Apparent velocity of acoustic waveforms and geophysical applications

Abstract

In the last few decades, theoretical predictions and experimental observations of superluminal electromagnetic phenomena have sparked a lot of interest and resulted in many publications. These phenomena are typically observed in anomalously dispersive and composite (meta) materials, or with complicated exotic sources such as Bessel beams. Recently it has been shown that similar effects also occur in free space close to a point source of the electromagnetic radiation, where apart from superluminal and anomalously slow velocities, negative and infinite velocities were also observed. The mathematical structure of the radiation formula derived from the Maxwell equations directly explains these observations. Radiation formulas usually contain the near-, intermediate-, and far-field components. This causes the waveform to deform as it travels away from the source.

In my thesis I show that a similar waveform deformation and subsequently all the anomalous velocity effects together with the apparent violations of causality and special relativity, can also be observed with the acoustic radiation. Analytical, numerical, and experimental results are presented to confirm the acoustic waveform deformation for a spatially extended source in free space. The following questions are discussed: the velocity of the acoustic signal, the origin of the anomalous velocity effects, information transmission, causality, and special relativity.

Some applications of the waveform deformation effect are also presented. It appears that the waveforms close to the source may contain much more information than the usual far-field waveforms. Several methods are proposed to extract this abundance of information and use it for imaging and full waveform inversion algorithms. For example. an algorithm is developed that recovers the source-receiver distance, the background-medium velocity, and the time-function of the source simultaneously, and without any a priori information.