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Random inhomogeneities in the lithosphere have been investigated through the analysis of coda waves that are thought to be generated by the inhomogeneities. The power spectral density of upper crustal inhomogeneities measured directly using borehole logs obeys power law for a wide range of wavenumber, which is the characteristics of the exponential or the von K~rman autocorrelation function. The methods preferentially used for the coda analysis are phenomenological modeling based on the energy transport theory or stochastic simulation of wave propagation based on the Born approximation in random media. The parameters estimated from the methods are the scattering coefficient and coda attenuation (Q-1c) of scattering media or the fractional fluctuation of seismic wave velocity and the correlation length of random inhomogeneities. Although the frequency and lapse time dependence of Q-1c has been widely recognized from the numerous works conducted in the last two decades, the physical meaning of Q-1c and its lapse time dependence have not yet been clarified completely. Some recent works tried to understand it by considering layered structures with different values of scattering coefficient and intrinsic attenuation. The estimated range of fractional velocity fluctuation and correlation length is 1-8% and 0.15-1.0 [km] in the crust and 2-8% and 1-20 [km] in the upper mantle, respectively. The magnitude of fractional fluctuation shows little difference between the crust and the upper mantle, however, the correlation distance exhibits large difference that reaches one order of magnitude. In addition, the horizontal correlation length is much longer than the vertical one, forming the anisotropic inhomogeneities in the lithosphere. The recent observations of high-frequency teleseismic Pn gave an additional evidence of random inhomogeneities in the upper mantle. Thus the coda methods have great advantage to get stochastic insight into realistic image of the lithosphere.

Random Inhomogeneities in the Lithosphere Inferred from Coda Analysis