Land subsidence surrogate models for normally consolidated sedimentary basins

This article presents a methodology for building a computationally-fast “surrogate model” to simulate land subsidence due to fluid extraction from normally consolidated sedimentary basins. The model relies on the extension of the classic nucleus of strain solution (NoS) in a homogeneous semi-infinite continuum to heterogeneous basins, in which the uniaxial vertical compressibility cM varies along the depth z following either a power or an exponential law. The NoS solution represents the horizontal and vertical components of the surface displacement associated with a unit volume at a given depth c in which a unit change of pore pressure occurs. The modified NoS solution is obtained by fitting the horizontal and vertical components of the surface displacement calculated using a finite-element (FE) numerical model. This is achieved through a regression algorithm that identifies four fitting parameters. By repeating such a regression over a set of combinations of the coefficients of the basin compressibility model cM(z), it is possible to identify four functions that emulate the variability of the four fitting parameters with respect to the compressibility model coefficients. The surrogate land subsidence model is then built by integrating the modified NoS equations within the subsurface region (e.g. an aquifer) where a change in pore pressure occurs due to fluid abstraction. Such formulation results in an explicit “response-matrix” approach, where the forcing terms depend on the pore pressure variations, and the matrix coefficients account for the selected basin compressibility model. The implementation approach is quite straightforward and powerful, as it allows, for example, to easily construct a land subsidence package “online” over any groundwater flow model, or estimate “offline” the land surface displacement associated with any simulated or observed 3D pore pressure change field. The surrogate land subsidence model is tested with a series of numerical experiments, and is shown to produce accurate results within the working assumptions of the model.