Abstract

The layered earth model is a fundamental interpretation aid for direct current resistivity data. This paper presents a solution for the layered earth problem for a buried current source and a buried receiver. The model is developed for source and receiver electrodes buried anywhere within a horizontally stratified layered earth containing an arbitrary number of resistivity layers.Model results for the normal well-logging array indicate that large departures between true and apparent resistivity can be caused by thin beds or highly resistant layers. A true resistivity distribution from well logs can be established by modeling when the effects from borehole rugosity and fluid resistivity are negligible.The equations derived for resistivity well logs can be used to interpret hole-to-hole, hole-to-surface, and conventional surface array data. A field example demonstrates that deviations between hole-to-hole field data and model results, based on well logs in the receiver hole, can be accounted for by combining the resistivity logging models in the receiver holes with information from geologic logs. Differences between the field data and the layered-model results are attributed to lateral changes between or near the source and receiver holes.

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