Asymptotic waveform inversion for unbiased velocity and attenuation measurements: numerical tests and application for Vesuvius lava sample analysis

SUMMARY Recovering physical properties such as attenuation and velocity of the Earth's heterogeneities is as important as recovering the shape and the surface reflectivity of the heterogeneities themselves. A reliable estimate of attenuation in the Earth is necessary to improve our knowledge of subsurface physical properties like the degree of fluid saturation. Moreover the attenuation may also be relevant to ‘ bright spot ’ studies in reservoir characterization. Within this context, this paper presents applications of asymptotic viscoacoustic waveform inversion to synthetic and ultrasonic laboratory data recorded to characterize the velocity and attenuation of a lava sample collected on the Vesuvius volcano. The waveform inversion method is based on a combination of ray theory and the Born approximation to linearize the relation between the scattered wavefield and the velocity and attenuation perturbation models. The iterative linearized inverse problem is solved using the classic least‐squares criterion. Asymptotic local analysis of the Hessian operator published in a previous paper by Ribodetti et al. showed the theoretical uncoupling between the velocity and attenuation parameters. The method is first applied to realistic and calibrated synthetic data computed using the discrete boundary integral wavenumber method. The reliability of decoupling between the velocity and attenuation parameters during the inversion is confirmed through two case studies corresponding to a local velocity heterogeneity without any associated attenuation perturbation and a local attenuation heterogeneity without any associated velocity perturbation, respectively. Second, the method is applied to an ultrasonic laboratory data set that was recorded to determine the velocity and attenuation of a tephrite rock sample collected on the Vesuvius volcano. A velocity of 3200 m s −1 and an attenuation factor of 480 were found, which are consistent with the geological nature of the analysed sample. The numerical tests presented in this paper validate former theoretical development of asymptotic waveform inversion for characterization of viscoacoustic media. Application to ultrasonic data confirms that the proposed method can be used for reliable estimations of the velocity and attenuation properties of rock from laboratory experiments. Comparable methodology can be extended for use with data from multichannel seismic reflection surveys, providing an opportunity to compare results of laboratory and field experiments.