Lloyd’s mirror and BBQ chicken

Hey, here’s my drawing from yesterday. It was an inverse theory day. I think that the conference got me all fired up about inverse theory for some reason. It might not be the best idea ever to change my term project two weeks before the end of the term… but my other project is sort of boring.

A whole chicken! A whole bottle of wine! And some inverse theory.

I’m in the process of writing code to do a couple of things. The first is to locate a whale (or any source) in the water column using earthquake location techniques. I’m assuming that I correctly pick the direct path arrival. So that part should be easy. I’m running it several times on an array of grid points.  So for each point I get a cluster of detections, and then I grab the eigenvalues and eigenvectors to get the semi-major and semi-minor axes (with orientation) of the error ellipse.  As you can imagine, this takes a long time.  It’s an iterative least squares problem, being done like 6500 times * 50 iterations for each time.  And 50 is sort of low.  Hooray for the brute force method!  Here’s a little peak at just one of those iterations.  Because the whale is not in the network, the position is not great.  It’s really difficult to resolve the range, in particular, although the bearing seems better constrained.

Fifty independent solutions for the location of a whale near a seismic network.

The second bit of code I’m writing up is not actually finished yet.  Or started.  All I have is the math, which tends to be the tough part anyway.  The whale call arrives at our seismic network via several paths.  There is sometimes a direct path arrival, but often multipaths, which have interacted some number of times between the surface and the bottom.  The multipath structure will change depending on where the whale is, and theoretically, it is possible to back out at least a range and depth using the multipath arrival times.  Again, this is a problem that has been solved before.  But it’s fun to figure it out for myself.

Some other things I’ve been thinking of trying:

  • Combine several range solutions from the multipath arrivals to locate the whale.  This shouldn’t be very hard.  It’s just like positioning a pinger on the bottom of Portsmouth Harbor!
  • Implement some kind of adaptive tracking algorithm… I feel some Kalman filtering coming on…

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