Formulation of the Mathematical Frame of the Joint Gravimetric-Seismic Modelling Problem Based on Analysis of Regionally Distributed Borehole Data

Abstract

Parametrization is very important in geophysical modelling. Its role is to describe mathematically the possible sources of the measured geophysical signal. Inadequate choice of parametrization lead to incorrect models of the subsurface. The content of this paper is to formulate a general parametrization, a mathematical frame, for the joint gravimetric-seismic modelling problem. The goal is to make it flexible, so that the most important aspects of the true distribution of the fundamental physical quantities (mass density, seismic velocity) are adequately described. The choice of parametrization described here evolved from the results of a detailed joint analysis of regionally distributed borehole data (density logs and sonic logs) in the Danish North Sea area. With respect to the joint gravimetric-seismic modelling, the log analysis revealed the complexity of the true joint distribution of the physical quantities.

The proposed general parametrization represents physical quantities on a number of grids associated with fixed thin and disjoint horizontal layers covering all depths from the surface to the base of the model. The parameters governing the resolution of the model are: the layer thicknesses (possibly different thicknesses in different depths) and the grid spacing. Furthermore, each grid (associated with a horizontal layer) is decomposed into a number of grids associated with the cross-section of the thin horizontal layer with a specific geological unit. In this paper a number of advantages of the proposed parametrization, both theoretical and practical, are discussed.