Asymptotic viscoacoustic diffraction tomography of ultrasonic laboratory data:: a tool for rock properties analysis

This paper presents an application of 2.5-D asymptotic viscoacoustic diffraction tomography to ultrasonic data recorded during a physically scaled laboratory experiment. This scaled experiment was used to test the reliability of our method when applied to a real data set to estimate the attenuation factor Q. Diffraction tomography relies on ray theory to compute the Green functions in a smooth background medium and on the Born approximation to linearize the relation between the scattered wavefield and the velocity and Q perturbations. The perturbations are inferred from the data by an iterative (linear) quasi-Newtonian algorithm. The inversion formula was specifically developed to account for the acquisition geometry designed in this study. The derivation of the Hessian operator shows that, for this acquisition, the velocity and Q perturbations are theoretically decoupled. The processing of the data was split into two steps: first, we applied the tomography to the data without deconvolving them. Second, we designed a post-processing procedure for the tomographic images to remove the source signature and to estimate the absolute Values of the velocity and the attenuation factor Q. At the conclusion of the first step, both the velocity and the 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 the viscoacoustic rheology was significantly better than for a purely acoustic one. In the second step, the post-processing allowed us to recover the shape of the target. We estimated the absolute values of the velocity and Q, although we had no quality control with regard to these results (the rheological properties of the material used in this study were unknown). The results suggest that the uncertainty of the velocity measurement is lower than that for Q. The application presented in this study suggests that the procedure that we designed (experimental set-up, tomography, post-processing) can be useful for estimating rock properties in the framework of a laboratory experiment. Generalization of the method to other acquisition configurations such as surface seismic data requires further work.