Ultrasonic wave propagation in heterogeneous elastic and poroelastic media

The influence of small- and large-scale heterogeneities on an incident wavefield was investigated in ultrasonic experiments. The field generated by conventional piezoelectric transducers was investigated separately. It was confirmed that the far-field diffraction was correctly predicted by Fraunhofer theory, but that the near-field diffraction exhibited significant deviations from the Fresnel theory. These deviations are attributed to the assumption that the source oscillates uniformly over its surface, which seems unrealistic for the actual transducers. Small rubber and teflon spheres with velocities in the range of the surrounding water acted as small-scale heterogeneities in an otherwise homogeneous medium. The influence on amplitude and traveltime was measured with a needle hydrophone, a focused transducer was utilized for wave generation. These experiments successfully validated first-order scattering theory where a Maslov correction is applied for non-linear effects resulting from a strong contrast between sphere and background medium. Ray theory was found to be unsuitable to properly predict the measured phenomena. Large-scale heterogeneities were also investigated. Ultrasonic reflection and transmission experiments at different angles of incidence were carried out on plane-parallel layers of aluminum. Here the signal was generated by a conventional plane piezoelectric transducer source and the recording was by means of an identical receiver. Unlike in the conventional bulk-wave transit-time method where successive reverberations within the sample are separated in time, we captured all direct and scattered energy by means of a special recording technique where the individual traces are added and compared with traces recorded in absence of the sample. We found that this recording technique gives much improvement over single-position measurements at normal incidence and is ideally suited for full wavefield analysis. Excellent agreement between experiment and Thomson-Haskell theory was obtained. Consequently, the same measurement technique was applied to plane-par-allel layers of poro-elastic materials. The samples were made out of sintered glass powder and had different grain sizes. The Thomson-Haskell theory was extended and new analytical expressions for the reflection and transmission coefficients were derived. These expressions were validated through comparison with the Kennett reflectivity method and stability regimes were determined. Effective medium parameters were obtained through inversion of transmission measurements. These effective parameters were found to be in good agreement with the conventional laboratory values although there was a systematic error in the permeabilities. Both the reflection and transmission experiments were generally found to be in good agreement with theoretical predictions although significant deviations were found for samples with larger grains and for larger angles of incidence. In the former case, deviations from continuum Biot theory are observed, whereas in the latter case the effect of reflections from the edges of the samples played an important role.

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