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.