A NEW JOINT INVERSION APPROACH APPLIED TO THE COMBINED TOMOGRAPHY OF DC RESISTIVITY AND SEISMIC REFRACTION DATA

Abstract

We present a new joint inversion approach that allows for a combined inversion of independent physical parameters by exchanging structural information. The technique is based on the ideas of robust modeling. Occurring gradients of one parameter facilitate the development of gradients in the other but does not enforce this. In the presence of boundaries that can be seen by both methods it leads to sharp contrasted models. Finally, a combined image of the subsurface is obtained by cluster analysis. The technique is applied to the inversion of dc resistivity and seismic refraction data. Two synthetic data sets show how different boundary types are resolved with and without structural coupling. It is demonstrated how the quality of the inversion results is improved by the new approach. Introduction The joint interpretation of different measurement types is a basic principle to confine the ambiguity of the inverse problems in geophysics. In the existing approaches one inverts for one parameter using an augmented data vector (Vozoff and Jupp, 1975). This is only possible if all measurements depend on the same parameter or if the parameters are interconnected by some petrophysical relationship. However, often such a relationship does not exist, as for electrical conductivity and seismic velocity. Nevertheless, we expect at least similar structures in the resulting models. Therefore we like to combine the otherwise independent inversions to allow for structural similarities. The challenge is to facilitate similar structures without enforcing it. Gallardo and Meju (2004) presented an algorithm where a combined data functional based on the cross-gradients of both models is minimized. However, one problem is the weighting of the individual data and model updates for different data numbers and convergence properties. Here we present an approach where two inversion runs are carried out separately. The combination of both models is accomplished by mutually controlled structural weights based on the principles of robust modeling. First we describe the minimization problem and the regularization procedure. Thereafter we introduce robust modeling and depict how structural information may be interchanged. We apply this technique to the dc resistivity and seismic refraction data on unstructured meshes. Two synthetic models using different model boundaries shows how the joint inversion improves the model concept. Inversion Minimization procedure Assume D data points di subsumed in a data vector d = (d1, . . . , dD). The parameter distribution p(~r) is discretized byM basis functions ψj and their coefficientsmj ,