Mathematics – Probability
Scientific paper
Oct 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991mgeo...16..313j&link_type=abstract
Manuscr. Geod., Vol. 16, No. 5, p. 313 - 325
Mathematics
Probability
Scientific paper
A common interpretation of the Earth's residual gravity field is that of a stationary, stochastic process. With only one realization of the process at hand, ergodicity is invoked to perform spectral and covariance analyses, as well as statistical prediction and estimation. To conduct statistical hypothesis testing, however, the probability distribution function of the residual gravity field may need to be known. The underlying probability law of a stationary, ergodic gravity field can be Gaussian (normal) on the infinite plane, but not on the sphere. In fact, it is argued that for the local gravity field to be a Gaussian process, it must be interpreted as a subset of a process strictly on the plane (not on the sphere in planar approximation). With this interpretation, tests may be applied to determine whether a given local gravity field is normally distributed. One particular test is applicable to the residual anomaly field after a long-wavelength reference field has been removed. Applied to a section of the residual North Carolina gravity field, the test suggests that it is normally distributed.
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