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

Abstract

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 τ1 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 objective functions with low gradient values.

A Review of Geophysical Modeling Based on Particle Swarm Optimization

“…The main applications of PSO to the geophysical inverse problem include the interpretation of: vertical electrical sounding (VES) (Fernández-Álvarez et al 2006 ; Fernández Martínez et al 2010a ; Pekşen et al 2014 ; Cheng et al 2015 ; Pace et al 2019b ); gravity data (Yuan et al 2009 ; Pallero et al 2015 , 2017 , 2021 ; Darisma et al 2017 ; Jamasb et al 2019 ; Essa and Munschy 2019 ; Anderson et al 2020 ; Essa and Géraud 2020 ; Essa et al 2021 ); magnetic data (Liu et al 2018 ; Essa and Elhussein 2018 , 2020 ); multi-transient electromagnetic data (Olalekan and Di 2017 ); time-domain EM data (Cheng et al 2015 , 2019 ; Santilano et al 2018 ; Pace et al 2019c ; Li et al 2019 ; Amato et al 2021 ); MT data (Shaw and Srivastava 2007 ; Pace et al 2017 , 2019a , c ; Godio and Santilano 2018 ; Santilano et al 2018 ) and radio-MT data (Karcıoğlu and Gürer 2019 ); self-potential data (Santos 2010 ; Pekşen et al 2011 ; Göktürkler and Balkaya 2012 ; Essa 2019 , 2020 ) and induced polarization (Vinciguerra et al 2019 ); Rayleigh wave dispersion curve (Song et al 2012 ) and full waveform inversion (Aleardi 2019 ). …”

“…self-potential data (Santos 2010 ; Pekşen et al 2011 ; Göktürkler and Balkaya 2012 ; Essa 2019 , 2020 ) and induced polarization (Vinciguerra et al 2019 );…”