Heterogeneity in Sedimentary Deposits: A Review of Structure‐Imitating, Process‐Imitating, and Descriptive Approaches

Numerical models that solve governing equations for subsurface fluid flow and transport are commonly applied to analyze quantitatively the effects of heterogeneity. These models require maps of spatially variable hydraulic properties. Because complete three‐dimensional information about hydraulic properties is never obtainable, numerous methods have been developed to interpolate between data values and use geologic, hydrogeologic, and geophysical information to create images of aquifer properties. Image creation approaches fall into three general categories: structure‐imitating, process‐imitating, and descriptive. Structure‐imitating methods rely on one or more of the following to constrain the geometry of spatial patterns in geologic media: correlated random fields, probabilistic rules, and deterministic constraints developed from facies relations. Structure‐imitating methods include spatial statistical algorithms and geologically based sedimentation pattern‐matching approaches. Process‐imitating models include aquifer model calibration methods and geologic process models. Aquifer model calibration methods use governing equations for subsurface fluid flow and transport to relate hydraulic properties to heads and solute information through history and steady state data matching. Geologic process models combine fundamental laws of conservation of mass and momentum with sediment transport equations to simulate spatial patterns in grain size distributions. At the sedimentary basin scale, multiprocess models include thermomechanical mechanisms of basin subsidence. Descriptive methods couple geologic observations with facies relations to divide an aquifer into zones of characteristic hydraulic properties. All approaches are capable of reproducing heterogeneity over a range of scales and considering some types of geologic information. Some approaches are strictly spatial while some are linked to the time evolution of sedimentation. Some approaches can be conditioned on measurements. Recent advances aimed at infusing geologic information into images of the subsurface include extracting more information from sedimentological facies models, incorporating qualitative geologic information into random field generators and simulating depositional processes. Classes of research missing from the literature include multiprocess models that incorporate diagenesis and three‐dimensional surface water flow, hybrid methods that combine features of existing approaches, and approaches that can make use of all available geologic, geophysical, and hydrologic data.