Joint inversion methods with relative density offset correction for muon tomography and gravity data, with application to volcano imaging

Abstract

Muography is a relatively new geophysical imaging method that uses muons to provide estimates of average densities along particular lines of sight. Muography can only see above the horizontal elevation of the detector and it is therefore attractive to attempt a joint inversion of muography data with gravity data, which is also responsive to density but generally requires combination with another geophysical data set to overcome issues related to non-uniqueness and poor depth resolution. Some previous work has investigated this joint inverse problem and demonstrated the potential improvements to be gained by jointly inverting muography and gravity data. However, there has yet to be a thorough investigation of different numerical approaches for formulating the joint inverse problem. Particularly important is how to account for the fact that even though the two data types are sensitive to the same physical quantity, density, they respond through different response functions. Moreover, the two measurements are affected by different systematic uncertainties that are difficult to model. In this work, we considered an approximation where the two density quantities, inferred from the two data types, can be related by an unknown scalar offset. We considered various existing and new joint inversion methods that might solve this problem and we applied them to a synthetic volcano imaging scenario based on the Puy de Dome volcano in the Central Massif region of France. We used unstructured meshes in our modelling to adequately honour the significant topography in that scenario. Our experiments indicated that the most successful joint inversion method for this type of geological scenario was one in which the data misfit function is reformulated to automatically determine the best-fitting offset following a least-squares minimization argument. However, other approaches showed merit and we suggest several of the investigated methods be applied and compared for any specific joint inversion scenario.