Geostatistical Reconstruction of Gaps in Near‐Surface Electrical Resistivity Data

Abstract

This study was motivated by the need to reduce the effects of various types of noise observed in geophysical field data. We focused on assessing the impact of noise and data gaps on electrical resistivity data and on evaluating whether geostatistical methods (in this case kriging) can be successfully used for restoring missing data before inversion. We used electrical resistivity forward and inverse modeling with a simple fault earth model to produce and invert synthetic datasets. We examined the effects of random background noise, data density deletion, and data gap and noise structure scenarios to study the influence of these factors on the inversion of resistivity data and the subsequent interpretability of the geologic structure. Our results suggest that geostatistical methods are potentially very useful for restoring data points deleted from noisy resistivity field data. Clearly, the efficacy of kriging depends on the level of noise and the amount of data deleted. The inversion RMSE of the kriged files is less than that of the original random background noise files containing all data. The magnitude of the improvement increases as random background noise increases. Even for cases where 80% of the original data were randomly eliminated and there was 10% random background noise, the kriging procedure resulted in significant improvement in the ability to resolve the basement and overburden structure, correctly place the orientation and location of the fault, and identify the downthrown block. At random background noise levels of 20 and 30%, kriging was effective at recovering the major geological features but to a lesser degree. The efficacy of the kriging procedure performed on the noisiest data appears to be a function of the location and magnitude of data gaps induced by editing or missing strings. Finally, the effect that coherent noise has on the efficacy of our approach was studied and contrasted to random deletion. Our study suggested that the geostatistical restoration approach improved the interpretability of electrical resistivity data that had been degraded by noise or data loss problems.