Assessing inversion uncertainty from initial-model variability in 3-D magnetotelluric inversion: Application to a geothermal field

Magnetotelluric (MT) inversion is widely used to image subsurface electrical resistivity structures, but three-dimensional (3-D) MT inversion is inherently non-unique, and the resulting models can depend strongly on the choice of the initial model. Despite this well-known sensitivity, systematic evaluation of initial-model-induced variability remains uncommon in practical 3-D MT studies due to the high computational cost of running multiple inversions. In this study, we propose a practical and computationally efficient framework to quantify inversion uncertainty arising specifically from differences in the initial model. The approach employs a low-dimensional parameterization based on representative points and uses Kriging interpolation to generate an ensemble of smooth, geologically plausible starting models. Each realization is inverted independently using identical inversion settings, allowing initial-model effects to be isolated under fixed regularization and data-error assumptions. The method is applied to a 3-D MT dataset from the Yuzawa geothermal field in northeastern Japan. A total of 100 inversions were performed, from which 55 well-converged realizations (final RMS ≤ 2.15) were selected for analysis. Ensemble statistics reveal that shallow conductive structures are reproduced consistently across realizations, whereas variability increases with depth and exhibits strong spatial dependence. Bootstrap resampling confirms that the depth-dependent variability patterns are statistically stable under the present ensemble size. Although the proposed framework does not account for all possible sources of inversion uncertainty, it provides an operationally realistic lower-bound estimate of model variability associated with initial-model choice. By identifying which parts of the resistivity structure are robust and which are weakly constrained, the method supports uncertainty-aware interpretation of 3-D MT inversion results and demonstrates its practical applicability through a geothermal case study.