I have been watching the news for buildings that blow up due to gas leaks. So far they have been too far away to detect. We had one on the weekend at a distance about double the distance at which I regularly detect quarry blasts (confirmed by my RShake). The distance is 117 km. Winds were calm.
This is what is left of the small shopping center where the explosion happened:
An out-of-the-blue question…do you know if it is possible to establish a proxy “magnitude” of event for this explosion? I have been asked several times, now by our local emergency response team, if this is possible.
Good question. I don’t think a seismometer can give you a good proxy since the explosion was above ground. I mean, if you recorded a nearby quake you could compare it with that but …
There is a standard comparison for above ground explosions and that is equivalent pounds (or kilograms) of TNT. There are a lot of papers on that subject that Google will find for you. All the ones I looked at tend to be concerned with pressures > 1 PSI (6894 pa) because that is where you start to see some structural damage. Distances are usually within a couple of miles.
So if you had an RBoom, you might (*) be able to tell them an “equivalent pounds of TNT”.
My distant RBoom registered a peak pressure of 10,000 counts and that is about 0.18 pascals - so about 0.000026 psi. That pressure and distance would be a pretty big extrapolation of the curves shown in the papers I saw. For example, in this reference:
figure 6 shows at 10,000 feet you need 10^7 pounds of TNT for one psi peak pressure wave. Therefore 10,000 counts on the RB would require 260 pounds of TNT.
But I detected that same pressure at a 38.5 times that distance which would mean 57,000 times the weight of TNT.
I don’t know where the blast wave stops and just plain old sound takes over but I am guessing it is within a few “wavelengths” where a wavelength is 1100 ft/sec times the duration of that first positive pressure transient.
Perhaps some experts in this area will show up and help us out.
BTW - the first reference has a section on leaking gas explosions.
Ken
(*) I say “might” because the peak may occur in a millisecond at close range and the frequency response of the RB is limited to 1/50th of a second. But you might catch most of it.
A Richter magnitude can be computed from that Rshake record if it was really seismic. At that close range it might just be air-shock converted to ground motion or shaking of the house. There is a possible seismic arrival about 10 seconds before that big acoustic arrival which is about what is expected for the distance at 340 m/s.
For Quantico activity I have seen both direct seismic and (much later) some minor seismic from the arriving infrasound wave. The first wave I think is being propagated along the surface and not going very deep so it is fundamentally different than what Richter is based on. But I guess you could say the earth movement was “equivalent” so such and such an earthquake. Looking it up there is a formula here: https://en.wikipedia.org/wiki/Richter_magnitude_scale
We know the distance to the center of the event. What is needed is the peak displacement. Readings from the RS are in velocity not displacement. However there are postings that show how to make the conversion from velocity to displacement using the instrument response and some python programs … (easy if you know how I suppose).
OK - I couldn’t resist. The problem is that at 0.8 Hz (part of the Richter definition) the magnitude of this event is really small. I found that a low pass filter at 2 Hz gives a nice looking single pulse of about 1.14 um so I tried that
The simplest relationship between displacement and velocity (a pure sine wave) is
D = V / (pi*F)
Since I am lazy, I just used that.
Filling in the numbers, I get 0.18 um at 2 Hz (at 2.2 miles distance)
Plugging that displacement/distance into the Richter formula gives ~ M2 quake.
If you include higher frequencies you can a higher peak velocity. But the frequency in the divisor is higher. You can play with the numbers, but I think you will still end up in the low M2 range.
Damage from this event (broken glass etc) was due to the air blast, not the shaking.
M = log10(D) - A(delta) where D is millimeters on the standard Wood-Anderson with magnification of 2800. A(3.5 km) = -1.4. See Richter page 342.
Let the measured shake peak ampliitude be V in microns/sec and assume a dominant period of 1/f second then D = 2800 * V /1000 / 2 / pi / f.
I estimate the peak amplitude at 2.2 miles to be about 1 micron/sec with a period of ~0.5 sec. Assuming the shake is really flat to velocity in that bandwidth.
