Summary A new approach is proposed for measuring the dispersion relation of surface waves in weakly anisotropic media using a single station, which consists of translational displacement and rotation or strain. The azimuth-dependent surface wave dispersion curve can be directly obtained by using the amplitude ratio of translational displacement to rotation or strain. Using observations from earthquakes from a variety of azimuths allows us to characterize the anisotropy of subsurface media. The amplitude ratio gives the localized azimuth-dependent dispersion relations of the formation beneath a receiver without requiring knowledge of the source or structure along the path. The theory shows that in anisotropic media the coupled quasi-Rayleigh (qR) wave and quasi-Love (qL) wave will result in elliptically polarized rotational motions. In addition, rotational motion information allows the determination of backazimuth even in general anisotropic media. We carry out numerical experiments, investigate the effects of noise and degree of anisotropy, and demonstrate the potential for field studies.

Summary We develop a novel approach for imaging subsurface lateral heterogeneities using six-component (6C) ambient seismic noise data, consisting of three translational components and three rotational components. We first derive the 6C cross-correlation functions (CCFs) from ambient seismic noise data for surface waves and then apply the modified frequency Bessel (MF-J) transform to the 6C CCFs for surface wave dispersion curves. The phase velocities of Rayleigh and Love waves can be directly calculated from the 6C CCFs of a single pair of stations. Traditional array-based surface wave methods derive the surface wave phase velocity based on the presumption of a horizontally layered model. When this assumption breaks down due to the presence of, for example, dipping layer or heterogeneities, the resulting phase velocity can be severely smeared. By contrast, the proposed approach is not limited by the layered model assumption because it relies on single-point measurements to calculate the localized dispersion relations of the formation right beneath a receiver. Our numerical modeling results demonstrate that this approach is applicable to heterogeneous models and can image small-scale subsurface anomalies with very high lateral resolution.

Summary We develop a generalized reflection and transmission coefficient method (GRTM) for generating six-component (6-C) synthetic seismograms in horizontally layered vertically-transversely-isotropic (VTI) media. Compared with the traditional seismic modeling approaches that only consider translational motion, our method can simultaneously produce three-component translational and three-component rotational data excited by a point vector force or a moment tensor source in a layered half-space. Horizontally layered models are widely used in near surface applications as the properties of near surface formations generally show small lateral variations and change mainly along the depth direction. The use of the VTI constitutive relation can make our method applicable to more general situations because it takes into account the characteristics of sedimentary formations. We compare our method with a finite-difference method (FDM) for a variety of velocity models and acquisition geometries. The numerical results demonstrate that accurate 6-C synthetic seismograms can be calculated using our method. The computational efficiency of our method for 6-C seismic modeling is much higher than the finite-difference method, because it can reduce a 3D modeling problem to 2.5D by eliminating the azimuthal dimension. Also, our method does not require to perform additional spatial interpolations to obtain the rotational components. These advantages make our method suitable to serve as a forward modeling tool for rotational seismology.

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