Elastic immersive wave experimentation

Abstract

Elastic wave propagation in earth materials is often studied through physical experiments in a size-limited laboratory. Such studies have strong limitations because waves reflect and mode convert at the closed boundary of an experiment and mask the waves related to the scattering within the materials. This problem is commonly mitigated by using waves at high frequencies (e.g., >1 MHz) in conventional laboratories. However, such an approach is not useful for studying wave phenomena that strongly depend on frequency. This thesis outlines a novel method of elastic immersive wave experimentation to overcome the boundary-related challenges in 3D elastic wave experiments. The boundary reflections and mode conversions are canceled by arrays of active sources deployed at the traction-free surface of the object. Furthermore, these sources can emit waves, which represent the interactions of the physical medium with a virtual exterior. Elastic immersive wave experimentation paves the way to the next generation of laboratories, in which wave experiments can be carried out with (1) an extended volume, and (2) significantly lower frequencies (1-20 kHz) than commonly used in conventional laboratories (> 1 MHz). Due to the inaccessibility of the interior of a solid, the desired time signatures of the boundary sources in an elastic immersive wave experiment have to be sought from the wavefield recordings made at the boundaries. I propose an iterative method, which involves alternating a physical experiment for recording free-surface data, a numerical simulation in which the data are injected along a transparent surface for separating outgoing wavefield constituents, and another numerical simulation for extrapolating the separated outgoing wavefield into a virtual environment. These two numerical simulations, implemented through a finite-difference (FD) method, are used to calculate source signatures corresponding to canceling boundary reflections and generating physical-to-virtual interactions. I propose a method of multiple point sources to implement FD-based wavefield injection and extrapolation in elastic media. I propose internal absorbing boundary conditions, which are incorporated into both the FD simulations to allow the physical experiment to involve an unknown interior medium. When using the iterative method, unwanted boundary reflections are canceled by active sources during a physical experiment. The same effect can be achieved by removing the imprints of the boundary reflections from recorded data afterward using a method of multidimensional deconvolution, which is applied to a two-dimensional acoustic waveguide experiment for a proof of concept. This work provides an insight into realizing elastic immersive wave experimentation by post-processing data recorded in physical experiments. Apart from developing the theories for immersive wave experimentation, I propose a method to compensate for physical source directivity in acoustic immersive wave experiments. Such a method will also help understand and suppress the effect of using imperfect sources in an elastic immersive wave experimentation laboratory.