Statistical confidence interval inference for subsurface electrical resistivity structure from magnetotelluric impedances and geomagnetic transfer functions, assisted by forward modeling

This paper proposes a scheme for the statistical confidence interval inference of a subsurface electrical resistivity model in magnetotellurics and geomagnetic depth soundings. The method assesses the confidence interval of resistivity for a target block in optimal model obtained through inversion. The target block consists of a number of model elements and is confined by an operator. By varying the target block’s resistivity and performing forward modeling, the scheme evaluated the change in data misfit of magnetotelluric impedances and geomagnetic transfer functions, then applies the paired t -test rather than the F -test to estimate the confidence interval. The statistical distribution of the raw data misfits (z misfits) of magnetotelluric impedances and geomagnetic transfer functions does not follow a normal distribution. Thus, we should not use the F -test that assesses the significant changes in χ 2 misfit, but the paired t -test to assess significant changes in the mean z misfit. When applying the paired t -test, the significant changes in the mean z misfit may include cases with improved misfit. These cases must be excluded from the significant change when applying the method to real data. Overly wide confidence intervals indicate insufficient dataset resolution for the target block size, whereas a vanishing confidence interval implies that the block size is excessively large relative to the dataset resolution. Examining various target block sizes thus allows the confidence interval to reveal the intrinsic dataset resolution scale. If the F -test is used, the confidence interval tends to be overestimated.