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Abstract:
Seismic and ultrasound tomography can provide rich information about spatial variations of elastic properties inside a material rendering this method ideal for geophysics and nondestructive testing. These tomographic methods primarily use direct and reflected waves, but are also strongly affected by waves scattering at small scale structures below the resolution limit. As consequence conventional tomography can unveil the deterministic large scale structure only, rendering scattered waves imaging noise. With Adjoint Envelope Tomography (AET) we propose a mathematically rigorous tomographic approach to image the distribution of small scale heterogeneity and absorption. AET is based on a forward simulation of energy propagation using Radiative Transfer Theory to synthesize seismogram envelopes and an adjoint (backward) simulation of the envelope misfit to obtain the gradient for iterative model updates -- in full analogy to full-waveform inversion (FWI). We present the mathematical concept, technical aspects of the simulations and applications of the approach to numerical experiments and an ultrasound experiment in a metric size concrete specimen. The trade-off between the quality factor Q used to quantify intrinsic attenuation and the fluctuation strength ε representing the characteristics of the heterogeneity reflects the similarity of the effects of absorption and scattering have on ballistic waves. We discuss a strategy to reduce the effect of this trade-off in the application of AET by using dedicated time windows for the imaging of both properties.
