1887
Volume 23 Number 1
  • E-ISSN: 1365-2478

Abstract

A

Approximation formulas for a cube's gravity field yield results which, for all practical purposes, are as accurate as those obtained by using the lengthy expressions defining the exact field. This fact is utilized in the development of a new gravity modeling scheme which uses cubes as building blocks.

A geologically feasible shape of the anomalous body is assumed and filled with cubes. To start with the largest cube which can be accommodated is placed inside the body. After that, the sidelength of the cube is halved, and as many cubes of that size as possible are placed into the remaining space. This procedure is repeated until the system of cubes has approached the shape of the body. The total gravity field due to all cubes placed represents the field of the body.

The placement of cubes is governed by an arrangement which is symmetrical with respect to the center of the first cube. Consequently, the data calculated for one cube may be used repeatedly for other symmetrically located cubes; this approach greatly reduces the number of calculations actually carried out. By reducing the size of the first cube and making it sufficiently small so that its density may be treated as uniform, the method can be used for evaluating the gravity field of an irregularly shaped body whose density varies in an arbitrary fashion.

The accuracy of the method is investigated by computing the gravity field of a sphere constructed from cubical blocks and buried at a shallow depth. A comparison of results with the analytical data obtained for the corresponding perfect sphere shows that a very high precision, of the order of microgals, is reached even at the end of the second cycle; moreover, depending on the accuracy desired, the method is three to five times faster than the Talwani‐Ewing algorithm. The method may be applied to borehole gravimetry, where very high precision is required, as well as to problems of topographic correction, where speed is the most important consideration.

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/content/journals/10.1111/j.1365-2478.1975.tb00688.x
2006-04-27
2024-03-29
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References

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http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1975.tb00688.x
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  • Article Type: Research Article

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