Minimum entropy constrained cooperative inversion of electrical resistivity, seismic and magnetic data

Geophysical methods are widely used to gather information about the subsurface as they are non-intrusive and comparably cheap. However, the solution to the geophysical inverse problem is inherently non-unique, which introduces considerable uncertainties. As a partial remedy to this problem, independently acquired geophysical data sets can be jointly inverted to reduce ambiguities in the resulting multi-physical subsurface images. A novel cooperative inversion approach with joint minimum entropy constraints is used to create more consistent multi-physical images with sharper boundaries with respect to the single-method inversions. Here, this approach is implemented in an open-source software and its applicability on electrical resistivity tomography (ERT), seismic refraction tomography (SRT), and magnetic data is investigated. A synthetic 2D ERT and SRT data study is used to demonstrate the approach and to investigate the influence of the governing parameters. The findings showcase the advantage of the joint minimum entropy (JME) stabilizer over separate, conventional smoothness-constrained inversions. The method is then used to analyze field data from Rockeskyller Kopf, Germany. 3D ERT and magnetic data are combined and the results confirm the expected volcanic diatreme structure with improved details. The multi-physical images of both methods are consistent in some regions, as similar boundaries are produced in the resulting models. Because of its sensitivity to hydrologic conditions in the subsurface, observations suggest that the ERT method senses different structures than the magnetic method. These structures in the ERT result do not seem to be enforced on the magnetic susceptibility distribution, showcasing the flexibility of the approach. Both investigations outline the importance of a suitable parameter and reference model selection for the performance of the approach and suggest careful parameter tests prior to the joint inversion. With proper settings, the JME inversion is a promising tool for geophysical imaging, however, this work also identifies some objectives for future studies and additional research to explore and optimize the method.