Physically Constrained joint inversion of seismic and electrical data for near surface applications

Geophysical methods require the solution of inverse problems that lead to the estimation of physical properties of the subsurface (model parameters) based on the minimization of the misfit function between theoretical and the experimental data. The inverse problems are often non-linear, ill-posed and affected by solution non-uniqueness and this leads to interpretation ambiguities. These criticisms can be mitigated with a joint inversion of different geophysical data to obtain a final multi-parametric model and to exploit the different sensitivity of each method to the different model parameters. This can also mitigate the inherent limitations which are peculiar of each technique. The joint inversion can be performed or by imposing the same structure of the subsurface to all the methods (structural approach) or using physical relationships among the model parameters (physical approach). The latter ensures the internal physical consistency of the model. The algorithm I propose imposes either the same structure as well as some physical relationships and it involves seismic data, related to geometrical dispersion of surface waves and refracted P-wave traveltimes, and apparent resistivity data. Such data allow respectively S-wave velocity, P-wave velocity and resistivity to be retrieved. The algorithm is based on a collection of 1D layered models located along the line and each model is linked to the neighbour ones trough spatial constraints. Also a priori information on the model parameters is taken into account. The physical relationships are introduced by imposing constraints on the Poisson’s ratio, that is expressed as function of S- and P- wave velocities, and by imposing equality between the porosity value estimated from seismic velocities and the porosity value estimated from resistivity. The algorithm was applied to both synthetic and field data and three examples were proposed combining different kind of data and physical relationships. The starting point was an existing algorithm on the joint inversion of surface wave and refracted P-wave data for S- and P- wave velocities and including the Poisson’s ratio as physical link between those model parameters. This algorithm was applied on experimental data acquired along a line crossing a fault in New Zealand and the seismic dataset was exploited not only to extract surface wave and refracted P-wave data, but also to perform a lateral variability assessment to tune the geometric regularization. Then the vertical electrical sounding was included in the algorithm and hence the apparent resistivity data were added to the data vector as well as the resistivity to the model one. The algorithm was tested on synthetic and field data related to a case study regarding a site in Norway affected by instability due to quick clay. Based on a 1D model, the third example is on the use of the porosity as link between the seismic and resistivity model parameters testing it on a synthetic and field data related to a saturated sand deposit. All of these examples show how the joint inversion provide a more reliable and physically consistent final model than the results from individual inversions. In addition, even if the Poisson’s ratio and the porosity are not primary objectives of the inversion, the final model, being internally consistent, provides a more reliable estimation of those physical parameters than the one from the results of the individual inversions.