Joint inversion of surface wave, refracted P-wave, and apparent resistivity data to retrieve porosity of saturated layers

Abstract

We present an algorithm for the joint inversion of surface wave, P-wave refraction ad apparent resistivity data. The algorithm solves the model parameters imposing the same earth structure as well as the respect of some petrophysical relationships. P- and S-wave velocities are linked to each other through the Poisson's ratio in order to avoid unrealistic values. Moreover, for layers made of saturated porous media, both seismic velocities and the soil resistivity are further constrained by using rock physics relationship and imposing a common value of porosity. The final model is thus internally consistent not only in term of geometry but also in terms of physical properties. A synthetic example is provided. Individual inversions of each set of data are compared both to a structural joint inversion, where no physical links are applied, and to the full joint inversion in which physical constraints are imposed. While the individual inversions fall in local minima far from the correct solution, the structural joint inversion supplies a very good final model that is further refined applying the physical links. Finally, since the seismic velocities and the resistivity of the saturated layer are solved imposing the convergence to the same value of porosity, this parameter represents an additional result of the joint inversion algorithm.