Induction Log Vertical Resolution Improvement in Vertical and Deviated Wells Using a Practical Deconvolution Filter
Authors: Woodhouse Richard , Greet David N. , Mohundro C. Ray 
Published: December 2007

Summary
Induction tool measurements can be affected as far as 30 ft from high-conductivity beds and the effect can be greater in deviated wells. A doconvolution filter was designed to improve the vertical response in both vertical and deviated wells. The filter described was tested on synthetic induction logs derived from formations of known resistivity. Several examples of deconvolved induction field logs are provided. The filter should not be used in areas where the general level of formation resistivities is less than about 3 ?·m; skin effects significantly alter the tool response in these areas.

Introduction
Thin-bed effects on the induction log have been well documented by the logging service companies, and correction charts1 have been available for many years. Examples are shown in Fig. 1. The charts are better suited to manual interpretation than foot-by-foot digital interpretation.
The deep induction log has been used as the main resistivity device in Prudhoe Bay field on the North Slope of Alaska. This choice was made because very fresh muds were used and because modern laterologs were not available at the start of field development. Invasion is considered shallow because, in very thick beds, it has been observed that the deep induction log (ILD), LLD, LLS, LL8, and SFL tools all show similar readings. Formation resistivities of 1000 ?·m or more exist in parts of the field and have been confirmed by occasional deep laterologs. Resistivity ratios at bed boundaries of greater than 100:1 can occur and induction log resistivity anomalies are still present as far as 30 ft [9 m] from these bed boundaries (Fig. 2). These conditions obviously are not ideal or even recommended for the running of induction logs, yet the magnititude of the resistivities recorded in thick beds are of generally acceptable accuracy.
The objective of this work was to find a mechanism for applying thin-bed corrections to digitized induction logs. The corrections were recquired to betechnically justified,applicable to continuous digital data, andapplicable at Prudhoe Bay conditions (e.g., hole deviation, formation resistivity range).
A deconvolution-type filter was appropriate for these practical requirements. An introduction to deconvolution processing is given in the Appendix.

Review of the Induction Log Response
Several authors have discussed the induction log radial and vertical response characteristics following the pioneering work of Doll.2 Doll used the geometrical factor concept without skin effect correction to develop departure curves for beds of finite thickness.
The influence of skin effect at bed boundaries was shown by Duesterhoeft et al.3,4 and Moran and Kunz.5 Inclusion of skin effect improves the vertical resolution of the coil array compared with the simpler Doll theory.
In more recent years, radial response has been studied by Woodhouse et al.6,7 Radial and vertical responses have been studied by Gianzero and Anderson,8 Thadani et al.,9,10 and Anderson and Chang,11 who showed that absolute conductivity values and bed thickness both affect the vertical response characteristics. Modern chart hooks indicate the complexity of the vertical response by the need for multiple charts to correct for thin beds (Fig. 1).
Except for Howell and Fisher,12 little attention has been given to the analysis of the dipping beds and deviated hole problem. The substantial radial depth of investigation of the tool means that deviated holes or dipping beds influence induction log measurements more than the comparable horizontal bed and vertical hole case.