Depth of investigation for multi-parameters inversions

We have developed a new robust concept for the calculation of the depth of investigation (DOI) for inversion problems described by several intrinsic parameters, like the spectral inversion of time-domain induced polarization data or the inversion of full-decay Nuclear Magnetic Resonance soundings. A calculation of the DOI is crucial for interpreting the geophysical models, as the validity of the model varies considerably with data noise and parameter distribution. Without the DOI estimate, it is difficult to judge when the information in the model is data-driven or is strongly dependent on the constraints and/or on the starting value. The proposed method is based on an approximated covariance analysis applied to the model output from the inversion while considering the data standard deviations. Furthermore, the crosscorrelations between intrinsic parameters are taken into account in the computations, which is crucial when strong cross-correlations are expected. The new DOI estimate is described in detail and compared to the full covariance analysis on the model parameters using 2D spectral inversion of time-domain induced polarization data as an example. The DOI presented here behaves as anticipated on a synthetic model and is suggested as a general approach for model-spaces with more than one physical parameter.