On the Mechanism of Earthquakes and Propagation of Seismic Waves

Abstract

In the present paper are treated the problems concerning the mechanism of earthquakes from the stand point of the seismological observation of earthquake waves. First of all the importance of generation of a fault is discussed for the occurrence of earthquakes. Then the fact so-called “quadrant distribution of first motion” which is observed in almost all cases of earthquakes of both shallow and deep origins can be considered as a naturally expected phenomenon if earthquakes occur first in the crust by breaking, in other words by fault, and the conservation of angular momentum be hold. Hitherto, oscillators are sometimes considered at the source of earthquakes to interpret the distribution of the first motion, such as “center of compression or dilatation” “doublet with moment” or “a pair of doublet with (without) moment” etc. Yet we have perhaps never heard of the simple explanation mentioned above that the distribution of the first motion can be interpreted by the motion caused by a doublet (with moment) and adding to it by that of the opposite sign caused by the reaction of the former.
Although the first motion of earthquakes can be considered to be caused by a pair of doublet oscillator, it is quite another phenomenon as to the crustal deformation observed in the epicentral region where sometimes a remarkable fault may be found in the case of large earthquakes. The latter phenomenon cannot be satisfactorily interpreted by the assumption that a pair of doublet nuclei of force act in the crust, but rather explained by the assumption that there exists only one doublet nuclei of force in the crust, each of them lies on each side of the fault surface in a certain depth.
A trial is made to obtain mathematically the crustal deformation at the surface occurred near the fault by a great earthquake. For the simplest case, the following assumptions are made. In a semi-infinite elastic body, surface. being z=0, the fault surface y=0 and z axis taken positive downwards, a nucleus of force exists at (0, -b, b.) and a force X₀ acts horizontally to x-direction, another nucleus at (0, -b, b), force acts there -X₀. As boundary conditions, stress must be vanish at z=0 and also at the fault surface y=0. The method used for this calculation is similar to that made by F. I. W. Whipple (M. N. of R. A. S. Geo. Sup. Vol. 3, No.6) and the approximate solutions obtained. The crustal deformation thus obtained resembles much to that actually observed.
In the last part, the problem of the wave propagation of shallow earthquakes is treated. Dr. H. Nakano treated theoretically this problem assuming oscillators in a general form at the origin. Dr. H. Honda proved that the actually observed result of seismic waves agrees just well with a special case of this theoretical result. Of couse this proof is good in general tendency but if we examine precisely the observed result, it may be found that the problem of propagation of seismic waves issued from a very shallow origin can not be treated under such a simple conditions as assumed by Dr. Nakano that the medium is uniform and perfect elastic and the origin lies just on the surface. He obtained that the amplitude of solid seismic waves decreases with epicentral distance as A_P∝Δ^-2, A_T∝^-1 in their principal directions respectively, and this theoretial result ascertained by Dr. Honda using many observational data. But in the practical case, the earth's crust is not homogeneous, the seismic-focus does not lie strictly on the surface and therefore the conditions of wave propagation must be somewhat different from this theoretical result.