TWO SIMPLE METHODS IN GEO-RECONNAISSANCE: THE VOTER-VETO-CONFIDENCE METHOD AND THE BACK-PROPAGATION OF ADVECTED GEOCHEMICAL SIGNALS

This talk will be an informal progress report on two simple techniques that we developed and continue to work on for our DoE-funded geothermal project, which began with reconnaissance and is expected to lead to drilling. They aren’t especially precise, but they can be applied in situations ranging from zero training data to copious training data, and their speed makes it possible to rapidly analyze very large areas—in other words, reconnaissance as distinct from exploration. Math warning: there will be equations, but a minimum of statistical jargon.

 The voter-veto-confidence method is a way to combine different types of spatial data to estimate a spatially varying presence-absence probability (or probability function if there are multiple possibilities) based on a combination of expert elicitation and statistics. It also estimates our spatially-varying confidence in that probability estimate. Absent any training data, some degree of expert elicitation is always needed, but the degree is reduced as the volume of data increases. Types of expert information include weighting, thresholding, and censoring. Extracting such information from experts is a field in itself, as even experts are more accurate when thinking in terms of natural frequencies rather than probabilities.

Imagine a well with a solute or contaminant anomaly—in what upstream area did it originate? If computation time were not a constraint we would simulate sources on a grid of possible locations and run the forward model for each possible location (and reasonable flow field) to get a numerical Green’s function. Unfortunately such a computation is seldom feasible in reconnaissance. Instead we use Claerbout’s principle: the transpose of a linear operator is a low-resolution, un-scaled approximation to the inverse of that operator. Using a reasonable flow field, we generate approximate stream and time functions then use those to propagate a homogeneous-flow Green’s function backward up the inhomogeneous flow field. It’s crude, but very fast, and appears to depend only weakly on the coordinate origin used to generate the approximate stream and time functions.