Figure 3 displays the average back azimuth found in the fk analysis. The angle of 155 degrees (in gray) is the observed bearing between DIA and the Etna. The real back azimuth of 152.5 degrees is given in red. The distance between DIA and the Etna is approximately 1785 km.
Identification of the signals
The infrasonic signals from the Etna have amplitudes less or equal to the noise, as follows from the bestbeam plotted in figure 1. The signal is identified by shifting the traces according the solution found for apperent sound velocity and back-azimuth from the fk-analysis. Similar waveforms will align and positively contribute to the bestbeam. This procedure is excuted for the 4 time intervals used in the fk analysis, figure 4 to 7 show the results. The most confincing result is displayed in figure 4, clearly a coherent waveform having travelled over the array. The 13 traces of DIA for the bin from 39 - 64.6 sec., band-pass filtered between 0.5 - 1.5 Hz. The traces are aligned which means that the travel time differences of the signal, while travelling over the array, are subtracted from each individual recording. The top trace is the bestbeam (i.e. sum of the 13 traces) following the calculated source characteristics in figure 2. The violet arrow point to a likely waveform from the Etna explosions, although more signals can be identified.
Atmospheric paths and traveltimes of the infrasonic waves
The atmospheric paths of infrasonic waves depend on the wind and temperature structure of the atmosphere. The lower atmosphere, up to 20 km, is well known through sampling by, for example, balloon measurements. For the higher atmosphere one depends on (empirical) models. Figure 8 shows two available models, in blue an empirical model up to 140 km and in brown the ECMWF model up to 60 km. An average model, in red, has been derived. The average model follows ECMWF's model for the first 20 km of the atmosphere. Between 20 and 60 km, the average model is calculated by cubic spline interpolation of the ECMWF and empirical model. The empirical model is followed from 60 km and upwards.
Raytracing is performed to gain insight in the exact paths through the atmosphere and to derive the traveltime of the waves from the Etna to DIA [Garcés et al., 1998]. Rays are launched from the Etna location toward DIA and traced, based on the derived averaged model, as shown in red in figure 8. Infrasonic energy is refracted from the thermosphere, between 110 and 130 km height, and from the stratopause, around 50 km, as can be seen in figure 9. The rays are also reflected by the earth's surface and show several hops before they reach DIA (at approx. 1800 km). It takes the energy between roughly 6000 and 7000 seconds to arrive from the Etna at DIA.
The calculated and real back azimuth between DIA and the Etna show an western offset for the calculated bearing, as follows from figure 3. Part of this offset is caused by cross winds experienced by the energy while travelling through the atmoshere. The zonal wind, in figure 8, has a predominant negative component between 15 and 85 km height, the major region through which the energy travels. Therefore, the infrasonic waves will be blown towards the west by these cross winds on their way from the Etna towards DIA. This explains the observed azimuthal deviation.
In figure 10 a quantification is given for the possible deviation. The range axis follows the straight line between the Etna and DIA along the earth's surface, thus toward the northwest (332.5 degrees). The offset axis represent the amount of deviation from the rays towards the west due to cross winds. The red dots are the positions at which the turning rays hit the earth's surface. The repetative pattern is caused by the hops between stratopause, thermosphere and the earth's surface (see also figure 9). After having travelled 1800 km, from the Etna towards DIA, the rays have a western offset from 75 to 175 km, causing azimuthal deviations of 2.4 to 5.5 degrees.
Evers, L.G., and H.W. Haak, Listening to sounds from an exploding meteor and oceanic waves, Geoph. Res. Lett., 28, 41-44, 2001.
Garcés, M.A, R.A. Hansen, and K.G. Lindquist, Traveltimes for infrasonic waves propagating in a stratified atmosphere, Geoph. J. Int., 135, 255-263, 1998.
Smart, E., and E.A. Flinn, Fast frequency-wavenumber analysis and Fisher signal detection in real-time infrasonic array data processing, Geoph. J. R. Astron. Soc., 26, 279-284, 1971.