The wave propagation in crystalline media plays a very significant role in seismology as well as in crystal physics. To investigate such problems, we first study the elastic constants of crystals of different classes and groups.
The problem of the propagation of Rayleigh waves in a system consist ing of a liquid layer of finite depth overlying a semi-infinite half-space of orthorhombic and cubic crystals is solved. In the limiting cases, Stoneley waves are discussed. The dispersion equations are derived and phase and group velocities of the waves are calculated as functions of wave number. Some interesting results are presented. The study of such waves brings some special features in seismology if certain part of the Earth is supposed to be composed of crystalline material.

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The problem of the propagation of Rayleigh waves in a system consisting of a liquid layer of finite depth overlying a semi-infinite half-space of monoclinic crystal is solved. The same problem in a hexagonal crystalline medium overlying an orthorhombic, cubic and monoclinic crystals is considered. The dispersion equations are derived and discussed. Some limiting cases are considered. Lastly, the effects of gravity on the wave propagation in crystalline media are investigated.

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Seismograms recorded at selected points along the travel path of a multiply reflected ray can be decomposed into three wavelets that in turn can be used to construct synthetic seismograms for each of the ray turning points. The three wavelets correspond to a source term and two terms that give the impulse response of the medium. The decomposion provides a direct source function estimate if the reflection and conversion coefficients can be determined for the depth at which the source is located. Application of the process to the construction of synthetic seismograms is demonstrated.

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This paper reports a possible effect of attenuative properties of an aftershock region on the nature of seismic body waves which travel through it, by taking as an example of the aftershock events of the Off-Izu Peninsula earthquake, which occurred on May 9, 1974 with magnitude 6.9. For the events in the northwestern end of the aftershock region, the two stations IRT and NHT are chosen for spectral analyses as both stations are located at nearly equal distances (14km) from these events, but the wave path to IRT passes through the aftershock region whereas that to NHT does not. The differences of overall frequency response of the observation systems at NHT and IRT, including station effects, recording, playback, compilation and digitization of the seismic traces on magnetic tape, have been found to be insignificant for the present study.
The ratio of the Fourier transform of direct waves observed at IRT to that at NHT is expected to give us information on the attenuative properties in the aftershock region in terms of Q_I/Q_N, where Q_I implies the dissipation factor in the aftershock region and Q_N that in the undisturbed region of the crust. The spectral ratio was estimated by applying a Wiener filtering. When sampled time-series are short-truncated and random errors are involved in the time-series, the spectral ratio in a least squares sense can be obtained by regarding the observed seismic trace at NHT as an input and that at IRT as an output through the Wiener filter. The Fourier transform of the obtained impulse responses can be considered as the optimum spectral ratio of the transfer characteristics. If we extract the slope κ from the optimum spectral ratio in the graph of amplitude in decibels plotted against frequency, then Q_I/Q_N can be obtained as Q_I/Q_N≅(1-κln10Q_N/20_πT_N)^-1 by taking Q_N as a parameter, where TN denotes the travel time of P-waves from the source to NHT.
The frequency decay in aftershock activities obeys the modified Omori's formula with p=1.3, and the spectral analyses are made for four different stages which can be specified by the decay curve. The most probable value of κ is determined from the superposed spectral ratios of appropriate events in each stage. If Q_N is assumed to be 500-2, 000, then Q_I is shown to be 100-300 in the first stage, one week after the main shock. This low value of Q in the aftershock region still holds in the second stage, three weeks after the main shock. However, Q_I tends to recover and will probably take the value from 300 to 600 in the third stage, five weeks after the main shock. The difference between Q_I and Q_N becomes rather small in the fourth stage, six months after the main shock. The temporal change of the dissipation factor in the aftershock region described above is closely related to the decay curve in aftershock activities.

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