Geophysical tomography by viscoacoustic asymptotic waveform inversion of ultrasonic laboratory data

In this paper, we develop viscoacoustic asymptotic waveform inversion to estimate velocity and attenuation factor Q of a medium. Then, we present an application to laboratory ultrasonic data. Viscoacoustic asymptotic waveform inversion is performed using an optimization approach based on the iterative minimization of the mismatch between the seismic data and the computed response. To obtain a fast analytical imaging procedure, we include an asymptotic theory for attenuation in a linearized inverse scattering formulation. The forward modeling is solved by the Born approximation for a smooth and attenuative background medium. An asymptotic ray tracing method is used to calculate travel time, amplitude and attenuation between source, receiver, and scattering points. The inversion formula was specifically developed to account for the acquisition geometry designed in this study. Viscoacoustic asymptotic inversion is applied to ultrasonic data recorded during a physical-scaled laboratory experiment. This scaled experiment was used to test the reliability of our method when applied to a real dataset to estimate attenuation factor Q. The results show that both the velocity and Q tomographic images allowed one to delineate the gross contour of the target. We obtained an excellent match between the observed data and the viscoacoustic Ray-Born synthetics. The match obtained with a viscoacoustic rheology was significantly better than for a purely acoustic one. The application presented in this paper suggests that the procedure that we designed (experimental setup, tomography) can be useful to estimate rock properties in the frame of a laboratory experiment.