A generalized grid connectivity–based parameterization for subsurface flow model calibration

TL;DR: In this article, a method of parameterization for spatial hydraulic property characterization is developed to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration, which is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure.

Abstract: [1] We develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration. The parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure. The basis functions represent the modal shapes or harmonics of the grid, are defined by a modal frequency, and converge to special cases of the discrete Fourier series under certain grid geometries and boundary assumptions; therefore, hydraulic property updates are performed in the spectral domain and merge with Fourier analysis in ideal cases. Dependence on the grid alone implies that the basis may characterize any grid geometry, including corner point and unstructured, is model independent, and is constructed off-line and only once prior to flow data assimilation. We apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models. Several different grid geometries are considered. In each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell. The special case corresponding to a constant multiplier is always applied through the constant basis function. Higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel. The parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data, otherwise leaving the prior model unchanged as desired.