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

Main Article Content

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.

Google Scholar           ARK: https://n2t.net/ark:/88439/y030173

Permalink: https://geophysicsjournal.com/article/163


Article Details

How to Cite
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


Austin, C.B., Keller, G.R. (1979) A crustal structure study of the Mississippi Embayment. In: Braile, L.W., Hinze, W.J., Sexton, J.L., Keller, G.R., Lidiak, E.G. (Eds.) An integrated geophysical and geological study of the tectonic framework of the 38th parallel lineament in the vicinity of its intersection with the extension of the New Madrid fault zone, U.S. Nuclear Regulatory Commission Rept. NUREG/CR-1014:101-133

Bhattacharyya, B.K. (1978) Computer modeling in gravity and magnetic interpretation. Geophysics 43:912-929

Cain, J.C., Hendricks, S.J., Langel, R.A., Hudson, W.V. (1967) A proposed model for the International Geomagnetic Reference Field, 1965. J. Geomagn. Geoelectr. 19:335-355

Carnahan, B., Luther, H.A., Wilkes, J.O. (1969) Applied Numerical Methods. J. Wiley and Sons, New York

Cordell, L. (1977) Regional positive gravity anomaly over the Mississippi Embayment. Geophys. Res. Lett. 4:285-287

Ervin, C.P., McGinnis, L.D. (1975) Reelfoot rift: Reactivated precursor to the Mississippi Embayment. Geol. Soc. Am. Bull. 86:1287-1295

Frese, R.R.B. von, Hinze, W.J., Braile, L.W., Luca, A.J. (1980) Spherical earth gravity and magnetic anomaly modeling by Gauss-Legendre quadrature integration. NASA Rept NAS5-25030

Hall, D.H. (1974) Long-wavelength aeromagnetic anomalies and deep crustal magnetization in Manitoba and Northwestern Ontario, Canada. Pageoph. 40:403-430

Heiskanen, W.A., Mortiz, H. (1967) Physical Geodesy. W.H. Freeman and Co., San Francisco

Ku, C.C. (1977) 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 42:610-622

Langel, R.A. (1979) Near-earth satellite magnetic field measurements: A prelude to Magsat. EOS (Trans. Am. Geophys. Union) 60:667-668

McCamy, K., Meyer, R.P. (1966) Crustal results of fixed multiple shots in the Mississippi Embayment; In: Steinhart, J.S., Smith, T.J. (Eds.) The Earth Beneath the Continents, Am. Geophys. Union Geophys. Monogr. 19:370-381

Sass, J.H., Diment, W.H., Lachenbruch, A.H., Marshall, B.V., Munroe, R.J., Moses, T.H., Jr., Urban, T.C. (1976) A new heat-flow contour map of the conterminous United States. USGS, Open-file Rept. 76-756

Shuey, R.T., Schellinger, D.K., Johnson, E.H., Alley, L.B. (1973) Aeromagnetics and the transition between the Colorado Plateau and the Basin and Range Provinces. Geology 1:107-110

Stroud, A.H., Secrest, D. (1966) Gaussian Quadrature Formulas. Prentice-Hall, New Jersey

Talwani, M., Ewing, M. (1960) Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape. Geophysics 25:203-225

Talwani, M. (1965) Computation with the help of a digital computer of magnetic anomalies caused by bodies of arbitrary shape. Geophysics 30:797-817

Warren, D.H., Healy, J.H. (1973) Structure of the crust in the conterminous United States. Tectonophysics 20:203-213

Wasilewski, P.J., Thomas, H.H., Mayhew, M.A. (1979) The Moho as a magnetic boundary, NASA Rept. NASA-GSFC TM80245

Woollard, G.P., Joesting, H.R. (1964) Bouguer gravity anomaly map of the United States. Am. Geophys. Union and U.S. Geological Survey, scale 1:2,500,000