Relation between coda-Q and stress loaded to an elastic body ~state parameters derived by stochastic measurement~

Coda-wave is the summation of the scattered waves caused by scatterers such as cracks and medium inhomogeneities in the rock. Coda-wave is composed of P-wave, S-wave and variety of other waves. When the spatial scale of inhomogeneities become comparable with seismic wavelength, it becomes very difficult to analyze the coda-wave quantitatively in terms of the location of scatterers, scattering mechanisms, etc. As a consequence, it is very hard in general to apply a method of deterministic structural analysis to use coda waves. For inhomogeneous meda, it is natural to deal with stochastic methdologies to interpret seismic data. In this regard, coda-Q, i.e., parameters of attenuation or decay of energy scattered by medium inhomogeneities, has been frequently used as a stochastic measure of the medium in which seismic waves propagate. Since objectives of recent structural surveys include spatiotemporal or time-lapse variation of physical properties of underground medium, we would like to exploit the stochastic parameters if these parameters reflect any changes of physical state of the medium. The purpose of this study is to relate this parameter to non-stochastic propertyies of the underground property. In this study, we performed a simulation on seismic wave propagation in an elastic medium using a two-dimensional finite difference method. In our numerical calculatoins, seismic scatters were randomly placed in the simulation model. Coda-Q values are estimated using simulated waveforms for a set of various loading stresses that was applied to the model. Since the scatters are displaced due to loaded stresses, Coda-Q values are obtained against loading stresses and directions. In order to estimate the magnitude of stress and the direction of the principal stress, we used a variation of the envelope of coda-wave. Analysis of coda-wave revealed proportional relations between the loading stress and attenuation factor of the envelope. For the direction of the principal stress, we may be able to use a tendency in which atteuation factor increases with the magnitude of loading stress. In conclusion, we would like to propose that the loading stress could be estimated if we obtain the change of attenuation factors varying with loaded stresses. It means that non-stochastic physical-state properties could be obtained from coda-wave and will lead to more clear deterministic model essential for engineering application of wave theories.