June 12, 2011 AT 12:31 pm

New Cave-Mapping Technique Uses Gunshots as Impulse Functions

(Photo of Mammoth Cave by David Fulmer – CC-BY-2.0)

I recently read this article from New Scientist, which described a new technique for mapping caves using gunshots and a pair of microphones. Here’s an excerpt:

a new system that can use sound waves from a gunshot to quickly map unknown caves and tunnels. The portable system, created by David Bowen of Acentech in Cambridge, Massachusetts, consists of two microphones placed at the entrance of a cave or tunnel, which are hooked up to a laptop loaded with software designed to decode acoustic signals.

A gun is fired four or five times, with about 5 seconds between each shot. Fifteen to 20 seconds later the map appears on the laptop’s screen, with simple graphs that display the area of the cave at different distances, and written explanations of the data, such as “30 feet ahead is a large opening”. A portable subwoofer can be used in place of a firearm as the source of the sound waves.

To infer a cave’s geometry, the device listens for subtle changes in the way sound reverberates through the chamber’s differently sized nooks and crannies. “Every time there is a sudden change in cross-sectional area, it changes the way sound is reflected,” Bowen says.

For example, a roomy cave that suddenly narrows into a cramped channel will only permit high frequencies to pass, says Mike Roan of Virginia Polytechnic Institute and State University in Blacksburg. Most of the low frequencies will rebound towards the cave’s entrance and the waiting microphones: the more low frequencies bounce back, the tighter the passageway. The device can also determine whether the sound waves struck a dead end or found an exit at the end of a tunnel.

It occurred to me that this is a wonderful illustration of an engineering concept known as impulse response. Impulse response is something engineers use to quantify systems. For example, you can quantify the resonance (and damping) of a system by looking at it’s impulse response. The response is dictated by the transfer function of the system. Anyone who has ever built a speaker cabinet, for example, is familiar with the concept of a transfer function. In speaker building, a larger enclosure results in a more damped resonance, but extended low-end response. Conversely, a smaller enclosure results in more resonance, but a higher cutoff frequency. Changing the size of the enclosure is one way to alter the transfer function of the speaker-enclosure system.

One of the cool things about impulse response is that, if you know what the impulse function looks like, you can determine the transfer function, and that’s what is going on here. The waveform of the gunshot sound is known data. By firing the gun and recording the resulting echos — the impulse response — the researchers can work backwards (via deconvolution) to determine the transfer function of the cave. By analyzing the transfer function for features like phase delays and frequency response, they are able to “map out” the cave.

It’s a pretty neat application of this stuff, but I can’t help wonder what the Laplace transform of gunshot(t) looks like…

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1 Comment

  1. That it were so easy years ago. We are the stewards of a cave in Perry County, Missouri called Berome Cave. The cave has about 20 miles of mapped passage. A couple of years ago I took a couple of surveying trips deep (miles in) in the cave. It is wet, cold, muddy work. We use four instruments: compass, clinometer, surveyors’ tape measure (or more modern rangefinder; I’ve never used one), and a sketch book. We survey forward, check the results by “backshooting” the last measurement, then sketch the cross-section of the passage. The result: a huge, beautiful, but probably inaccurate map. At our last meeting, some people involved in early surveys of Berome proposed using new technology to remap the cave, I think that it used lasers. This sonography would be useful for us because surveying is prone to human error (e.g. forgetting to adjust for magnetic declination), magnetic anomalies (irregular ferromagnetism in the cave walls), and the limitations of the instruments (it is difficult to sight a line when your head “conflicts” with a wall).

    Why survey a cave? These caves have active streams, streams that sometimes become a roiling boiling mass of water during a rainstorm. Hydrology is of huge interest to biologists, farmers, and geologists; it helps explain where rivers disappear and springs appear. It also forms a more complete picture of the geology of the karst (the cave is the hole in the swiss cheese, the karst is the actual cheese). Also, access to caves is critical. And surveys show the cave’s dimensions in relation to the surface geography. Knowing the “shape” of the cave may reveal new entrances. If cave access is forbidden on one property, it may be open on another, more friendly landowner’s property. Once you enter the cave on the friendly guy’s property, you can legally go anywhere you want, at least in Missouri.

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