Pressure Sensitivity Kernels Applied to Time-reversal Acoustics

Time-reversal is a method of focusing sound in the ocean that has found a variety of applications in recent years, ranging from underwater communications to biological stone destruction. In order to produce a focal spot, the time-reversal process first needs to acquire the Green's function between source and receiver. This Green's function is time-reversed and retransmitted in order to produce a spatio-temporal focal spot at the original source location. If the medium properties in between the source and receiver change between the acquisition of the Green's function and the subsequent retransmission, the quality of the focal spot can degrade or even disappear. However, the time-reversal focal spot has been found to be surprisingly robust to changes in medium properties, which are chiefly sound speed fluctuations in underwater acoustics. At 445 Hz, the focal spot was seen to persist for a week, while at 3.5 kHz, the focal spot persists for about an hour.Sensitivity kernels have the ability to linearly map sound speed perturbations to a perturbation of an acoustic parameter such as travel-time or pressure. Sensitivity kernels have a Fresnel-like interference pattern with regions of positive and negative sensitivities in the medium. Time-reversal, which causes different arrival paths to arrive at the same time, results in overlapping sensitivity kernels that leads to a net reduction in pressure sensitivity at the focal spot. Upon expressing the pressure at the focal spot in terms of sensitivity kernels, source transmissions are derived that are even more robust than time-reversal.The theory developed using pressure sensitivity kernels is tested on experimental data, along with an internal wave model, using various metrics. The linear limitations of the kernels are explored in the context of time-evolving Green's functions. The optimized source functions are then tested using experimental Green's functions and their behavior is seen to be in the right sense.Finally, thermistor chain data gathered during a similar experiment allowed for the testing of a 'synthetic aperture thermistor chain'. Temperature observations, presumably caused by displacements of a reference temperature profile, are inverted to provide an estimate of the background temperature profile