Joint inversion of seismic and electrical data in saturated porous media

Joint inversion strategies and physical constraints on model parameters may be used to mitigate equivalence problems caused by solution non-uniqueness. This strategy is quite a common practice in exploration geophysics, where dedicated rock physical studies are usually carried out, while it is not so frequent in near surface geophysics. We use porosity as a constraint among seismic wave velocities and electrical resistivity in a deterministic joint inversion algorithm for surface wave dispersion, P-wave traveltimes and apparent resistivity from vertical electrical sounding. These data are often available for near surface characterization. We show that the physical constraint among model parameters leads to internally consistent geophysical models in which solution non-uniqueness is mitigated. Moreover, an estimate of soil porosity is obtained as a relevant side product of the procedure. In particular, we consider a clean sand deposit and hence the appropriate formulations for the computation of porosity from seismic velocities and resistivity are implemented in the algorithm. We first demonstrate how the non-uniqueness of the solution is reduced in a synthetic case and then we applied the algorithm to a real-case study. The algorithm is here developed for one-dimensional condition and for granular soils to better investigate the physical constraint only, but it can be extended to the two-dimensional or three-dimensional case as well as to other materials with the adoption of proper rock physical relationships.