Using surface waves to describe subsurface density.

[norman_h]

Imagine a rock being dropped into a shallow pond of water to create a nearly perfect impulse signal originating at the point at which the rock touches the pond. Waves from this impulse action ripple outwards. The resultant waves on the surface are observed and recorded. At the bottom of this shallow pond there is a change in density from water to an inhomogeneous watery/muddy substance to substances of greater density. The unobserved subsurface waves interact with, and move lower, through the lower boundaries causing changes to the observed waves on the surface of the pond.

The surface of the pond is considered to be an upper boundary through which waves do not pass. As the waves can continue downwards they become attenuated.

I'm hoping to find the density of the watery/mud at any depth for two different cases:

1. A case where a single straight line of wave action is observed. This line extends outwards from a first point, where the rock is dropped, to a second point in space. The wave action along this entire line can be measured. I hope to find the 2D structure/density beneath this line
2. The 3 dimensional case, whereby the entire surface wave can be seen rippling away from the point at which the rock touches the pond.

I've been looking at both Green's and Stokes' theorems, and I'm wondering if it is even possible to find a solution from the wave which is observed at the surface alone.

If someone provides me with a quick solution, this would be nice and I would be forever grateful, but, more importantly I would like to know if I am hoping to find a solution "is this a futile effort with the information that I have?". If it is futile, what information would I need to find what I am looking for.

If I can keep up with any replies, I'd like to participate in discussion, but, I'm probably a little slow. *sigh*

Thanks for reading!

 

[norman_h]

~500 views in 2 years.

I shall refine the question in another year or so.

Bump.