Abstract
Time-reversal has been found to be more robust to sound speed perturbations than a one-way transmission. Various explanations have been advanced to account for the lower sensitivity of time-reversal. In this contribution, the robustness of time-reversal is quantitatively examined using sensitivity kernels. A first-order Born approximation is used to obtain the pressure sensitivity of the received signal to small changes in medium sound speed. The pressure perturbation to the received signal caused by medium sound speed changes is expressed as a linear combination of single-frequency sensitivity kernels weighted by the transmit signal in the frequency domain. This formulation can be used to predict the response of a source transmission to sound speed perturbations. The stability of time-reversal is studied and compared to that of a one-way transmission using sensitivity kernels. In the absence of multipath, a reduction in pressure sensitivity using time-reversal is only obtained with multiple sources. This can be attributed both to the presence of independent paths and to cancellations that occur due to the overlap of sensitivity kernels for different source-receiver paths. [Work supported by ONR.]
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