SUMMARYAnalytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E ) and shear modulus (G ) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, and remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain-displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, V P , V SV , and V SH , and the wave vectors, l P l SV , and l SH , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E , G /E , and / ); and (3) the phase angle, . Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium.
The objective of this study is to investigate the amplification spectra of the single layered soil medium subjected to various SH sources from distinct locations. The source of model I is treated as a harmonic plane SH source, of which the generated wave propagates in one direction. To make the source approach the seismic mechanism, the harmonic line SH source is adopted as the one used by model II, by which the amplification spectra at distinct locations can be obtained. Frequently, the applied duration of the seismic source is limited, so the generalized ray theory is a powerful mathematic tool for dealing with the propagation problem of waves generated by a transient line SH source. This is the source of model III in this study. Then the obtained results show that the amplification effects decrease with an increasing damping factor, and the spectra vary with distinct sources, locations and even applied durations.
SUMMARYThis paper seeks to reconstruct the parameters of elastic layered media such as P-wave velocity, S-wave velocity, density and thickness from the multioffset seismic reflection data. Since the data are highly non-linear to the low-wavenumber components, the non-linear waveform inversion method, with the aid of generalized ray theory, is proposed to solve this problem in space-time domain. As opposed to the layer-stripping method, the present method attempts to invert all layer parameters simultaneously, thus reducing the cumulative errors resulting from the upper layers. The parameters are inverted by minimizing the weighted square error between the observed data and the calculated data of the layered model, the optimization of which is based on the quasi-Newton method. In synthetic tests, we find that the inverted results are good when the variation of parameters between layers is not too large. The modified method for large variation of parameters is first to fix those of deeper layers and neglect the signals reflected from them, then recover some other parameters simultaneously until those of upper layers attain a stable value, and finally, invert all parameters simultaneously. The results so obtained show a significant improvement. This method was tested to be stable in the presence of noise in seismograms.
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