Maximum Entropy Inversion of Induction-Log Data

Abstract

Summary This paper describes the development and application of some new algorithms based on the maximum entropy method (MEM) for inverting (i.e., deconvolving) induction-log data. The MEM has earned a reputation in many physical science fields as a technique that provides robust and accurate reconstructions of instrumentally blurred data. Dyos recently applied a MEM algorithm to the inversion of synthetic deep-induction-log data. This paper develops some new MEM algorithms that are applied to inversion of model data and to field data from the PhasorSM induction tool. The new algorithms overcome some of the limitations of previous inversion methods and inverse-deconvolution-filter techniques. This paper examines two different MEM algorithms. The first algorithm is based on a functional used to study MEM inversions of synthetic data with a Doll approximation forward model. A second, more efficient MEM algorithm, based on a new Lagrangian functional, is used with an exact forward model to study the inversion of a field log and some model formations. Use of an exact forward model is essential in obtaining accurate and high-resolution MEM inversions in the presence of skin and shoulder effects. The MEM inversions of model data and field logs exhibit vertical resolution, accuracy, and stability that exceed those obtainable with state-of-the-art linear inverse filters. An example of the MEM inversion of a field log in a formation with numerous high-contrast thin beds is discussed and compared with the spherically focused log (SFLSM) and the deep enhanced-resolution Phasor- (IDERSM-) processed log. The MEM inversion exhibits resolution comparable to that of the SFL. It is shown that, as a byproduct, the MEM provides synthetic logs that serve as a self-consistency check on both the quality of entered data and the validity of the Rt profile obtained from inversion.