Spherical-Earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration

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R.R.B. von Frese
W.J. Hinze
L.W. Braile
A.J. Luca


The usefulness of long-wavelength potential field anomalies in lithospheric interpretation is greatly increased with spherical Earth modeling techniques. Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles. The distribution of equivalent point sources is determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.

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von Frese, R., Hinze, W., Braile, L., & Luca, A. (1981). Spherical-Earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration. Journal of Geophysics, 49(1), 234-242. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/163
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