Structural joint inversion of electrical and seismic tomography data

This research project has been focused on the achievement of the structural joint inversion of two geophysical methods. The final target is to obtain a high resolution characterization of the shallow subsurface. The aim of determining petrophysical properties, structural boundaries, etc, can be obtained through the integration of different information that derives from various geophysical methods. In fact, since each method is sensitive to a specific physical property, their integration can lead to an accurate final model. However, if such integration is conducted individually inverting the data sets, the final model will be affected by the resolution limitations of each method. For this reason, an important tool has been developed in geophysical applications: the joint inversion. Two different approaches can be used to carry out the joint inversion: the petrophysical one, in which a petrophysical relationship is used, and the structural one, in which a structural similarity between models is imposed (Gallardo and Meju, 2004). Specifically, I decided to implement the algorithm for the structural joint inversion and specifically the structural approach developed by Gallardo and Meju (2003, 2004), since from literature it results to be the most robust method in the joint inversion (Moorkamp, 2017). In this process, an objective function that includes the objective function of each geophysical method is build and simultaneously minimized. In conclusion, the joint inversion may improve the resolution of each geophysical model and bring to models that are more accurate and easier to interpret. Specifically, in this thesis, the electrical resistivity tomography (ERT) and the seismic refraction tomography (SRT) have been used to carry out the joint inversion. Both these high-resolution methods can be crucial in environmental and engineering applications, as for the geotechnical characterization of a site or for the detection of hydrological resources. Since the resistivity range overlaps for the different materials, resistivity measurements cannot be related to a specific soil or rock. Because of that, it would be better to obtain other information, for example from the seismic tomography. In fact, this method allows not only the reconstruction of the seismic wave velocities with depth, but also to obtain a good lateral resolution. Instead, the Ground Penetrating Radar (GPR) has not been considered since it presents some limits in the investigation depth, due to the high attenuation of electromagnetic energy in porous conductive media. In addition to the integrated inversion, another goal has been obtained in this thesis: the implementation of the forward modeling for the seismic method and specifically, the Multistencils Fast Marching Method (MSFMM). This method can be seen as an extension of the FMM, that is considered from literature the fastest and the most efficient method for the solution of the eikonal equation and accordingly for the computation of the first arrivals traveltimes. In particular, the MSFMM improves the accuracy and the efficiency of the FMM, since it considers also the information that derives from the diagonal directions. Both the algorithms, the one of the joint inversion and the one of the forward modeling for the seismic method, have been implemented in Python language and integrated in the open-source software pyGIMLi.