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Seismology Research
Bringing together seismology and atmospheric sciences
8. Modeling of the observed data by raytracing
January 2004
Läslo Evers
8.3 Mesosphere and thermosphere: exploding meteor
Low frequent infrasonic energy is displayed in figure 8.3.1. The lower frame
shows coherency as a function of time and frequency. The middle frame displays
the resolved azimuths of the energy (with respect to the North). The energy seems
to come dominantly from the northwest (270 to 360 degrees), denoted by the yellow
to red colors. Between 120 and 240 seconds energy also arrives from a eastern
direction, as indicated by the blue colors in the middle frame.
Figure 8.3.1: Low frequent energy coherently traveling over DIA. Coherency as
a function of time and frequency in the lower frame. Resolved azimuths as a function
of time and frequency in the middle frame. The best beam for the energy coming from the
east (blue colors in the middle frame), in the top frame.
In the top frame of figure 8.3.1, the best beam for the energy arriving from the
east is shown. The energy appeared to come from a direction of 82 degrees and was
identified as a meteor explosion (Evers and Haak, 2001).
The bolide was observed in The Netherlands and
Germany, an origin time was obtained from cameras in the Czech Republic. Two
arriving packages of energy can be seen in the best beam. The first after 130 seconds
and the second after 185 seconds. The seconds arrival is somewhat more low frequent
(0.1 Hz with respect to the first arrival of 0.15 Hz).
Figure 8.3.2: The different available wind and temperature profiles. The higher
atmosphere, above 50 km, is described by empirical models.
The available wind and temperature information is evaluated in figure 8.3.2. Actual balloon
measurements from KNMI are given in blue, and sample the atmosphere up to 20 km height. ECMWF
models, in green, follow these KNMI measurement and extent towards a height of 60 km,
with decreasing resolution. Empirical models are available throughout the total atmosphere.
To create the best velocity model from these profiles, a weighted average is taken. The
KNMI balloon measurements are taken for the first 20 km of the atmosphere. From 20 to
60 km height, the average of the empirical models and the ECMWF model is taken, with
less weight for the ECMWF model with increasing height. The two empirical models are averaged
for heights between 60 and 200 km. The resulting model, called weighted average,
is shown in light blue.
Figure 8.3.3: The delay time function, tau, as a function of launch angle
and height. The launch angle is defined from a source at 15 km height and is measured
with respect to the vertical (i.e. 0 degrees is vertically upwards).Tau reflects
the time a ray spends traveling vertically through a layer.
From the weighted average model, a velocity model is constructed which serves as
input model for the raytracing. The delay time function, tau, is evaluated in figure
8.3.3. Tau is presented as a function of height and launch angle, and is calculated
for a source at 15 km height. The launch angle is measured with respect to the vertical
(i.e. 0 degrees is vertically upwards). The part up to 15 km represents rays launched
at angles between 90 and 180 degrees (i.e. towards the surface). The upper part of
figure 8.3.3 (between 15 and 200 km) is for rays launched upwards, from 0 to 90 degrees.
This follows from the symmetry of the sine function on which tau depends (Petit,
2000). Tau reflects the travel time of the vertical path
of a ray through an atmospheric layer. Large values of tau mean a more vertical path
than small values of tau. If tau approaches zero, rays will turn towards the surface, since
they no longer have a vertical component in their path (refraction).
It follows from figure 8.3.3 that rays departing near vertical from the source,
between 0 and 20 degrees, will travel upwards to areas where their energy is lost
due to the absence of a medium. The same counts for rays leaving the source with angles
between 160 and 180 degrees. These rays travel to the surface first and will disappear into
the upper atmosphere after reflection. Rays launched with angles between 20 and 50 degrees
will be refracted by the thermosphere. Equivalently, rays leaving at 130 and 160 degrees
will return from the thermosphere after their surface reflection. Rays will be trapped
in a duct, between the thermosphere and troposphere, for launch angles between 50 and
70 degrees (or 110 and 130 degrees). A duct between the mesopause and troposphere will
trap rays launched between 70 and 110 degrees.
With known origin time and observation time, differential travel times of 1424 and 1479
seconds are calculated for, respectively, the first and seconds arrival. In figure
8.3.4, the results are shown for a height of 15 km for the meteor's explosion.
Figure 8.3.4: Results of modeling through raytracing. The velocity model is shown
in the lower frame. The effective sound speed (wind and temperature effects) in brown,
and the temperature depend sound speed, in green, are shown to the right of the lower
frame. In white are the various rays plotted. The rays depart from a source
height of 15 km, at intervals of 5 degrees from the vertical. The top frame shows
the travel times for rays reaching the surface, in red, also the best beam for
DIA is plotted in this frame at 330 km distance.
The combination of a height of 15 km for the meteor's explosion and source receiver
distance of 330 km, is the most reliable solution matching the differential travel times
as boundary condition. The four travel time branches, in the top frame, represent, from
bottom the top: high thermospheric, low thermospheric, first to the surface and than
a high thermospheric and first to the surface and than low thermospheric refraction.
The first two arrivals, which have traveled directly upwards, are not observed in the data.
Since the meteor is moving towards the earth surface, energy is radiated only downwards
and not upwards as in the point source analysis done. This explains the absence of the
first to arrivals.
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