Numerical studies of the coda falloff rate of multiply scattered waves in randomly layered media

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Abstract
We study the falloff rate of the coda of acoustic signals after transmission (net forward-scattering) through a stack of thin layers (compared to the wavelength of the signal) with randomly fluctuating impedances. We find that the change in coda energy with time after the first arrival can be modeled as a decaying exponential with falloff rate c∝ω−1x−3/2σ−1 where ω is the center frequency of a frequency band of the coda, x is the source-receiver distance, and σ is the standard deviation of the impedance fluctuation in a band centered about 2 ω. The dependence of the falloff rate of net forward-scattered coda on ω and σ is opposite to that of single back-scattered coda, and distinguishes the two types of scattering.