Image-guided inversion of electrical resistivity data

Abstract

Electrical resistivity tomography (ERT) is based on solving a Poisson equation for the electrical potential and is characterized by a good sensitivity only in the vicinity of the electrodes used to gather the data. To provide more information to ERT, we propose an image-guided or structure-constrained inversion of the apparent resistivity data. This approach uses structural information obtained directly from a guiding image. This guiding image can be drawn from a high resolution geophysical method based on the propagation equation (e.g. migrated seismic or ground penetrating radar images) or possibly from a geological cross-section of the subsurface based on some prior geological expertise. The locations and orientations of the structural features can be extracted by image processing methods to determine the structure tensor and the semblances of the guiding image at a set of pixel. Then, we introduce these structural constraints into the inversion of the apparent resistivity data by weighting the four-direction smoothing matrix to smooth along, but not across, structural features. This approach allows preserving both discontinuities and coherences in the inversion of the resistivity data. The image-guided inversion is also combined with an image-guided interpolation approach used to focus a smooth resistivity image. This yields structurally-appealing resistivity tomograms, while the whole process remains computationally efficient. Such a procedure generates a more realistic resistivity distribution (closer to the true ones), which can be, in turn, used quantitatively using appropriate petrophysical transforms, to obtain parameters of interest such as porosity and saturation. We check the validity of this approach using two synthetic case studies as well as two real datasets. For the field data, the image used to guide the inversion of the electrical resistivity data is a GPR section in the first case and a combination of seismic and structural information in the second case, which corresponds to a geothermal site at Pagosa Springs, in Colorado.