Direct Transform of TDEM Data into 1D Resistivity Models Via Cumulative Conductance Mapping

Inverting Time-Domain Electromagnetic (TDEM) data is a problem where the solution is inherently non-unique. We present a fully data-driven method that directly transforms 1D TDEM data into layered resistivity models through cumulative conductance mapping. Our method defines a cumulative conductance model, based on the concepts of longitudinal conductance and diffusion time, that integrates the influence of overlying layers into the subsurface model, and we utilize the S-transformation to convert the TDEM data into a conductance vs time representation. We then establish a mapping function Ξ between the cumulative conductance model and the data to transform the TDEM data into a cumulative conductance model. We recover a 1D resistivity model by applying a numerical derivative to the transformed data. To estimate the mapping function for data where the model is unknown, we trained a neural network to directly transform the data into a 1D cumulative conductance model, which is differentiated to recover its corresponding resistivity model. Validated on synthetic TDEM data, our results demonstrate that our method accurately retrieves high-resolution resistivity models while preserving the physical sensitivity of the data without the need of a priori information, introducing a new perspective for tackling the 1D TDEM inversion problem.