Application of the telegraph model to coda Q variations in southern California

Abstract

We examine waveforms and data used to construct coda magnitude in southern California to estimate the spatial variation of coda Q and its dependence on frequency. Our analysis combined with independent borehole data suggests that coda is mainly generated by multiple scattering in the upper few kilometers of the crust where large impedance contrasts occur because of surface layering or fracturing. The ubiquitous observation that coda Q increases with frequency is explained as arising from multiple reverberations in the upper crust. We suggest that the telegraph model that has been successfully used to describe reflection seismogram multiples in the exploration industry may also apply to earthquakes. Under this model the apparent increase of Q with frequency is due to trapping of high-frequency energy in the upper crust. This behavior is expected if the associated reflector series has an exponential autocorrelation function, a feature of the telegraph model. At lower frequencies, trapping is less efficient. The combined effects give rise to an apparent absorption band that we suppose is superimposed on frequency-independent intrinsic attenuation. Maximum apparent attenuation occurs at wavelengths equal to the dimensions of the regions of upper crust that contain the scattering layers. At lower frequencies, trapping is less effective, and attenuation decreases as the longer-wavelength waves sample the deeper crust and upper mantle where because of overburden pressures, acoustic impedance contrasts are less extreme. By taking spectral ratios of coda waves to direct S, we estimate that intrinsic Q is high (∼3000) and that coda may be modeled as multiple scattered S waves in a region of anisotropic scattering. The exponential decay of the coda is a result of the perfectly reflecting surface of the Earth with backscattering from random near-surface layers causing progressive leakage and loss of energy downward into the more transparent lower crust and mantle.

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