Cross-gradient joint inversion and clustering of ERT and SRT data on structured meshes incorporating topography

Summary The combination of electrical resistivity and seismic refraction tomography is a common practice for the characterization of subsurface features. Presently, the cross-gradient inversion scheme stands out as one of the most robust joint approaches, and some authors modified it to manage complex topographies on unstructured meshes even if at the expense of introducing additional parameters in the inversion process. We propose in this work a cross-gradient algorithm for jointly inverting electrical and seismic tomographic data on structured meshes in cases with non-flat topography. The proposed approach preserves the benefit of the classical cross-gradient approach without the need to impose physical length scales, as for irregular meshes. The quality of the results is evaluated in comparison with independent inversion through a new standardized cross-gradient index and a fuzzy c-means analysis that provides an assessment of the reconstruction accuracy through the membership function. The proposed method was applied to both synthetic models and field-scale examples located in Central Italy, where an accurate geophysical reconstruction is needed for the rehabilitation of existing dams. For all cases, joint inversion yielded superior results compared to independent inversion, demonstrating better agreement with available borehole data. The effectiveness of the joint approach was also demonstrated by the post-inversion tools, where the new cross-gradient index highlighted changes in structural similarity whilst fuzzy c-means clustering allowed for a quantitative reconstruction (position and shape) of the main units at the sites, facilitating the detection of site layering modifications.