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Min Chen extends the spectral-element simulations of global and regional seismic wave propagation to incorporate three-dimentional, fully anisotropic Earth models. For weakly anisotropic media, we benchmark the numerical simulations against asymptotic, ray-theoretical predictions for surface and body waves.

Theory in weakly anisotropic Earth media

Surfacewave phase speeds (Smith & Dahlen 1973) We demonstrate that compressional and shear body-wave speeds can be written as:

Surfacewave anisotropy is governed by 13 elastic parameters, and the azimuthal dependence of the phase speed is represented by even Fourier series involving degrees two or four; body-wave anisotropy involves all 21 elastic parameters, bodywave speeds are even Fourier series of incidence angle, but their azimuthal dependence involves degree one, two, three and four, which is unlike surface waves. Table 1. Comparison of the directional effects of all 21 independent elastic coefficients on body- and surface-wave speeds.

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Regional Spectral-element Simulation:

Figure 1. Regional experimental setup.The model dimensions are 516 km (EW) X 507 km (NS) X 60 km (depth). The source is pure strike-slip event locate at the middle of this regional chunk (yellow star). The green circles with green bars denote a ring of staions at an epicentral distance of 90 km. The fast direction of constant anisotropy in this homogeneous chunk associated with the 1-zeta Jc parameter makes 45 degrees incidence angle, indicated by black dashes. The reference model is isotropic, with a density of 3g/cm^3, Vp of 7.8 km/s, and Vs of 4.5 m/s.

Figure 2. Body-wave traveltime anomalies due to 1-zeta (Jc, Kc, and Mc) and 3-zeta (Dc) anisotropic parameters for P waves (left column), and SH waves (right column) at a epicentral distance of 90 km. (At the free surface SV waves are obscured by P-to-SV conversions and generation of Rayleigh wave.) Lines: ray-theoretical predictions. Symbols: measurents of SEM synthetics.

Figure 3. Comparison between isotropic SH synthetics (left) and anisotropic SH synthetics (right) for the 3-zeta anisotropic parameter Dc. The traces are plotted in the direction of their source azimuth. In both figures the directional theoretical traveltime is indicated by the closed curves, which is circle in the isotropic case and a degree-three Fourier series in the anisotropic case. The anisotropic traveltime anomalies have been exaggerated by a factor of six to make the degree-three pattern more visible.The source-time function is a Gaussian with a half-duration of 2 seconds.

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