Full waveform inversion of a 3-D source inside an artificial rock

A full waveform inversion of the kinematics of a 3-D source inside an artificial rock plate is presented. The source is provided by a piezoelectric disc embedded inside a gypsum plate, excited by an arbitrary electrical signal. Elastic waves emitted from the source propagated through the plate and were recorded by an array of wide-band high-fidelity microseismic displacement sensors. These microseismic data are then inverted by deconvolving the recorded signals with the theoretical Green's functions to obtain the kinematics of the source modeled by force couples. The force time functions thus inverted are justified qualitatively by the known mechanical behavior and compared quantitatively to simplified electro-acoustic equations. For the first time, the combined use of a wide-band high-fidelity sensor, Green's functions incorporating Q damping, effective point source theory, and linear deconvolution yield physically justified time functions of the source kinematics.