Imaging of Small-Scale Heterogeneity and Absorption Using Adjoint Envelope Tomography: Results From Laboratory Experiments

Abstract

To complement the information provided by deterministic seismic imaging at length scales above a certain resolution limit we present the first application of adjoint envelope tomography (AET) to experimental data. AET uses the full envelopes of seismic records including scattered coda waves to obtain information about the distribution of absorption and small-scale heterogeneity which provide complementary information about the investigated medium. Being below the resolution limit this small-scale structure cannot be resolved by conventional tomography but still affects wave propagation by attenuating ballistic waves and generating scattered waves. Using ultrasound data from embedded sensors in a meter-sized concrete specimen we image the distribution of absorption and heterogeneity expressed by the intrinsic quality factor Q−1 and the fluctuation strength ɛ that characterizes the strength of the heterogeneity. The forward problem is solved by modeling the 2-D multiple nonisotropic scattering in an acoustic medium with spatially variable heterogeneity and attenuation using the Monte-Carlo method. Gradients for the model updates are obtained by convolution with the back-propagated envelope misfit using the adjoint formalism in analogy to full waveform inversion. We use a late coda time window to invert for absorption and an earlier time window to infer the distribution of heterogeneity. The results successfully locate an area of salt concrete with increased scattering and concentric anomalies of intrinsic attenuation. The resolution test shows that the recovered anomalies constitute reasonable representations of internal structure of the specimen.