Relation between direct waveQand codaQ:a numerical approach

Abstract

S U M M A R YUsing the boundary integral method to simulate SH waves numerically in 2-D homogeneous full-or half-space media with randomly distributed cavities, we compare the amplitude attenuation of direct waves with the temporal decay of the coda. The boundary integral method includes the effect of any degree of multiply scattered waves for a wide frequency range, up to wavelengths smaller than the size of the cavities. We consider seismograms on the free surface so that heterogeneities exist only on one side of the receivers, a situation that resembles actual seismic observations. Seismograms are computed for a vertically incident plane wave and for an isotropic line source. In both cases, the value of Q-' as a function of kd, where k is the wavenumber and d is the cavity diameter, peaks around kd = 2 for the direct wave, which is consistent with some single-scattering models. Coda Q-' determined by the temporal decay of the coda envelope agrees well with Q-' for the direct wave for models with a root-meansquare fluctuation of velocity, Q, of about 10 per cent in a half-space. On the other hand, the coda Q-' is systematically larger than the direct wave Q-' in full-space models, that is, without the inclusion of the reflection at the free surface. When the cavity density is doubled (a>20 per cent), the coda energy increases rapidly and its temporal decay decreases, so that coda Q-' becomes smaller than the direct wave Q-', even for full-space models. With a smaller value of cr (about 5 per cent), the coda decays rapidly and the relation between the two types of Q-' is reversed: the coda Q-' becomes larger than the direct wave Q-'. By comparing results from seismograms composed only of singly scattered waves with those that include multiply scattered waves, we can compare the relative contribution of each singly and multiply scattered wavefield to the two measures of Q. Single scattering mainly determines both the direct wave Q-' and the coda Q-' for the smallest value of a, while the values of both kinds of attenuation, particularly the direct wave Q-', are strongly affected by multiple scattering when a is large. Our results imply that a reasonable estimate of scattering attenuation can be obtained by measuring the temporal decay of the coda, if the scattering character of the Earth is similar to our models with a Q of around 10 per cent, where the single scattering is found to be dominant.

Spatial variation in coda Q in the northeastern part of Niigata–Kobe Tectonic Zone, central Japan: implication of the cause of a high strain rate zone

“…A numerical simulation shows that the most effective scattering occurs in the case that the wavelength is twice the characteristic scale of the scatterer (Yomogida and Benites 1995). Applying this relation, together with the average S-wave velocity at a 10 km depth and at a 25 km depth (Nakajima and Hasegawa 2007), we can estimate a characteristic scale length is to be 0.4-0.9 km at a 10 km depth and 1-2 km at a 25 km depth.…”

A new view of earthquake and volcano precursors

“…According to Yomogida and Benites (1995), the scattering of seismic waves by a fracture is most effective when the wave length is comparable to twice the characteristic length of the fracture. The seismic wave length for which the change in coda Q and N (Mc) for California.…”

Envelope syntheses of cylindrical vector-waves in 2-D random elastic media based on the Markov approximation

“…Complex waveforms have been deterministically and numerically simulated in inhomogeneous media (Frankel and Clayton, 1986;Yomogida and Benites, 1995). On the other hand, the radiative transfer theory with the statistical characterization of medium inhomogeneity has been often used as the basic framework of the envelope synthesis of high-frequency seismograms.…”