CodaQin two-layer random media

Abstract

Using the indirect boundary integral scheme for multiple scattering of seismic waves developed by Benites, Aki & Yomogida (1992), we compute SH-wave seismograms and measure frequency-dependent characters of coda Q in 2-D random media with a flat layer over a half-space. Many circular cavities are randomly distributed in both the upper layer and the half-space, down to a certain depth (called the lower layer), simulating the upper and lower crusts. The scattering strength and the intrinsic attenuation, Qi, are varied for each layer, and the S-wave velocity is prescribed to be constant throughout the medium so that the computation of Green's functions for the boundary integral is simple. Considering two basic parameters of our random media, scattering strength and intrinsic attenuation Qi, we represent the shallow-earth structure by an upper crust with large intrinsic attenuation and a lower crust with effective scatterers. Computations of coda Q for several values of those parameters show that when the scattering is relatively strong, coda Q-1 is roughly independent of frequency. This result differs from the case of a uniformly random model where coda Q-1 peaks around kd = 2, where k is the wavenumber and d is the cavity diameter. If the scattering strength in the lower layer is large enough for multiple scattering to dominate over single scattering, coda Q-1 strongly depends on the intrinsic attenuation in the lower layer, Q-1i2, and these two values (coda Q-1 and Q-1i2) become similar. We explain this feature as follows. Waves scattered in the upper layer attenuate quickly due to high intrinsic attenuation and contribute little to the coda envelope in a time window starting at twice the traveltime of the direct wave. Multiply scattered waves in the lower layer eventually arrive at the surface, dominating the coda envelope, which decays at a rate determined by the intrinsic attenuation in the lower layer, Q-1i2. The hypothesis that the temporal decay of coda is controlled not by the scattering but by the energy leakage into a ‘transparent’ underlying mantle is ruled out in general by our numerical simulations, except at low frequencies. Although our model may be too simple to simulate the details of observed coda Q, coda Q is likely to reflect the intrinsic attenuation in the Earth's lower crust