The tangent at the origin to the ellipse is parallel to the major axis of the ellipse for the dike model, whereas it is perpendicular to the major axis for the vertical step. This property may be used to distinguish whether the source is a dike or a vertical step. For both of the models, the angle made by the axis of symmetry of the ellipse with the coordinate axis is equal to θ, the combined magnetic angle. The ratio between the lengths of the major and minor axes of the ellipse is directly related to the width‐to‐depth ratio of the dike or the bottom‐to‐top depth ratio of the vertical step. A few characteristic points defined on the ellipse are used to evaluate the body parameters. The major portion of the ellipse is obtained in the close vicinity of the source. Because of symmetry, the ellipse may be extrapolated easily outside the data length, and hence the effect of noise caused by adjacent objects is kept at a minimum.

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