A novel rapid inversion method has proved to be one of the fastest methods designed for accurate, multi-dimensional interpretation of array resistivity logs. In this paper, we discuss the development of this method as a basis for future well-site anisotropy interpretation, using data recorded with the 3D ExplorerSM multi-component induction instrument (3DEXSM).
The new method demonstrates the feasibility for a substantial reduction of computing time by partitioning the two-dimensional (2-D) inverse problem into a sequence of smaller one-dimensional (1-D) problems (radial inversion). It rapidly converges to a true earth model. In the case of a vertical well (2-D), the method requires multiple 1-D, yet only a few 2-D forward model calculations. To achieve this substantial extra increase in computing speed, 1-D forward responses are pre-calculated and stored as look-up tables to be consulted at inversion time. The computations required for a full 2-D interpretation process is thus reduced to a set of four to five 2-D forward response calculations at a limited number of observation points. As a result, the proposed method allows the entire spectrum of measurements to be combined as a part of an interpretation scheme suitable for well-site processing. The method is capable of providing a consistent and accurate picture of formation resistivity anisotropy.
The potential for the technique is presented and illustrated by anisotropy interpretation results from 3DEX data acquired in a vertical well in the Gulf of Mexico. These results are shown to be in excellent agreement with what is inferable directly from the raw 3DEX logs. They are also in good agreement with results from an independently performed anisotropy interpretation based on a rigorous 2-D inversion technique.
A field example confirms the capability of the proposed technique to deliver comparable quality results now achievable with standard log analysis center processing in run times comparable to run times for other familiar well-site deliverables.
Introduction
The recently introduced multi-component induction logging technology, 3D ExplorerSM (3DEXSM), allows the log analyst to obtain a comprehensive picture of the formation resistivity distribution around the borehole, including formation anisotropy. The 3DEX tool yields five magnetic field components acquired at ten distinct frequencies.1 Due to near-borehole and shoulder-bed effects, such measurements produce merely apparent resistivities. Consequently, they must be further interpreted to yield the required true horizontal and vertical formation resistivities. This paper describes an inversion process that has been developed for this purpose.
The inversion of multi-component induction logging data can be described in terms of a process to map a data space into a formation parameter space. The inversion process thus furnishes a distribution of horizontal and vertical resistivities surrounding the borehole, whose synthetic tool responses match the observed data within a given range of uncertainty. The use of inverted 3DEX data in petrophysical interpretation results in a more accurate reservoir description, as well as in a much improved hydrocarbon saturation determination.
By now, the industry has developed numerous fast resistivity logging data interpretation techniques. These are mainly based on either an approximate solution to an inverse problem,2 or on focusing concepts.3 The results of the application of a very fast, so-called ‘turbo boost’ method4 to multi-component induction data have not yet been published.
