On the Effect of the Block Structure of the Earth's Crust on the Propagation of Seismic Waves

Abstract

It is cleared by the recent research that the earth's crust is bulit up of blocks. but still it's sense on seismic waves is scarcely studied. Accordingly, the author tried some discussion on this problem and found that it plays a very important rôle especially in energetic problem of seismic waves, though it is small so long as we deal with the initial motion such as P and S waves. Some of the results obtained are as follows.
1. The so-called Omori's coefficient has never determined distinctly owing to the irregularity of the wave velocity in each block, and the scale of blocks and the irregularity of the wave velocity in each block can be calculated from this amount and they are about as follows,
the scale of blocks 10-40km in shallow crust
400-1000km in deep crust
the irregularity of the
wave velocity 10% in shallow crust
2% in deep crust
2. The analysis of the proper oscillation of the ground was done.
3. The observation of seismic waves has done macroscopically in usual for example, and hence, the calculated values from such observation, the velocity of P or S waves have only the meaning of average, and the idea “macroscopic elastic constant” is introduced corresponding to the macroscopical observation. And it is shown that the macroscopic elastic constant is not always isotropic even it is isotropic microscopically.
4. The so-called anomalous propagation of seismic waves can be explained with this macroscopic elastic constant and the fact that seismic waves propagate earlier to the direction of earth layer than the other coincides with above thought.
5. The macroscopic equations of seismic waves in the medium which has very complexed block structure are deduced, and found following equations for sp_??_cal cases. The first is so-called telegraphic equation which used by Prof. H. Nagaoka to explain the formation of tail of distant earthquake, and the last is the equation of waves in viscoelastic medium which often applied for seismic waves.
6. The decay of the maximum amplitude of seismic waves which calculated from the stand point of the block agrees well with the observed value, and the relation between the absorption coefficient and the period discovered by Dr. K. Wadati can also be explained from this standpoint.
7. The total duration of seismic waves has following nature,
(a) it depends a little on the epicentral distance,
(b) it is proportional to the square of the period of the maximum amplitude,
(c) the distribution of the region where it is smaller than normal coincides approximately with the abnormal distribution of seismic intensity.
8. The nature of (b) in 7. can be explained as the damped proper oscillation of seismic waves in visco-elastic medium which expected from the present point of view, and the coefficient of the visco-elastic constant of the crust has calculated and found that it is about 10^R c. g. s. which agrees with the usual valuc.
9. The energy of seismic waves can propagated not as waves but something like heat in the medium which has very complexed block structure as in actual crust, and the equation of heat conduction is applied for propagation of the energy of seismic waves and the result is
The equation of heat conduction is also applied for the propagation of the energy of the pulsatory oscillation, and it is given by approximately
Both results agree well with the observation at least qualitatively.
10. Some notes on the pulsatory oscillation are also made.