Theory and Practice of Geophysical Data Inversion Proceedings of the 8 th International Mathematical Geophysics Seminar on Model Optimization in Exploration Geophysics 1990

Formulas described in this paper were designed for the use in least-squares tomographic inversion methods with improved flexibility of parametrizing the density-velocity model. The gravity effect of the considered volume fl is the sum of gravity effects of 2-3 or 2 1/2-D bodies of polygonal cross-sections which form the disjunctive decomposition of fi. For this geometrical arrangement analytical and numerical ray tracing algorithms were developed assuming either linear or parabolic dependence of quadratic slowness (square of reciprocal wave speed) in Cartesian coordinates. Partial derivatives of calculated gravity and traveltime with respect to geometrical parameters, which are necessary for the control of the first derivative inverse algorithms, are given in an explicit form. Two expressions for the traveltime derivative with respect to vertex coordinates were obtained : one for the straight rays based on Fermat's principle and the other based on the geometrical approximation not affected by the curvature of the ray. Results of the numerical experiment based on the formulas are presented.