Geophysical tomography by viscoacoustic asymptotic waveform inversion of ultrasonic laboratory data

In this paper, we develop viscoacoustic asymptotic waveform inversion to es timate velocity and attenuation factor Q of a medium. Then, we present an a pplication to laboratory ultrasonic data. Viscoacoustic asymptotic waveform inversion is performed using an optimizat ion approach based on the iterative minimization of the mismatch between th e seismic data and the computed response. To obtain a fast analytical imagi ng procedure, we include an asymptotic theory for attenuation in a lineariz ed inverse scattering formulation. The forward modeling is solved by the Bo rn approximation for a smooth and attenuative background medium. An asympto tic ray tracing method is used to calculate travel time, amplitude and atte nuation between source, receiver, and scattering points. The inversion form ula was specifically developed to account for the acquisition geometry desi gned in this study. Viscoacoustic asymptotic inversion is applied to ultrasonic data recorded d uring a physical-scaled laboratory experiment. This scaled experiment was u sed to test the reliability of our method when applied to a real dataset to estimate the 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 v iscoacoustic Ray-Born synthetics. The match obtained with a viscoacoustic r heology 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 p roperties in the frame of the laboratory experiment.