Experimental Design Applied to Borehole DC Resistivity

Abstract

This article explores various aspects of geophysical experimental design (ED) applied to single-borehole DC resistivity. For resistivity problems, an experiment or survey is defined as the set of electrode configurations used to collect a data-set. The systematic design of such surveys, whose purpose is to optimally query a target, is termed experimental design. The borehole problem is cast in cylindrical coordinates, and because only one borehole is modeled, resistivity is treated as azimuthally invariant, permitting the problem to be treated as a form of electrical resistivity tomography. The nature of the experimental design space is thoroughly explored, culminating in several novel insights into electrical resistivity tomography problems that are useful for ED. Multiple ED functions are proposed, whose distinguishing characteristic is that they can be executed serially, rather than en masse. That is, these functions are such that experiments can be designed one observation at a time, instead of the traditional approach, in which the entire experiment is designed at once. Because traditional ED approaches are fundamentally combinatoric, the size of the experimental search space is greatly reduced by our method, expediting the optimization algorithms and making experimental design a practical possibility. Several basic design strategies are explored and compared with random and standardized surveys to quantify the effectiveness of these techniques. Lastly, adaptive experimental design procedures are examined, wherein surveys are specifically adapted to a heterogeneous target. The results of this work show that ED produces real improvements in data quality, as compared with standardized and random surveys.