Joint inversion of muon tomography and gravimetry - a resolving kernel approach

Both muon tomography and gravimetry are geophysical methods that provide information on the density structure of the Earth's subsurface. Muon tomography measures the natural flux of cosmic muons and its attenuation produced by the screening effect of the rock mass to image. Gravimetry generally consists in measurements of the vertical component of the local gravity field. Both methods are linearly linked to density, but their spatial sensitivity is very different. Muon tomography essentially works like medical X-ray scan and integrates density information along elongated narrow conical volumes while gravimetry measurements are linked to density by a 3-dimensional integral encompassing the whole studied domain. We develop the mathematical expressions of these integration formulas -- called acquisition kernels -- to express resolving kernels that act as spatial filters relating the true unknown density structure to the density distribution actually recoverable from the available data. The resolving kernels provide a tool to quantitatively describe the resolution of the density models and to evaluate the resolution improvement expected by adding new data in the inversion. The resolving kernels derived in the joined muon/gravimetry case indicate that gravity data are almost useless to constrain the density structure in regions sampled by more than two muon tomography acquisitions. Interestingly the resolution in deeper regions not sampled by muon tomography is significantly improved by joining the two techniques. Examples taken from field experiments performed on La Soufri\`ere of Guadeloupe volcano are discussed.Comment: Submitted to Geoscientific Model Developmen