Comparison of two data-driven approaches enabling the probabilistic integration of geophysical tomograms and hydrologic logging data for the prediction of spatially continuous hydrologic parameter distributions fully accounting for tomographic ambiguity and scale differences

Abstract:

Probabilistic prediction of 2D or 3D images of hydrologic parameters measured in boreholes can contribute to solve hydrological exploration tasks. Geophysical tomograms can guide the interpolation between boreholes albeit uncertainty about the relations between geophysically imaged and measured hydrologic parameters exists. Data-driven approaches learning optimal relations between the considered tomographic and borehole data appear appealing integration and prediction approaches due to their high flexibility. Recently, Asadi et al., (2016)^a and Paasche et al., (accepted)^b presented powerful probabilistic integration approaches building on artificial neural networks (ANN) and fuzzy sets (FS), respectively. Geophysical Radar, P-wave and S-wave tomographic data sets have been inverted searching the solution space of the inverse problems globally. This resulted in ensembles of radar-, P- and S-wave velocity tomograms whose members fit the underlying data sets equally well. These tomogram ensembles discretely illustrate tomographic reconstruction ambiguity and are considered learning optimal petrophysical prediction models to infer hydrological parameters where no borehole logging data have been measured. Scale differences between tomogram discretization and logging data sample interval are fully considered. Both approaches result in highly similar predictions when ignoring logging data errors and tomographic imaging errors, which results in overfitted prediction models learned. However, results start to differ if overfitting the prediction models shall be avoided. Both approaches follow Gaussian error theory but in two different considerations. While the FS approach uses least-squares averaging principles, the ANN-based approach considers accumulated relative errors in a weighted rms-error objective function when learning the prediction models. Both approaches result generally in similar effects, e.g., reduced prediction ranges. However, differences between both approaches increase when striving to avoid overfitting leaving doubts on the general suitability of error handling based on Gaussian assumptions.

^a: Environmental Earth Sciences, 75, 1487.

^b: Geophysics.