Single-channel time reversal in elastic solids

Reverberant volume time reversal in 3D elastic solids (doped glass and Berea sandstone) using a single channel are presented. In spite of large numbers of mode conversions (compressional to shear wave conversions at the walls), time reversal works extremely well, providing very good spatial and time focusing of elastic waves. Ceramics were bonded to the surface as sources (100-700 kHz); a broadband laser vibrometer (dc-1.5 MHz) was used as detector. Temporal and spatial time-reversal focusing are frequency dependent and depend on the dissipation characteristics of the medium. Doped glass (inverse dissipation Q between 2000 to 3000) shows time-reversed spatial focal resolution at about half of the shear wavelength. The Berea sandstone (Q = 50) yields a wider focusing width (a bit more than the shear wavelength) due to its lower Q. Focusing in the doped glass is better because the time-reversal (virtual) array created by wave reflections is larger than in the highly attenuating sandstone. These are the first results reported in granular media, and are a first step toward geophysical and field applications.