Outline of a new space-domain method of forward modeling

Abstract

The present paper outlines the main aspects of a new method of forward space-domain modeling of the gravitational attraction from known sources. Compared to the methods known from the literature– the presented method has a potential to improve decisively. Complicated mass density models (reflecting the real geology) will not increase the computational task, because, unlike in the existing methods, the field point computations are not done by integrating the source attraction for each field point, but from the pre-computed and stored mass density information. This is done only once and completely independent of the field point. A very large class of functions approximating the mass density distributions and interfaces between geological layers can be used. Expressions for higher order derivatives of the gravitational potential are automatically obtained and make use of the same stored mass density information. The mathematical formulation, based on power series expansion of the reciprocal distance function, uses a setup with local Cartesian coordinates, but is able to handle the ellipsoidal Earth’s models (for positioning and for reference gravity) automatically. The quality of approximation for all derivatives of the gravitational potential is predefined and controlled. The paper outlines the mathematical structure of the method and shows clearly that ‘it can be done’. However, to be fully operational a good strategy for storing the integrated mass density information must be invented. The brute-force implementation of the method will not work because the dimensionality of the problem is too big.