## Physical limitations of travel time based shallow water tomography

**O.C. Rodríguez **orodrig@ualg.pt

**S.M. Jesus **sjesus@ualg.pt

UCEH - Universidade do Algarve,

Campus de Gambelas,

PT-8000 Faro, Portugal.

** Comments:** download pdf file.

** Ref.:** J. Acoust. Soc. Am., Vol.108(6),pp.2816-2822, December
**2000**.

**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 for the constant
sound speed. The results of this paper are of central importance for the
understanding of travel time based shallow water tomography.