Generalised Series Expansion (GSE) used in DC geoelectric–seismic joint inversion

Abstract

Horizontally layered (1D) earth models are often assumed as a model estimate for the interpretation of geophysical data measured along 2D geological structures. In this process, the individual data sets are usually inverted independently, and it is considered only in a later phase of interpretation that these local (1D) models have common characteristic features. Taking account of these common attributes, instead of the successive independent interpretations, the lateral variations of geometrical and petrophysical parameters can be efficiently determined for the whole 2D structure by applying a series expansion. Using global basis functions, two advantages can be achieved: (i) choosing an appropriate number of basis functions helps us to restrict the complexity of the model; (ii) the integration of all the data sets measured along the profile gives rise to the application of simultaneous or joint inversion methods. This results in a decrease of the number of independent unknowns, a higher stability during the inversion and a more accurate and reliable parameter estimation. In this paper, a joint inversion algorithm is presented using DC geoelectric apparent resistivities and refraction seismic travel times measured along various layouts above a 2D geological model. To describe lateral variations series, expansions are used, and furthermore, to improve the often used approximation of a (locally) 1D forward modelling, the integral mean value of the horizontally changing model parameters (calculated along an appropriately defined interval) is introduced. We call the inversion procedure that combines series expansions and the concept of integral mean Generalised Series Expansion (GSE) inversion. The method was developed and tested for both the simultaneous (integrating data sets of one method or methods on the same physical basis) and the joint inversion (where data sets of methods on different physical bases are joined together), using synthetic and field data sets. It is also demonstrated that the equivalence problem inherent in the independent inversion of DC geoelectric data can efficiently be resolved by the use of the joint GSE inversion method in the cases of conductive and resistive equivalent geological models.