Geophysical Prospecting: Constrained polynomial fitting for recovery of regional gravityIsolation of a regional field from a Bouguer map has always been an ambiguous and troublesome problem. It is often argued that the ambiguity arises from lack of specific criteria under which the problem may be formulated. In this paper, I show that by adopting Skeels’ definition of the regional field and its corollary, criteria needed to extract the field with minimum ambiguity may be developed. The definition and its corollary allow formulation of the regional field separation problem as a weighted (robustified) and constrained least‐square fitting problem with constraints extracted directly from the Bouguer map. To emphasize the constraints, I formulate the problem from the perspective of prior information constrained by observational data. The new formalism offers several advantages: weighted fitting is more robust than ordinary least squares fitting, providing a simple mechanism to eliminate data outliers and reduce the undesirable influence of local gravity disturbances. Introducing constraints into the fitting procedure effectively reduces ambiguity and increases the resolution of the fitted regional field. Moreover, imposing conditions on the fitted regional field directly from the Bouguer map is tantamount to incorporating prior information about the underlying geology and structure of the area with minimum human subjectivity. The procedure was tested on simulated and actual data sets with excellent results. Indeed the test results indicate that with properly placed constraints, the regional field may be recovered in a manner that closely emulates the graphical method.
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