Pulse propagation in time dependent randomly layered media

TL;DR

This paper extends the understanding of wave pulse stabilization to time-dependent randomly layered media, showing how slow changes preserve pulse shape while rapid fluctuations alter both shape and arrival times.

Contribution

It introduces a new integral equation for wave front propagation in time-dependent media, expanding previous models to account for temporal fluctuations and providing explicit examples.

Findings

Slow media changes do not affect the pulse shape.

Rapid media fluctuations influence pulse shape and timing.

Explicit solutions are possible in certain simplified media cases.

Abstract

We study cumulative scattering effects on wave front propagation in time dependent randomly layered media. It is well known that the wave front has a deterministic characterization in time independent media, aside from a small random shift in the travel time. That is, the pulse shape is predictable, but faded and smeared as described mathematically by a convolution kernel determined by the autocorrelation of the random fluctuations of the wave speed. The main result of this paper is the extension of the pulse stabilization results to time dependent randomly layered media. When the media change slowly, on time scales that are longer than the pulse width and the time it takes the waves to traverse a correlation length, the pulse is not affected by the time fluctuations. In rapidly changing media, where these time scales are similar, both the pulse shape and the random component of the arrival time are affected by the statistics of the time fluctuations of the wave speed. We obtain an integral equation for the wave front, that is more complicated than in time independent media, and cannot be solved analytically, in general. We also give examples of media where the equation simplifies, and the wave front can be analyzed explicitly. We illustrate with these examples how the time fluctuations feed energy into the pulse.