Full-waveform inversion of complex resistivity IP spectra: Sensitivity analysis and inversion tests using local and global optimization strategies on synthetic datasets

We implement two different inversion strategies for solving the full-waveform inversion of spectral induced polarization data: the first is a local inversion based on the Levenberg–Marquardt algorithm, whereas the second is a global optimization that makes use of the Particle Swarm Optimization algorithm. In addition, the analysis of the residual function maps and the singular value decomposition of the inversion kernel are used to analyse the complexity of the objective function and the ill-posedness of this inverse problem. We limit the attention to synthetic data with the aim to maintain the inversion at a simple level and to draw essential conclusions about the ill-conditioning of the considered inverse problem and about the suitability of the two inversion approaches we use. We consider two differexnt double-dispersion reference models that generate resistivity amplitude and phase spectra with different characteristics. Realistic noise is added to the synthetic data to better simulate a field data set. We also apply a dedicated processing sequence to increase the signal-to-noise ratio of the observed data. It turns out that the full-waveform inversion of spectral induced polarization is a well-posed problem in case of double-peaked resistivity spectra, whereas it becomes hopelessly ill-conditioned when the subsurface model generates single-peaked spectra. In particular, the analysis of the residual function maps demonstrates that in case of double-peaked spectra the objective function is characterized by a well-defined single minimum. Conversely, elongated valleys with similar misfit values arise for single-peaked spectra. In this case, the eigenvectors in model space demonstrate that the estimate of the τ 1 and c1 parameters is a non-unique problem, and for this reason it would be advisable to reparametrize the inverse problem by considering a single-dispersion model. In addition, our tests demonstrated the superior exploitation capability of the linearized inversion with respect to the global optimization, that is the ability to converge towards the minimum in case of the objective functions with low gradient values.