(meteorobs) Meteor triangulation from sonics

Jake S jakeschaeferml at gmail.com
Thu Feb 9 14:59:21 EST 2012


For the Texas fireball there was not enough seismographs to build a
trajectory. My goal was to produce a data set to help verify the
trajectories given from the all sky cameras (which it verifys Bill
Cooke's trajectory very well). There was 1 seismograph that was about
55 miles from the trajectory which saw a clear hit, a second one is
about 150 km away and saw a small spike in noise but I believe this to
not be the direct air pressure wave passing over.

In terms of atmosphere I use the standard atmosphere tables on 1976,
which can be corrected for nonstandard days and winds.

For terminal bursts I usually do a least squares fit based on the
error in arrival times.

As for reconstructing the trajectory, basically i solve for two
angles, a point in space, and a time. Within the computation is the
total distance the wave traveled to the station. This includes the
curvature or "ray tracing" you mention due to the variations in the
speed of sound and the wave expanding. If you don't account for this
you may expect to see sonic booms where there are none, where the wave
is actually propagated back up into space. Interesting the doppler
radars also do this and have a set equation for refractivity of the
atmosphere. I wonder what impact a nonstandard day does, how much it
will shift those blips.

I have a lower fidelity method i do by hand that just looks at the
trajectory and factors in mach angle to derive a linear distance from
the station to the pressure wave origination point along the
trajectory.

One thing i have not looked into very much is examining the magnitude
of the seismograph accelerations and relate that back to wave strength
and thus size of the meteor. Is this even possible?



On Thu, Feb 9, 2012 at 10:12 AM, Matson, Robert D.
<ROBERT.D.MATSON at saic.com> wrote:
> Hi Jake,
>
> Just to confirm, I assume you are using a temperature profile for the
> atmosphere and not just a constant temperature when modeling the sound
> time-of-flight. Also, in the case of large meteoroids that do not
> have a prominent terminal burst, the sonic boom delay for each ground
> site depends on that site's closest "distance" (see caveat below) to
> the meteor *trajectory* (to first-order, a 3-D line), rather than to
> a single point in space. So different sites will be experiencing
> sonic booms from different points of the trajectory.
>
> For a terminal burst, you need a minimum of only three ground sites
> to do triangulate it (thus the term). Of course, more sites is better
> so that you can do a least-squares fit.
>
> For a traveling bow shock, you need a minimum of four ground sites
> to determine the 3D line in space (and again more sites is better
> to allow for a least squares fit).
>
> Final caveat to confuse things further: the path taken by the earliest
> sound wave to reach each observer is not really a straight line, and
> in fact deviates significantly from a straight line for sites that
> are distant from the supersonic trajectory. It takes some serious
> number crunching to solve the high-fidelity meteor triangulation
> problem since all the sound wave paths are curved. So, if one is
> not up to the task of doing sonic "ray tracing", you should only
> use the receiving sites that are closest to the trajectory.
>
> Cheers,
> Rob
>
> -----Original Message-----
> From: meteorobs-bounces at meteorobs.org
> [mailto:meteorobs-bounces at meteorobs.org] On Behalf Of Jake S
> Sent: Wednesday, February 08, 2012 7:34 PM
> To: Meteor science and meteor observing
> Subject: Re: (meteorobs) 2012/02/01 TX Fireball Trajectory Solutions v1
>
> I've made some revisions as well. With the altitude data from Bill
> Cooke. Given that it was so shallow and still at 60 km when it passed
> by the seismograph greatly alters what I had expected. I would have
> expected the sonic boom to not generate such a large pressure wave
> until in the more dense lower air. But anyways this high altitude
> brings the trajectory farther south. Based on my calculations from the
> seismograph, the trajectory Bill Cooke has provided is only about 3km
> off which is easily within the uncertainty in my calculations
> (especially if the speed of sound is slightly off, colder than a
> standard day?)
>
> http://3dradar.wordpress.com/2012/02/09/dfw-tx-222012-0157-utc/
> -jake
> mailman/listinfo/meteorobs
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