Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous lithosphere

A unified model is proposed for explaining the frequency dependent amplitude attenuation and the coda wave excitation on the basis of the single scattering process in the randomly inhomogeneous lithosphere. Adopting Birch's law and a direct proportion between density and wave velocity, we statistically describe the inhomogeneous medium by one random function characterized by the von Karman autocorrelation function. We calculate the amplitude attenuation from the solid angle integral of scattered wave energy on the basis of the Born approxiimation after subtracting the travel-time fluctuation effect caused by slowly varying velocity inhomogeneities. This subtraction is equivalent to neglect energy loss by scattering within a cone around the forward direction. The random inhomogeneity of the von Karman autocorrelation function of order 0.35 with the mean square fractional fluctuation of 7.2×10^–3 1.3×10^–2 and the correlation distance of 2.15.1 km well explains observed backward scattering coefficientg and the ratioQ _P ^–1 /Q _S ^–1 , and observed and partially conjecturedQ _S ^–1 for frequencies between 0.5 Hz and 30 Hz.