Determining bed boundaries from inversion of EM logging data using general measures of model structure and data misfit

In this paper we propose a new method to locate bed boundaries by carrying out a 1-D nonlinear inversion of electromagnetic (EM) logging data. We first solve for 1-D resistivity structure in which the earth is modeled using layers of constant thickness. This thickness is determined based upon the tool resolution and the desired resolution from the user. We use general measures of data misfit and model structure in the inversion to construct piecewise-constant models through the iteratively reweighted least-squares (IRLS) procedure, and we minimize a generic global model objective function subject to data constraints. The general measure includes the traditional l (sub p) norm as a special case. The recovered piecewise-constant models simulate traditional models comprised of a few uniform layers and hence permit easy determination of bed boundaries. The generic model objective function allows the incorporation of prior geological information and provides measures of the closeness to the reference model and the amount of structure in the recovered model. We develop an efficient scheme to incorporate the IRLS procedure into the search for the appropriate regularization parameter at each iteration. The iterations required by the IRLS algorithm are combined with those for the linearized, iterative inversion procedure. The applicability of the algorithm is demonstrated using synthetic and field data examples.