CHARACTERISTICS OF EARTHQUAKE GROUND MOTION PROPAGATING THROUGH THE MEDIUM WITH RANDOM GEOLOGICAL PROPERTIES

Abstract

In order to predict the reliable earthquake damage of structural systems, it has become recently important to acquire some indications of the correspondence between the physical conditions associated with wave traveling path and source movement and the principal quantities for aseismic design of structure such as spectral characteristics, peak ground motion and duration time. The multiple reflection and refraction of traveling wave motions due to the irregular property and topography of transmission path give the spatial and time fluctuations on their amplitude and phase characteristics. It is so called multiple scattering effect which would play important role on the formation of the characteristics of earthquake ground motion. This paper investigates statistically the effect of the irregular geological properties of transmission path on the characteristics of earthquake ground motion propogating from the focus of an earthquake to the observation point. It seems, however, to describe the soil ground with irregular geological properties by a random medium because it is very difficult to evaluate the actual distribution of the geological characteristics of wave traveling path. The problem of the radiation intensity of earthquake ground motion in an elastic continuous random medium is examined by applying the smoothing approximation method proposed by J. B. Keller. The multiple scattering effect of wave motion is estimated equivalently by the effective wave numbers of longitudinal and transverse waves which are derived from the stochastic dispersion equation. The fluctuations of average surface displacements due to a point source in a semi-infinite random medium are investigated comparing with those of a non-random medium according to the variable inhomogeneity correlation length and perturbating parmeter. The analyses and illustrative examples suggested the following conclusions : 1) When wave motion propagates in a random medium, the main influence contributed from fluctutions due to the superposition of the scattered waves and primary wave seems to be the multiple scattering. The phase velocity of a random medium becomes generally smaller than that of a non-random medium by multiple scattering effect which depends on inhomogeneity correlation length, wave number and traveling distance. Whereas, the inverse tendency is pointed out for the wave motion propagating in a viscoelastic medium. 2) The multiple scattering produces the apparent damping effect on the amplitude characteristics of traveling wave motion even if the medium has no damping mechanism. It is typically multiple scattering effect. This apparent damping capacity becomes generally larger as inhomogeneity correlation length and wave number increase. 3) From the fact that multiple scattering effect makes wave length broaden and amplitude characteristics of average surface displacement decreasing, the inhomogeneity correlation length of transmission path would become important parameter to describe the spectral characteristics and the peak earthquake ground motions. 4) Q-value is generally evaluated from the internal friction damping characteristics of transmission path. Since the apparent damping due to multiple scattering gives tremendous effect on the evaluation of Q-value, the attenuation mechanism should be investigated on the basis of not only frictional hysteretic dissipation damping but apparent damping associated with scattering. 5) If the same autocorrelation function is assumed for all random variables describing the inhomogeneity of transmission path, the scattering effects contributed from their fluctuations show almost same tendency with respect to wave propagation distance, respectively. 6) The multiple scattering gives stronger fluctution to rotational wave motion than to dilatational wave motion for the same frequency range and autocorrelation function concerning with random inhomogeneity. 7) That

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