Rapid Well-Site 2-D Inversion of Full-Spectrum Array Induction Data
Authors: Frenkel M. , Beard D. , Mezzatesta A.G. , Strack K.-M. 
Published: December 2007

Abstract
There has been a distinct trend during the past 10 years toward developing new multisensor-type acquisition systems in well logging. In contrast to conventional logging tools, the high-definition induction log developed by Western Atlas Logging Services provides multiple measurements with different vertical resolution and depth of investigation. It combines several subarrays, each one associated with a specific spacing between a transmitter and receiver that works at multiple frequencies covering a wide dynamic range. Data from the array induction instrument allow the log analyst to obtain, more than ever before, a comprehensive picture of the resistivity distribution around the borehole. At the same time, more emphasis is placed on the data interpretation.
Two-dimensional (2-D) inversion techniques represent an excellent way to interpret array induction data. These techniques allow for accurately and simultaneously considering both the 2-D distribution of formation resistivity and the full spectrum of array data in a single, unified interpretation scheme. Results of inversion represent a single earth model consistent with the entire set of array induction data. However, 2-D inversion schemes require a significant computational time, and, in the case of full-spectrum inversion of array induction data, they become impractical. The rapid 2-D inversion method drastically reduces the computer time requirements and provides a rapid convergence to a valid 2-D earth model.
A modification of the rapid 2-D inversion method further reduces computer time requirements by use of precalculated sensor responses and allows for interpreting the full-spectrum array data to deliver results at the well site. Results from a number of synthetic examples are presented that show the proposed technique's ability to recover formation parameters in multilayer environments. Results from inversion of field data using the new approach show improved estimates of formation resistivities.

Introduction
Resistivity measurements play a fundamental role in the evaluation of movable and residual hydrocarbons. In the last decade, a distinct trend toward developing new multisensor-types acquisition systems in well logging has occurred. The high-definition induction logging system, recently introduced by Western Atlas Logging Services, has seven coil arrays with spacings varying from 6 to 94 in., each making simultaneous measurements at eight different frequencies covering the range from 10 to 150 kHz. The combination of spacings and frequencies provides a complete set of measurements that make them suitable for inversion techniques.
Inversion of resistivity logging data can be described as a process used to map the data space into the formation parameter space. As such, the inversion process provides the distribution of resistivities around the borehole for which synthetic tool responses match the observed data within their range of uncertainty. Two-dimensional inversion techniques represent an excellent way to interpret the high-definition induction logging measurements since they allow for accurately and simultaneously considering the effects of borehole, invasion, and shoulders. However, conventional inversion schemes require multiple solutions of the forward problem. The computer resources necessary to solve the inverse problem grow rapidly with dimensionality, size of the earth model, and the number of data points. The rapid 2-D inversion method provides an efficient computational scheme for interpreting borehole resistivity data.
Although the multifrequency array induction logging device provides a number of high-resolution measurements, they represent apparent resistivities, and consequently, they need to be interpreted to extract the true formation resistivities. An inversion process has been selected for that purpose.
P. 111