Probe Waveforms and Deconvolution in the Experimental Determination of Elastic Green's Functions

We propose a new time domain method for the experimental determination of the "impulse response" of linear systems. The technique centers around the use of specifically designed probe waveforms. These waveforms are particular C∞ approximations to the Dirac δ-function and the Heaviside unit step function, and lead to a subsequent time domain deconvolution problem which can be implemented as a Cauchy initial value problem. This approach allows for continuous deconvolution, a powerful option in the presence of noise. We orient the discussion to the context of acoustic emission and elastic Green's functions, and present several numerical reconstructions of sharp signals from smooth synthetic data.