Discussion on “Digital Convolution of Computing Gravity and Magnetic Anomalies Due to Arbitrary Bodies,” by B. K. Bhattacharyya and M. E. Navolio (GEOPHYSICS, December 1975, p. 981–992)

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 663-663
Author(s):  
I. R. Qureshi
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Numerical Integration ◽  
Magnetic Anomalies ◽  
Point Mass ◽  
Mathematical Approach ◽  
Gravity And Magnetic ◽  
Small Side

I congratulate the authors on their elegant mathematical approach to the computation of gravity and magnetic anomalies due to arbitrary bodies. But I consider their concluding remark, “In this approach, it is not necessary to perform integration of the dipolar magnetic field or the gravitational field due to a point mass,” to be inaccurate and misleading. The method proposed by the authors represents, in effect, the division of arbitrary bodies into cubes of a small side and numerical integration [their equations (20) and (25)] of the effects of “equivalent” dipoles or point masses located at the centers of these cubes. Hence, the smaller the side of the cube, the better the accuracy of the method.

Reply to I. R. Qureshi by the Authors

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 663-663
Author(s):  
B. K. Bhattacharyya ◽  
M. E. Navolio
Keyword(s):  
Magnetic Field ◽  
General Practice ◽  
Gravitational Field ◽  
Potential Field ◽  
Gravity Anomalies ◽  
The Body ◽  
Point Mass ◽  
Convolution Approach ◽  
Magnetic And Gravity Anomalies

In order to determine expressions for magnetic and gravity anomalies generated by a body of known shape, it is the general practice to integrate the dipolar magnetic field or the gravitational field due to a point mass over the volume occupied by the body. The digital convolution approach, as discussed in the above paper, makes it unnecessary to perform the integration analytically and to use a complicated expression for computing the anomalous potential field.

Simultaneous computation of gravity and magnetic anomalies resulting from a 2‐D object

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 801-806 ◽  
Author(s):  
Bijendra Singh
Keyword(s):  
Magnetic Field ◽  
Joint Inversion ◽  
Mass Density ◽  
Magnetic Anomalies ◽  
Volume Density ◽  
Pole Density ◽  
Surface Mass ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Surface Mass Density

This paper presents a new algorithm for the simultaneous computation of gravity and magnetic anomalies resulting from an infinitely long (2‐D) body with an arbitrary polygonal cross‐section. With the assumption of uniform volume density and magnetization, the gravity or magnetic field may be expressed as the field resulting from an equivalent distribution of surface mass density or surface pole density, respectively, over the surface of the source body. The resulting surface integrals are reduced to new line integrals using Stokes' theorem. The components of the fields for each bounding surface are expressed in terms of a new line integral and the solid angle subtended by the surface at the point of observation. Since these analytical solutions are similar in form, a direct relation is derived between gravity and magnetic fields, which allows their simultaneous computation. Hence, the same computer program can be used to compute the gravity field, the magnetic field, or both fields simultaneously. This new approach will find wide applications in the joint inversion of potential field data, as it will make the numerical computations much faster.

scholarly journals Geodesy, Geophysics and Fundamental Physics Investigations of the BepiColombo Mission

2021 ◽  
Vol 217 (2) ◽  
Author(s):  
Antonio Genova ◽  
Hauke Hussmann ◽  
Tim Van Hoolst ◽  
Daniel Heyner ◽  
Luciano Iess ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Surface Composition ◽  
Current Knowledge ◽  
Laser Altimeter ◽  
Fundamental Physics ◽  
Radio Science ◽  
Nasa Mission ◽  
Gravity And Magnetic ◽  
Working Groups ◽  
Science Investigations

AbstractIn preparation for the ESA/JAXA BepiColombo mission to Mercury, thematic working groups had been established for coordinating the activities within the BepiColombo Science Working Team in specific fields. Here we describe the scientific goals of the Geodesy and Geophysics Working Group (GGWG) that aims at addressing fundamental questions regarding Mercury’s internal structure and evolution. This multidisciplinary investigation will also test the gravity laws by using the planet Mercury as a proof mass. The instruments on the Mercury Planetary Orbiter (MPO), which are devoted to accomplishing the GGWG science objectives, include the BepiColombo Laser Altimeter (BELA), the Mercury orbiter radio science experiment (MORE), and the MPO magnetometer (MPO-MAG). The onboard Italian spring accelerometer (ISA) will greatly aid the orbit reconstruction needed by the gravity investigation and laser altimetry. We report the current knowledge on the geophysics, geodesy, and evolution of Mercury after the successful NASA mission MESSENGER and set the prospects for the BepiColombo science investigations based on the latest findings on Mercury’s interior. The MPO spacecraft of the BepiColombo mission will provide extremely accurate measurements of Mercury’s topography, gravity, and magnetic field, extending and improving MESSENGER data coverage, in particular in the southern hemisphere. Furthermore, the dual-spacecraft configuration of the BepiColombo mission with the Mio spacecraft at higher altitudes than the MPO spacecraft will be fundamental for decoupling the internal and external contributions of Mercury’s magnetic field. Thanks to the synergy between the geophysical instrument suite and to the complementary instruments dedicated to the investigations on Mercury’s surface, composition, and environment, the BepiColombo mission is poised to advance our understanding of the interior and evolution of the innermost planet of the solar system.

Large scale magnetic anomalies over western Canada and the Arctic: a discussion

1976 ◽  
Vol 13 (6) ◽  
pp. 790-802 ◽  
Author(s):  
R. L. Coles ◽  
G. V. Haines ◽  
W. Hannaford
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Elevated Temperatures ◽  
Magnetic Anomalies ◽  
The Arctic ◽  
Evolutionary Development ◽  
Magnetic Feature ◽  
Western Canada ◽  
Arctic Regions ◽  
The Magnetic Field

A contoured map of vertical magnetic field residuals (relative to the IGRF) over western Canada and adjacent Arctic regions has been produced by amalgamating new data with those from previous surveys. The measurements were made at altitudes between 3.5 and 5.5 km above sea level. The map shows the form of the magnetic field within the waveband 30 to 5000 km. A magnetic feature of several thousand kilometres wavelength dominates the map, and is probably due in major part to sources in the earth's core. Superimposed on this are several groups of anomalies which contain wavelengths of the order of a thousand kilometres. The patterns of the short wavelength anomalies provide a broad view of major structures and indicate several regimes of distinctive evolutionary development. Enhancement of viscous magnetization at elevated temperatures may account for the concentration of intense anomalies observed near the western edge of the craton.

scholarly journals ELECTROMAGNETIC FIELDS OF CHARGED AND MAGNETIZED CYLINDRICAL CONDUCTORS IN NUT SPACE

2005 ◽  
Vol 14 (03n04) ◽  
pp. 687-695 ◽  
Author(s):  
B. J. AHMEDOV ◽  
A. V. KHUGAEV ◽  
N. I. RAKHMATOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Electromagnetic Fields ◽  
Electric Charge ◽  
Maxwell Equations ◽  
Analytic Solutions ◽  
Vertical Magnetic Field ◽  
General Relativistic ◽  
Azimuthal Current ◽  
Cylindrical Conductors

We present analytic solutions of Maxwell equations for infinitely long cylindrical conductors with nonvanishing electric charge and currents in the external background spacetime of a line gravitomagnetic monopole. It has been shown that vertical magnetic field arising around cylindrical conducting shell carrying azimuthal current will be modified by the gravitational field of NUT source. We obtain that the purely general relativistic magnetic field which has no Newtonian analog will be produced around charged gravitomagnetic monopole.

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.

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