Application Of Laplace Interpolation In The Analysis Of Geopotential Data

Abstract

Geophysical data is often collected at irregular intervals along a profile or over a surface area. But most methods for the treatment of geophysical data often require that any data collected at irregular intervals have to be interpolated to obtain values at regular grid. Unlike the common 2-dimensional interpolation procedures, the Laplace (finite-difference) method can be applied to regions of high data gradients without distortions and smoothing. However, by itself, this method is not convenient for the interpolation of geophysical data, which often consists of regions of widely variable data densities. In this paper a procedure is developed which allows that by combining it with the method of quadratic weighting, the Laplace method can be successfully applied to interpolate two-dimensional geophysical data. These methods were applied to some geopotential data. The results show that there is no significant difference between aeromagnetic maps derived from data as observed and maps obtained when the data is interpolated in a region of thick sedimentary formation. This is attributed to the fact that the magnetic body in such region are deeply buried. However, interpolated aeromagnetic map over a region of outcropping granitic bodies exposes more shallow features which are otherwise not seen on the map derived from the observed data that are not interpolated. Similar observation was recorded for a gravity anomaly map produced from data collected in basement terrain. It was concluded that since it is impossible to observe every point in a given surface area in order to produce an accurate map that will reflect the distribution of the various shallow subsurface anomalies, it is better to interpolate the observed data prior to the production of the desired geopotential map.

Keywords: Geophysical, Geopotential, Lapalce interpretation, finite difference, quadratic, weighting.

Nigerian Journal of Physics Vol. 19 (1) 2007: pp. 129-138