Sensitivity Analysis of Quasi-Wavelet Models of Heterogeneous Materials

Quasi-wavelet cascade models are a recent method for simulating heterogeneous, multi-phase materials and other media as random fields, but their sensitivities to various modeling choices have not previously been thoroughly characterized. Doing so is essential to support future efforts to infer robust but parsimonious models of terrestrial media. The objectives herein are to present (i) the theory of quasi-wavelet cascade models of spatially intermittent fields, (ii) statistical metrics for characterizing the morphology of phases in random heterogeneous media, and (iii) variance-based global sensitivity analysis to deduce which model parameters strongly influence the morphology metrics selected for characterizing a simulated ensemble produced by sampling the quasi-wavelet cascade parameters. Global sensitivity analysis of metrics sensitive to the shapes of phase clusters are found to effectively highlight which parameters in the quasi-wavelet cascade model are essential to producing the phase morphology observed across a simulated ensemble. I Introduction T ERRESTRIAL environments exhibit multi-scale, irregular distributions of natural and artificial objects. Such environments often are heterogeneous (i.e., composed of multiple material phases spanning length scales larger than the smallest length scale of interest) and spatially intermittent, such that one or more phases exhibit clustering cover distances large enough to alter signal transmissions. The performance of sensing and communications systems depends strongly on their specific operating environments. Even when high-fidelity physics models are available and the properties of disturbances are well known, these environments typically cannot be characterized with sufficient detail to permit precise predictions of detection performance. Figure 1 offers an example of sporadically distributed volcanic rock (basalt), which strongly alters the propagation of localized seismic disturbances. Owing to the broad, multifaceted uncertainty in the properties of these sensing environments, probabilistic models of their constitutive properties and the resulting signal propagation characteristics are essential. The field of random heterogeneous materials (RHM) 1,2 has been developed for describing the constitutive properties through their statistics, and sampling-based simulations, e.g., Monte Carlo simulation (MCS), are estimating the resulting response uncertainty. Quasi-wavelets (QW) 3,4 are a recently developed approach for simulating random fields, with recent applications featuring simulations of turbulent flow fields and RHM. When quasi-wavelets at various scales are combined via types of cascade reactions that obey conservation properties, they provide a powerful approach to simulating intermittent RHM. However, the relative importance of the parameters and chosen cascade reaction types in determining the statistics of QW field ensembles has not been thoroughly examined. Doing so is essential to ensuring QW are used wisely for simulating random fields in general and for facilitating future efforts to infer QW field models of RHM from measured properties. Variance-based global sensitivity analyses were conducted to quantify the connections between factors that govern QW field ensembles, and the sample statistics of these ensembles. The ensembles were characterized through several metrics for describing the spatial distribution of phases, i.e., their morphology. This study is part of a project to develop metrics to assess the quality of quasi-wavelet models of intermittency in RHM, with a primary objective to support the inference of related QW models from field data.