It feels like I’ve been doing nothing but estimating source levels lately (exciting times!). I started to outline it in the research section of this site (See Source Levels) – although that was ages ago and is now a bit outdated.
Measuring source levels of marine mammal vocalizations is complicated, and even more so when using ocean bottom seismometers. I’m trying to look at some of these complications and sources of error and uncertainty.
One of these is the interference between the direct path arrival and the surface bounce. Because they take different paths to reach the receiver, they arrive at slightly different times. These offsets result in interference patterns – sometimes constructive and sometimes destructive.
I wrote some code to model these effects, and I’ll just start out with a little video clip that shows what I mean by constructive and destructive interference. I’m plotting the RMS (root-mean-square) amplitude of the received signal. You can see that in addition to the interference pattern, the amplitude of the input signals is decreasing – this is to account for transmission losses along the travel paths, modeled simply using a spherical spreading assumption (scaled by range).
Next, I wanted to see how this effect might manifest itself in our particular setup. I ran the code using an approximate receiver depth of 2200 meters, a source depth varying between 0 and 100 meters, and a horizontal range of 0 to 2200 meters. I chose the source depths based on what I think are likely depths from which a fin whale might call. The horizontal ranges are restricted such that the incidence angles will be small(ish) – a constraint that is imposed in part to reduce ambiguity with later multipath arrivals, and in part because of the physics of converting ground motion back to an acoustic pressure level (details I won’t go into here). The surface bounce is given a 180 phase flip (and no loss of amplitude) since the surface is treated as a perfect pressure release boundary.
Here are the results of that model:
Wow, that is a lot of possible variability! This has been just a quick little experiment, and there’s a significant possibility that I’m still doing something wonky in my code, but based on looking at examples from the literature (for example, Charif et al., 2002), it seems to be in the right ballpark. Very interesting – this will definitely affect how I interpret my source level estimates.