The Theory of Generation of the Rayleigh-waves an Internal Source of Multiplet-type, in an Elastic Body and its Application to Shallow Earthquake. (I)

[摘要] In the observations of shallow earthquakes made at stations near the epicente, we can find sometimes an azimuthal distribution of maximum vertical amplitude. Generally speaking, this distribution shows the maxima at places where the azimuthal angle ω=0 and π, and minima at ω=π/2 and 3/2π. This result of observation is in good agreement with that obtained theoretically considering Rayleigh waves generated by distorsional waves issued from an internal source of doublet in a semi-infinite elastic body. But when the axis of multiplet lies horizontally, the amplitude must become zero at ω=π/2 and 3/2π theoretically exceping the case of point source. Neverthless in actual observations, for example the Tenryûgawa earthquake occurred at Apr. 9th, 1935, the amplitudes at ω=0 and π did not show such a singularity. So that the author has examined whether these amplitude distribution.Can be explained or not by the Rayleigh wave cased by distorsional source of doublet, after Prof. K. Sezawa's method.Taking the free surface at, _??_=0 and the positive sense of the axis _??_ is di_??_ected downwards, the primary waves generated from the multiplet source (γ=0, z=§) may be expressed by in which and j2=ρσ2/μ, and θ1 is the inclination of axis of the multiplet, ωx' is the rotation about the axis perpendicular to the axis of the multiplet. ωy' is the rotation about the axis perpendicular to x-z plane. By the method of induction and proper transformation of axis, we can find the term which does not vanish at ω=π/ 2 and 3/2π, in the case of n=2, θ1=0, and takes the following form:By this term, we know that the Rayleigh wave can also be generated at ω=π/2 and 3/2π, and shows maximum amplitudes when the inclination of axis of multiplet θ1=0.This term is proportional to H1(2)(κγ)/γ, in which κ is the positive root of F (κ)=0. But the Rayleigh wave caused by the dilatational point source contains a term, proportional to H0(2)(κγ) etc. So that, if we know the stress distribution at origin, we shall determine whether the maximum amplitude actually observed in vertical component for shallow earthquakes is due to the former or latter mechanism of generation. But, in this paper, this problem is left till a future investigation.

[学科分类] 大气科学