Physical limitations of travel-time-based shallow water tomography

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Abstract
Travel-time-based tomography is a classical method for inverting sound-speed perturbations in an arbitrary environment. A linearization procedure enables relating travel-time perturbations to sound-speed perturbations through a kernel matrix. Thus travel-time-based tomography essentially relies on the inversion of the kernel matrix and is commonly called “linear inversion.” In practice, its spatial resolution is limited by the number of resolved and independent arrivals, which is a basic linear algebra requirement for linear inversion performance. Physically, arrival independency is much more difficult to determine since it is closely related to the sound propagating channel characteristics. This paper presents a brief review of linear inversion and shows that, in deep water, the number of resolved arrivals is equal to the number of independent arrivals, while in shallow water the number of independent arrivals can be much smaller than the number of resolved arrivals. This implies that in shallow water there are physical limitations to the number of independent travel times. Furthermore, those limitations are explained through the analysis of an equivalent environment with a constant sound speed. The results of this paper are of central importance for the understanding of travel-time-based shallow water tomography.

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