Truncated geoid and gravity inversion for one point-mass anomaly

The truncated geoid, defined by the truncated Stokes' integral transform, a n integral convolution of gravity anomalies with the Stokes' function on a spherical cap, is often used as a mathematical tool in geoid computations v ia Stokes' integral to overcome computational difficulties, particularly th e need to integrate over the entire boundary spheroid. The objective of thi s paper is to demonstrate that the truncated geoid does, besides having mat hematical applications, have physical interpretation, and thus may be used in gravity inversion. A very simple model of one point-mass anomaly is chos en and a method for inverting its synthetic gravity field with the use of t he truncated geoid is presented. The method of inverting the synthetic held generated by one point-mass anomaly has become fundamental for the authors ' inversion studies for sets of point-mass anomalies, which are published i n a separate paper. More general applications are currently under investiga tion. Since an inversion technique for physically meaningful mass distribut ions based on the truncated geoid has not yet been developed, this work is not related to any of the existing gravity inversion techniques. The invers ion for one point mass is based on the onset of the so-called dimple event, which occurs in the sequence of surfaces (or profiles) of the first deriva tive of the truncated geoid with respect to the truncation parameter (radiu s of the integration cap), its only free parameter. Computing the truncated geoid at various values of the truncation parameter may be understood as s patial filtering of surface gravity data, a type of weighted spherical wind owing method. Studying the change of the truncated geoid represented by its first derivative may be understood as a data enhancement method. The insta nt of the dimple onset is practically independent of the mass of the point anomaly and linearly dependent on its depth.