# Cylindrical spreading transmission loss (underwater acoustics)

In underwater acoustics, transmission/propagation loss can be calculated using a spherical spreading formula out to a certain distance which we can call the transition range, after which a cylindrical spreading formula is used instead.

This article gives an example equation for cylindrical transmission loss for range R: TLcylindrical(R) = 10 Log(R) + 30 dB. (valid when R > 1000 m). The example assumes the ocean is exactly 2000m deep and the acoustic source is exactly 1000m deep (halfway between the surface and sea floor). The math they've used makes sense for those specific conditions. What I'm unclear about is, how would the equation change if the acoustic source was not exactly halfway between the surface and sea floor? For example, what if the acoustic source was at the surface (0m deep) or 500m deep?

I have looked at many other sources but they all seem to explicitly or implicitly assume that the depth of the acoustic source, and therefore the transition range, is half the depth of the sea floor.

• What actual physics cases spherical spreading to transition to cylindrical spreading? It would have to be the boundaries of the ocean (surf, and floor). In which case you'd have a change from using the Green's function exp(-ikR)/R to using a Henkle function. If you can derive the above TL or understand the derivation you'd be in a position to identify the parameters that need changing.
– user196418
Commented Apr 9, 2020 at 13:54

It looks like a pretty rough approximation. They chose 2000 m because that is the average depth of the ocean. They chose to put the source half way down because then the expanding sphere touches the top and bottom at the same time, and the side looks enough like a cylinder to pretend it is one.

Instead of 2000 m, you could choose to use the depth of the ocean where you are. You could put the source at the surface. Perhaps you might pretend the expanding sphere looks like a cylinder at the range where the sphere hits the bottom.

But if these differences matter to you, you might be trying for more accuracy than the crude approximations warrant.