GNGTS 2022 - Atti del 40° Convegno Nazionale

528 GNGTS 2022 Sessione 3.3 A STOCHASTIC ENSEMBLE BASED APPROACH FOR TIME-LAPSE ERT INVERSION A. Vinciguerra 1,2 , M. Aleardi 2 , L. Meldgaard Madsen 3 , T.S. Bording 4 , A.V. Christiansen 3 , E. Stucchi 2 1 Università di Firenze, Dipartimento di Scienze della Terra, Firenze, Italy 2 Università di Pisa, Dipartimento di Scienze della Terra, Pisa, Italy 3 Hydrogeophysics Group, Department of Geoscience, Aarhus University 4 Aarhus GeoInstruments Introduction. The investigation of the subsurface has becoming of increasing interest to mitigate environmental risks. The development of Electrical Resistivity Tomography (ERT) monitoring station systems has triggered the application of Time-Lapse ERT technique to detect the resistivity variations in time. Indeed, the resistivity change can be associated with subsurface processes such as groundwater recharge (Descloitres et al. , 2018) and aquifer contamination (Maurya et al. , 2017). The ERT data inversion is an ill-posed, non-linear problem that it is usually solved through a deterministic least-square algorithms. Nevertheless, this approach is prone to get stuck in local minima of the error function. A strategy to tackle this issue is to apply stochastic inversion algorithms that consider the model parameters as random variables and the subsurface model as a realisation of a probability density function. However, the main drawback of this approach is the computational burden related to the several forward model evaluations needed to sample the parameter space (Vinciguerra et al. , 2022). The Ensemble Based (EB) algorithm is an iterative data assimilation method that assimilates the observed data multiple times with an inflated covariance matrix (Aleardi et al. , 2021). The result of this algorithm is an ensemble of realisations from which an approximation of the posterior probability density function (ppd) can be numerically assessed. This algorithm requires less computational time compared to standard Monte Carlo Markov Chain algorithms due to the lower number of forward modelling runs to estimate the ppd. (Aleardi et al. , 2021). Nowadays, there exists different Time-Lapse inversion strategies: independent approach in which the data are inverted independently; the cascaded inversion, in which the inversion result of the first dataset is considered as starting model of the second dataset (Miller et al. , 2008); or strategies such as the difference inversion that attenuate the effects of the systematic error during the acquisition (Labreque et al. , 2001). To perform a Time-Lapse inversion, we rearrange the EB algorithm to obtain the posterior mean model, its variation in time and the uncertainties affecting the solution. In this work, we apply the Time-Lapse EB algorithm to field data acquired by a landfill monitoring station in Pillemark (Samsø, Denmark). Methods. The aim of the conventional Ensemble Based algorithm is to recover the posterior uncertainties. This algorithm has been validated for the 2.5D ERT tomography case (see Aleardi et al. , 2021 for details). In this work, we modify that inversion framework making it suitable for Time-Lapse ERT intent. Let ρ 0 be the subsurface resistivity at the initial time, t 0 , ρ 1 the subsurface resistivity at the second time t 1 = t 0 + Δt and Δρ the resistivity variation, the problem is formulated as follows: Δρ = ρ 1 / ρ 0 = {(1, ∞) if ρ 0 < ρ 1 resistivity increment 1 if ρ 0 = ρ 1 no variation (0, 1) if ρ 0 > ρ 1 resistivity reduction (1) (2) Where G represents the forward operator, m is the model vector, d 0 and d 1 are the observed data at t 0 and t 1 respectively; note that the unknowns of the problem are ρ 0 and Δρ . Parametrizing the resistivity variation as the ratio between ρ 0 and Δρ implies two different resolutions when the resistivity increases or decreases. It is evident from Equation 1 that when the resistivity increases from t 0 to t 1 the Δρ range is wide (1, ∞), whereas when the resistivity decreases the Δρ values are in the range (0, 1). The definition of Δρ has been chosen