A. Ribodetti et al., Asymptotic viscoacoustic diffraction tomography of ultrasonic laboratory data: a tool for rock properties analysis, GEOPHYS J I, 140(2), 2000, pp. 324-340
This paper presents an application of 2.5-D asymptotic viscoacoustic diffra
ction tomography to ultrasonic data recorded during a physically scaled lab
oratory 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 th
e relation between the scattered wavefield and the velocity and Q perturbat
ions. The perturbations are inferred from the data by an iterative (linear)
quasi-Newtonian algorithm.
The inversion formula was specifically developed to account for the acquisi
tion geometry designed in this study. The derivation of the Hessian operato
r shows that, for this acquisition, the velocity and Q perturbations are th
eoretically 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 pos
t-processing procedure for the tomographic images to remove the source sign
ature and to estimate the absolute Values of the velocity and the attenuati
on 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 tar
get. We obtained an excellent match between the observed data and the visco
acoustic ray-Born synthetics. The match obtained with the viscoacoustic rhe
ology 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, althoug
h we had no quality control with regard to these results (the rheological p
roperties of the material used in this study were unknown). The results sug
gest that the uncertainty of the velocity measurement is lower than that fo
r 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 s
urface seismic data requires further work.