Stochastic Inverse Modeling and Parametric Uncertainty of Sediment Deposition Processes Across Geologic Time Scales

Abstract

In this work an integrated methodological and operational framework for diagnosis and calibration of Stratigraphic Forward Models (SFMs) which are typically employed for the characterization of sedimentary basins is presented. Model diagnosis rests on local and global sensitivity analysis tools and leads to quantification of the relative importance of uncertain model parameters on modeling goals of interest. Model calibration is performed in a stochastic framework, leading to estimates of distributions of model parameters (and ensuing spatial distributions of model outputs) conditional on available information. Starting from a considerable number of uncertain model parameters, which is typically associated with SFMs of the kind analyzed, the approach leads to the identification of a reduced set of parameters which are most influential to drive stratigraphic modeling results. Probability distributions of these model parameters conditional on available data are then evaluated through stochastic inverse modeling. To alleviate computational efforts, this step is performed through a combination of a surrogate model constructed through the Polynomial Chaos Expansion approach and a machine learning algorithm for efficient search of the parameter space during model inversion. As a test bed for the workflow, focus is on a realistic synthetic three-dimensional scenario which is modeled through a widely used SFM that enables one to perform three-dimensional numerical simulations of the accumulation of siliciclastic and carbonate sediments across geologic time scales. These results constitute a robust basis upon which further deployment of the approach to industrial field settings can be designed.

Permeability extraction from multiple well logs using particle swarm optimization based factor analysis

“…In the knowledge of the data covariance matrix including the data variances in its main diagonal, one can derive the covariance matrix of the estimated model parameters using linear inverse theory (Menke 1984). The PSO method as intelligent optimization tool has been implemented in a stochastic calibration context, specifically for the estimation of subsurface properties (Russian et al 2019;Patani et al 2021). Its efficiency has been shown in some applications in well logging inversion, too.…”

Modelling parametric uncertainty in large-scale stratigraphic simulations

“… The screening step features a global sensitivity analysis whose aim is to diagnose the response of model outputs to uncertain input parameters based on the elementary effects method 31 , 32 . Then, a Principal Component Analysis (PCA) is performed to rank parameters importance 7 , 33 . As a result we discard parameters displaying a negligible influence on model outputs and we revise the initially defined parameters ranges.…”

“…The key advantage of SFMs is that they address geological processes through a dedicated physically-based quantitative model, i.e. mathematical expressions which can be explicitly tied to the physical, chemical and biological drivers affecting the systems 7 (e.g., sediment discharges, sediment transport coefficients, carbonate production rates). The output of a SFM is a simulated basin-filling sedimentary succession and a set of paleoenvironmental conditions, such as paleo-bathymetry and sediment properties distribution, over the spatial domain and simulation time interval 8 .…”

“…The goal of this work is to demonstrate how a probabilistic approach can further enhance the capability of Stratigraphic Forward Models (SFMs) to allow efficient risk-assessment analysis 3 , 16 while fully acknowledging the uncertainty which is inherent to process-based parameter values. We address these issues upon leveraging the method proposed by Patani et al 7 , previously validated in a synthetic scenario and here applied and extended for the first time to handle a field case scenario.…”

Impact of multiple uncertainties on gravimetric variations across randomly heterogeneous aquifers during pumping

“…Amongst various available alternatives, here we rely on an approximation of model outputs based on the Polynomial Chaos Expansion (PCE; Sudret, 2008;Wiener, 1938), other approaches being fully compatible with the methodological framework we consider. This technique has been successfully employed in the context of diverse Earth science settings (including, e.g., Crestaux et al, 2009;Fajraoui et al, 2011;Formaggia et al, 2012;Ciriello et al, 2013;Porta et al, 2014;Garcia-Cabrejo and Valocchi, 2014;Sudret and Mai, 2015;Bianchi Janetti et al 2019;Patani et al, 2021).…”