Waveform joint inversion of seismograms and electrograms for moment tensor characterization of fracking events

Abstract

Electromagnetic signals have been observed in association with fracking experiments in the laboratory, and in the field. We have developed a seismoelectric forward modeling approach to produce synthetic seismograms and electrograms generated by fracking events using the finite-element method with perfect matched-layer boundary conditions. The poroelastodynamic equations are solved in the frequency domain using a formulation based on the solid phase displacement and the pore pressure. These results are used to compute the electrical field disturbances of electrokinetic nature. Three types of electrical signals are generated: Type I disturbance is associated with the seismic source itself, Type II disturbance corresponds to seismoelectric conversions, and Type III corresponds to coseismic signals. This model is applied to simulate the seismic and electrical signals corresponding to the occurrence of a fracking event in a two-layers system. We perform a stochastic joint inversion of the seismograms and electrograms using the adaptive Metropolis algorithm (AMA) to obtain the posterior probability density functions of the parameters characterizing the seismic source assuming that the velocity model is perfectly known. The joint waveform inversion is performed on synthetic noise-free data and the AMA algorithm is successful in retrieving the true values of the unknown parameters. The proposed approach is then tested on the same synthetic data after being contaminated with 15% random noise with respect to the maximum amplitude of the signals. The model parameters are better determined for the joint inversion of seismic and electrical data by comparison with the inversion of the seismic time-series alone. We also propose a deterministic tomographic algorithm that is successful in locating the in situ source current density distribution for Types I and II anomalies from the electrical data alone.