scholarly journals Interpretation of gravity and magnetic anomalies for non-specialists

1996 ◽  
Author(s):  
A Goodacre ◽  
P Keating
Keyword(s):  
Magnetic Anomalies ◽  
Gravity And Magnetic

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.

Magnetic anomaly of a circular lamina

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 102-107 ◽  
Author(s):  
S. K. Singh ◽  
R. Castro E. ◽  
M. Guzman S.
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Gravity Anomaly ◽  
Magnetic Anomaly ◽  
Magnetic Anomalies ◽  
Hankel Transform ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Gravity And Magnetic

Closed form expressions for the gravity anomaly of a circular lamina and the gravity and magnetic anomalies due to a vertical right circular cylinder have been obtained previously (Singh, 1977a; Singh, 1977b; Singh and Sabina, 1978) by a method which avoids complicated integrations commonly used in deriving such solutions (e.g., Nabighian, 1962; Rao and Radhakrishnamurty, 1966). The method involves use of the Fourier‐Hankel transform of Poisson’s equation. The final expressions are obtained in closed form by employing certain tabulated integrals.

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