The ray method is used to compute high-frequency seismic vector wavefields in weakly attenuating layered anisotropic structures. The attenuating effects are introduced by substituting the real elastic parameters for perfectly elastic media by complex frequency dependent elastic parameters with small imaginary parts. The imaginary parts are formally considered to be of the order of omega-1 for omega --> +infinity. Under this assumption, it is possible to work with real rays, only the eikonal is complex. The approximate computations based on this algorithm are only a few percent slower than those for perfectly elastic anisotropic media. The range of applicability of the weak attenuation concept is investigated by comparison of ray computations with results of the reflectivity method for an isotropic, constant gradient model. The study indicates that the region of applicability of the weak attenuation concept may be broader than expected. The combined effects of anisotropy and attenuation on the propagation of seismic waves in a three-dimensional model of the uppermost crust with an anisotropic attenuating layer are then studied. The anisotropy as well as the attenuation are supposed to be caused by aligned partially liquid-filled cracks. Hudson's formulas to compute complex effective elastic parameters are used. Frequency responses and VSP synthetic seismograms for different degrees of viscosity of the liquid, and, thus, different degree of attenuation, show the effects of attenuation on the propagating waves. Nine-component VSP vector wavefields are computed for two different source-borehole directions along the strike of the cracks and 45 degrees off the strike of the cracks. The seismograms for the attenuating model are compared with seismograms for the corresponding perfectly elastic model.
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