# Claude Shannon versus Gus Archie: Information Theory as a Guide to Log Evaluation without Petrophysics

## Abstract

Around 1950 Gus Archie, working at Shell Oil, changed petroleum exploration by developing a theoretical foundation for e-log interpretation based on certain electrical properties of rocks. From this discipline of petrophysics, Archie's Equation is universally used and needs no introduction. At about the same time Claude Shannon, working at Bell Labs, changed communication by developing a mathematical structure for messaging. Oversimplifying the explanation here, information theory uses the received signal to assess if data have changed the probability that some predictable outcome is valid. Verification of the expected outcome is redundant and provides no new information. New data add information only if they change the weight of evidence to suggest that an unexpected event (a surprise) has occurred. For information theory, the message itself is understood only to be a choice between possible alternatives; the actual meaning of the message is not relevant. This paper proposes that the principles of information theory provide a suitable framework for a “theory-less” evaluation of triple-combo log data by identifying unexpected or anomalous pairings in key log parameters. Further, geologic interpretations derived from these anomalies generate significant results for exploration in shale resource plays. Examples of key cross-plot pairs (independent variable -v- dependent variable) from log data will be shown: (1) shale (clay) volume -v- average neutron-density porosity and (2) average neutron-density porosity (log scale) -v- resistivity (log scale). Where the dependent variable is predictable from the independent variable (typically a linear trend), redundancy dominates and no significant information is present. In contrast, an anomalous positive deviation of the dependent variable from the predictable baseline trend signals “surprising” information and the probability is quantifiable based on the amount of deviation. From these plots we can make geologic interpretations concerning (1) effective porosity in the shales and (2) hydrocarbon charge. In this way the meaning of the message is separated from the probability that it is valid. Pay zones can be identified on the logs and mapped based on the coincidence of a high probability for effective porosity and hydrocarbon saturation.

AAPG Datapages/Search and Discovery Article #90193 © 2014 Rocky Mountain Section AAPG Annual Meeting, Denver, Colorado, July 20-22, 2014