Seismology Research
Bringing together seismology and atmospheric sciences
8. Modeling of the observed data by raytracing
January 2004
Läslo Evers
8.1 Troposphere and stratopshere: near field sonic boom
In figure 8.1.1, the recording of coherent energy traveling over DIA is shown. The top
frame displays the best beam and in the bottom frame coherency is plotted. Around
the time of the event, approximately after 15 seconds, coherency increases.
Figure 8.1.1: The recording of a near field (N wave form) sonic boom at DIA. Coherency
as a function of time and frequency is plotted in the lower frame. The best beam for the
resolved source characteristics is shown in the top frame.
Based on its N wave form, the energy is identified to result from a plane flying
through the sound barrier. The N wave is formed at a certain distance from the source,
generating the characteristic double bang. The actual wave shape follows from compression
at the front of the plane and expansion of the air at the back. The amplitude of the
N wave (i.e. 5 Pa) is large, indicating a direct or carpet zone arrival.
The source is located through cross bearing. The bearing of DIA is combined with the bearing
obtained in De Bilt (DBN), see figure 8.1.2.
Figure 8.1.2: Cross bearing for source localization
The distance from the source to DIA is 76 km as derived from the cross bearing analysis
shown in figure 8.1.2.
ECMWF atmospheric data is used to build a velocity model of the atmosphere. The data from
ECMWF is validated by balloon measurements at the KNMI in De Bilt. The correlation between
ECMWF and KNMI data gives confidence in the model up to 25 km height. Balloon measurements
are not available for heights larger than 25 km.
Figure 8.1.3: 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 an estimated source height of 10 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.
The results from raytracing through the atmospheric model are shown in figure 8.1.3. The lower
frame shows the effective sound speed indicated by various colors. To the right of the lower
frame, the effective sound speed (in brown) and temperature depend sound speed (in green) are
plotted. It follows from the velocity model that at a height between 25 and 35 km, a
velocity gradient is present. Therefore, upward traveling rays will refract from
these height, bending towards the surface. The rays are also plotted in lower frame.
The source is locate at 10 km height and emits infrasound through rays at a 5 degree interval
with respect to the vertical.
The travel times for rays reaching the surface are shown in the top frame, in red. The carpet
zone exists up to a distance of 50 km. The zone where the first refracted waves arrive, starts
at 95 km. DIA and its best beam are plotted in the top frame, at a distance of 76 km as follows
from the cross bearing analysis. Although, DIA recorded a clear and strong N wave arrival, it
appears to be located within in the shadow zone. Either the velocity model or applied raytrace
theory fails to explain the clear observation. Accounting for turbulence and/or inhomogeneities
might solve this ambiguity.
