The downward continuation to the Earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies

Details The downward continuation to the Earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies The downward continuation to the Earth's surface of truncated spherical and ellipsoidal harmonic series of the gravity and height anomalies

Dec 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981dces.rept.....j&link_type=abstract

Unknown

Computer Science

Numerical Analysis

1

Earth (Planet), Earth Gravitation, Geopotential Height, Gravitational Fields, Gravity Anomalies, Spherical Harmonics, Approximation, Ellipsoids, Numerical Analysis, Topography

Scientific paper

The problem of divergence of the geopotential spherical harmonic series at the Earth's surface is investigated from a numerical, rather than a theoretical approach. It is shown that previous numerical evaluations, based on the expansion of the potential generated by the masses between the point of computation and the bounding sphere, are inconclusive with respect to the magnitude of the downward continuation error that is attributable to series divergence. A more representative model of the Earth's potential is devised on the basis of a density layer, which, in the spherical approximation, generates a gravity field whose harmonic constituents decay according to an accepted degree variance model. This field, expanded to degree 300, and a topographic surface specified to a corresponding resolution of 67 km are used to compute the differences between truncated inner and outer series of the gravity and height anomalies at the surface of the Earth model. Up to degree 300, these differences attain RMS values from 0.33 microgal to 86 microgal for the gravity anomaly and from 0.32 micrometer to 410 micrometer for the height anomaly, in areas ranging respectively from near the equator to the vicinity of the pole. In addition to these values, there is an expected truncation effect, caused by the neglect of higher degree components of the inner series, of about 30 mgal and 36 cm, respectively.

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