Minimization of self-potential survey mis-ties acquired with multiple reference locations

Abstract

Self-potential (SP) surveys often involve many interconnected lines of data along available roads or trails, with the ultimate goal of producing a unique map of electric potentials at each station relative to a single reference point. Multiple survey lines can be tied together by collecting data along intersecting transects and enforcing Kirchhoff's voltage law, which requires that the total potential drop around any closed loop equals zero. In practice, however, there is often a nonzero loop-closure error caused by noisy data; traditional SP processing methods redistribute this error evenly over the measurements that form each loop. The task of distributing errors and tying lines together becomes nontrivial when many lines of data form multiple interconnected loops because the loop-closure errors are not independent, and a unique potential field cannot be determined by processing lines sequentially. We present a survey-consistent processing method that produces a unique potential field by minimizing the loop-closure errors over all lines of data simultaneously. When there are no interconnected survey loops, the method is equivalent to traditional processing schemes. The task of computing the potential field is posed as a linear inverse problem, which easily incorporates prior information about measurement errors and model constraints. We investigate the use of both l2 and l1 measures of data misfit, the latter requiring an iterative-solution method with increased computational cost. The l1 method produces more reliable results when outliers are present in the data, and is similar to the l2 result when only Gaussian noise is present. Two synthetic examples are used to illustrate this methodology, which is subsequently applied to a field data set collected as part of a geothermal exploration campaign in Nevis, West Indies.