A Simple 3d Model?

One of the most difficult things in underwater acoustics is to see wood for trees.The most straightforward approach is often a computer-intensive numerical solution.Frequently this does not lead to much insight into the physics.This paper discusses some simple underwater propagation models with improving understanding in mind.We start with some simple laws for at bottoms and range-dependent environments.and rapidly drift into three dimensions.In particular we look at three-dimensional effects with variable bathy-metry and describe them with analytical models.These are useful as benchmarks for numerical models and for providing insight into acoustic behaviour.It is often also important to be able to generalise these effects for operational research purposes and system design.Above all we must be able to tell whether the new effects are important, or not, in practice.understand the behaviour of the mechanisms.Often a fully comprehensive correctly run numerical propagation loss plot is no more enlightening than trials data despite the fact that the basic equations for the treatment are obviously known.The alternative, on which we concentrate in this paper, is the construction of analytical formulae.There are several bene ts that a simple or analytical approach can provide, and these can be grouped as follows. UnderstandingAnalytical formulae are useful for showing the essence of the problem through the dependence of the output on the various inputs.However it is important that the formulae are relatively simple so that dependencies are either explicit or can be easily and quickly evaluated. BenchmarksQuite apart from the problem of matching theory with experiment there is the problem of checking that computer-intensive approaches provide correct solutions to the posed mathematical problem.Analytical solutions, whether simple or otherwise, provide useful checks on benchmarks.