Global Harmonic and Statistical Analysis of Gravimetry

  1. Hyman Orlin
  1. W. M. Kaula

Published Online: 18 MAR 2013

DOI: 10.1029/GM009p0058

Gravity Anomalies: Unsurveyed Areas

Gravity Anomalies: Unsurveyed Areas

How to Cite

Kaula, W. M. (1966) Global Harmonic and Statistical Analysis of Gravimetry, in Gravity Anomalies: Unsurveyed Areas (ed H. Orlin), American Geophysical Union, Washington, D.C.. doi: 10.1029/GM009p0058

Author Information

  1. Institute of Geophysics and Planetary Physics, University Of California, Los Angeles

Publication History

  1. Published Online: 18 MAR 2013
  2. Published Print: 1 JAN 1966

ISBN Information

Print ISBN: 9780875900094

Online ISBN: 9781118664018



  • Harmonics;
  • Linear auto-analysis;
  • Nonlinear auto-analysis;
  • Satellite geoid;
  • Statistical analysis of gravimetry


The most general possible linear auto-analysis (i.e., one assuming that statistical properties can be expressed by mean double products as a function of distance) of gravimetry obtains a result that agrees with the best independent test (Guier and Newton's latest satellite geoid) within 30° for the location of the eight principal extremums of the worldwide geoid. However, this geoid still gives an impression of falling short of exploiting the available data. Part of the difficulty is computational, but substantive improvement seems practicable in three directions:

  • Linear cross analysis. The topography has, of course, always been recognized as of primary importance, particularly in view of its influence on observation distribution. More recently, heat flow measurements and seismically deduced crustal thicknesses have become extensive enough to promise geophysically fruitful cross analyses with gravimetry.

  • Use of a reference model derived from satellite orbits. Satellite orbits continue to yield improved results of the low-degree tesseral harmonics. Since the long-wave variations are the part of the field for which gravimetry is statistically weakest (essentially a case of small sample size), the logical optimization would be to define the reference model for the gravity anomalies to be analyzed as a third- or fourth-degree geoid determined from satellite orbits.

  • Nonlinear auto-analysis. Part of the inadequacy of the linear analysis is that gravity anomalies obviously do not have the Gaussian distribution and randomness of relationship between phases which such analysis assumes; there is a definite tendency toward certain patterns such as circum-ocean arcs. Hence significant information would be obtained from mean triple products ("coskewness") and quadruple products ("co-excess"). Such higher-order spectrums would be more likely to be suggestive of geophysical laws of formation. Nonlinear analysis would, however, be a considerable computational problem.