A probabilistic approach to establishing the resistivity-lithology relationship using co-located tTEM data and lithological logs

Geophysical surveying with electrical and electromagnetic data is commonly used for e.g. groundwater assessment and resource exploration. These methods measure subsurface resistivity, whereas the primary end-user interest is in subsurface properties like lithology. Inferring lithological information from resistivity data is, thus, a fundamental challenge in geological modeling that requires a quantitative resistivity-lithology relationship. Often, local resistivity log data is lacking, and this relationship is therefore reliant on subjective manual interpretation, based on experience from similar geological settings. This study presents a novel probabilistic methodology for establishing a quantitative, site-specific resistivity-lithology relationship based on co-located towed transient electromagnetic (tTEM) data and lithological logs. The probabilistic approach inverts co-located tTEM soundings using uninformative priors to generate posterior samples of 1D resistivity models that are consistent with the observed data. These models are then combined with co-located lithological descriptions from boreholes to establish a probabilistic resistivity-lithology relation. The method incorporates a weighting function that accounts for uncertain layer boundaries and the resolution limitations of the tTEM method. The distributions are modeled using Kernel Density Estimation to establish the final probabilistic relationship. It is exemplified, how this relationship can be used to generate a joint prior of lithology and resistivity models across an entire survey area, enabling the generation of probabilistic lithology maps with quantified uncertainty. The methodology is first validated using two synthetic test cases and subsequently applied to field data from two survey areas in Denmark. The results demonstrate that well-defined relationships can be established when high-quality, co-located data are available.