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Wave localization characteristics in the time domain.

We present an analytical solution to the problem of pulse backscattering from a randomly stratified half-space. It is shown that the power spectrum p for the backscattered wave is characterized by a function of I, where X=(distance traveled by the pulse at time r)/(the frequency-dependent localization length). For the matched-impedance and the total-reflection boundary conditions, p is given by t/(I +t) 2 and 4X, respectively. Implications for the time-domain measureinent of the localization length are discussed.