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We describe the application of the rotated staggered‐grid (RSG) finite‐difference technique to the wave equations for anisotropic and viscoelastic media. The RSG uses rotated finite‐difference operators, leading to a distribution of modeling parameters in an elementary cell where all components of one physical property are located only at one single position. This can be advantageous for modeling wave propagation in anisotropic media or complex media, including high‐contrast discontinuities, because no averaging of elastic moduli is needed. The RSG can be applied both to displacement‐stress and to velocity‐stress finite‐difference (FD) schemes, whereby the latter are commonly used to model viscoelastic wave propagation. With a von Neumann‐style anlysis, we estimate the dispersion error of the RSG scheme in general anisotropic media. In three different simulation examples, all based on previously published problems, we demonstrate the application and the accuracy of the proposed numerical approach.

Reliable models of in‐situ shear‐wave velocities of shallow‐water marine sediments are important for geotechnical applications, lithological sediment characterization, and seismic exploration studies. We infer the 2D shear‐wave velocity structure of shallow‐water marine sediments from the lateral variation of Scholte‐wave dispersion. Scholte waves are recorded in a common receiver gather generated by an air gun towed behind a ship away from a single stationary ocean‐bottom seismometer. An offset window moves along the common receiver gather to pick up a local wavefield. A slant stack produces a slowness–frequency spectrum of the local wavefield, which contains all modes excited by the air gun. Amplitude maxima (dispersion curves) in the local spectrum are picked and inverted for the shear‐wave velocity depth profile located at the center of the window. As the window continuously moves along the common receiver gather, a 2D shear‐wave velocity section is generated. In a synthetic example the smooth lateral variation of surficial shear‐wave velocity is well reconstructed. The method is applied to two orthogonal common receiver gathers acquired in the Baltic Sea (northern Germany). The inverted 2D models show a strong vertical gradient of shear‐wave velocity at the sea floor. Along one profile significant lateral variation near the sea floor is observed.

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Seismic anisotropy is often neglected in seismic studies of the earth's crust. Since anisotropy is a common property of many typically deep crustal rocks, its potential contribution to solving questions of the deep crust is evaluated. The anisotropic seismic velocities obtained from laboratory measurements can be verified by computations based on the elastic constants and on numerical data pertaining to the texture of rock-forming minerals. For typical lower crustal rocks the influence of layering is significantly less important than the influence of rock texture. Surprisingly, most natural lower crustal rocks show a hexagonal type of anisotropy. Maximum anisotropy is observed for rocks with a high content of aligned mica. It seems possible to distinguish between layered intrusives and metasediments on the basis of in situ measurements of anisotropy, which can thus be used to validate different scenarios of crustal evolution.