3D geostatistical inversion of induced polarization data and its application to coal seam fires

Abstract : We applied the principal component geostatistical approach (PCGA) to the inversion of time-domain induced polarization data in terms of resistivity and chargeability distributions. The PCGA presents two major advantages over standard methods: (1) It avoids the storage of the usually large covariance matrix, which contains the geostatistical information, by factorizing it in a product of low-rank matrices. (2) It does not assemble the Jacobian matrix per se. We determine the robustness of this approach with three examples. We first reconstruct the electrical conductivity and chargeability fields of two synthetic models generated using the geostatistical software Stanford Geostatistical Modeling Software. The PCGA approach performs better than the Tikhonov-based regularization approach when the true fields are very heterogeneous and the amount of data is limited. The third example is devoted to a field study over the former Lewis coal mine in Colorado (USA). We perform a 3D localization of the burning front of this coal seam fire by applying our geostatistical inverse methodology to a time-domain induced-polarization data set. In this case, the horizontal components of the semivariogram are determined from a self-potential map and the correlation length scale for the vertical component is determined from the known thickness of the coal bed. The tomogram presents a high normalized chargeability associated with the burning front. We evaluate the high normalized chargeability of the burning front in terms of the physical mechanism associated with the cation exchange capacity of the coal and the effect of temperature. This demonstrates the potential of the geostatistical inversion and its suitability for inverting geophysical data, especially when the data density is sparse. In the case of coal seam fires, we determine the suitability of the induced polarization method to localize the burning front and the effect of temperature on the normalized chargeability.