Page 7 - Winter 2008

TIME REVERSAL
Brian E. Anderson, Michele Griffa, Carène Larmat, Timothy J. Ulrich, and Paul A. Johnson Geophysics Group EES-11, Los Alamos National Laboratory Los Alamos, New Mexico 87545
This article provides an historical
overview of Time Reversal (TR),
introduces its basic physics,
addresses advantages and limitations,
and describes some applications of this
very active research area of acoustics. In
the Geophysics Group at the Los Alamos
National Laboratory, we conduct studies
of TR of elastic waves in solids. Our
work includes application of TR to non-
destructive evaluation of materials, as
well as to earthquake source characteri-
zation, and ground-based nuclear explo-
sion monitoring. We emphasize the term
elastic waves here to underscore that we
include both compression and shear waves, in contrast to purely acoustic waves that are only compressional.
Introduction and a brief history
Imagine the following movie: drop a pebble into a pond, and
ripples propagate outward from the location where the peb-
ble strikes the water (see Fig. 1). Now, stop the movie, and
reverse it. The ripples propagate backwards and eventually
converge upon the original source location reproducing the
impulse due to the pebble impact that originally created the
ripples. Conceptually, this is TR. Meaning, TR can be
thought of as a method that uses backward propagation of
waves to focus wave energy onto a specific location in space
1
Today we can perform time reversal, leading not to the foun- tain of youth, but to very interesting physics and applica- tions. The concept as applied to waves dates back a number of years. In 1965, Parvulescu and Clay2 studied what they termed a matched signal technique. In their experiment, they transmitted a signal from a source to a receiver, time reversed the received signal and broadcast it from the source to the receiver again. Parvulescu and Clay’s experiment was the first demonstration of TR. This matched signal tech- nique compensated for the coloration of the received signal due to reverberation (multi-path distortion) thereby improving the signal to noise ratio. In addition, the matched signal technique also focused the arrival of the waves in space. During the 1970s and 1980s, researchers, first in the Soviet Union, and later in the United States, created a unique mirror, called an Optical Phase Conjugator (OPC). This mir- ror provided the means to return an incoming wave back
3,4
and time.
Reversing time has been a compelling idea for ages.
Thus OPCs are similar to TR in that they reverse wave energy but they differ from TR in that they function only with quasi-monochromatic waves while TR functions with waves of any frequency bandwidth.
along the same incident ray path.
“Reversing time has been a compelling idea for ages. Today we can perform time reversal, leading not to the fountain of youth, but to very interesting physics and applications.”
TR was again studied in 1991 in under- water acoustics to correct for multi-path distortion and to improve the focusing of transmitted acoustic energy into a nar-
5
row beam. An important practical out-
come of this work was that TR provided the means to track a moving target. Advances in microelectronics and array technologies during the beginning of the 1990s, coupled with new theoretical tools, led to the development of the acoustic Time Reversal Mirror (TRM)6-8 by Fink and collaborators at the University of Paris VII, Laboratoire Ondes et Acoustique (LOA).
Let us return to the mechanics of how the TR process is conducted experimentally and how it differs from the movie of a pebble dropped in a pond. Normally, TR consists of a forward propagation step and a backward propagation step. In the forward propagation step, a source emits waves that travel through a medium, which are then detected by one or more receivers. The signals detected at each receiver are then reversed-in-time and rebroadcast from their respective receiver positions. The set of receivers makes up what is referred to as a TRM. The wave paths that were tra- versed in the forward propagation are also traversed in the backward propagation. The back-propagating waves simul- taneously arrive at the original source location in phase, producing a time reversed focus, which is a reconstruction of the original source, albeit reversed in time.
To perform TR for a pebble dropped in a pond, in an attempt to exactly duplicate the reversed movie playback, one would need to have an infinite set of receivers that surround the drop location to detect the ripple motion. The detected
Fig. 1. Snapshot of the ripples created from a pebble dropped into a pool of water.
Time Reversal 5