Abstract Existing three-dimensional (3-D) geologic systems are well adapted to high data-density environments, such as at the mine scale where abundant drill core exists, or in basins where 3-D seismic provides stratigraphie constraints but are poorly adapted to regional geologic problems. There are three areas where improvements in the 3-D workflow need to be made: (1) the handling of uncertainty, (2) the model-building algorithms themselves, and (3) the interface with geophysical inversion. All 3-D models are underconstrained, and at the regional scale this is especially critical for choosing modeling strategies. The practice of only producing a single model ignores the huge uncertainties that underlie model-building processes, and underpins the difficulty in providing meaningful information to end-users about the inherent risk involved in applying the model to solve geologic problems. Future studies need to recognize this and focus on the characterization of model uncertainty, spatially and in terms of geologic features, and produce plausible model suites, rather than single models with unknown validity. The most promising systems for understanding uncertainty use implicit algorithms because they allow the inclusion of some geologic knowledge, for example, age relationships of faults and onlap-offlap relationships. Unfortunately, existing implicit algorithms belie their origins as basin or mine modeling systems because they lack inclusion of normal structural criteria, such as cleavages, lineations, and recognition of polydeformation, all of which are primary tools for the field geologist that is making geologic maps in structurally complex areas. One area of future research will be to establish generalized structural geologic rules that can be built into the modeling process. Finally, and this probably represents the biggest challenge, there is the need for geologic meaning to be maintained during the model-building processes. Current data flows consist of the construction of complex 3-D geologic models that incorporate geologic and geophysical data as well as the prior experience of the modeler, via their interpretation choices. These inputs are used to create a geometric model, which is then transformed into a petrophysical model prior to geophysical inversion. All of the underlying geologic rules are then ignored during the geophysical inversion process. Examples exist that demonstrate that the loss of geologic meaning between geologic and geophysical modeling can be at least partially overcome by increased use of uncertainty characteristics in the workflow.

Abstract The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.