Infrasound from a sub-sonic airplane

 Läslo Evers

The De Bilt Infrasound Array (DBN) often measures infrasound from passing sub-sonic airplanes. Figure 1 shows the recording of such an event on 2003, August 18. The time axis gives the time in seconds since 01h12m34.0s GMT. Coherent infrasonic signal is visible in the individual traces between at least 250 and 370 seconds. The air pressure fluctuations are measured with KNMI microbarometers. The addition of "micro" is validated by the measured amplitude values of approximately 0.2 Pa. This value corresponds to a drop in air pressure in the atmosphere experienced over a height of 1.5 cm, i.e. moving the microbarometer over a distance of 1.5 cm upwards will give a reading of 0.2 Pa.

Figure 1: Recordings of the 6 KNMI microbarometers of DBN. The time axis zero time is 01h12m34.0s GMT on 2003, August 18. The data are band-pass filtered with a second order Butterworth filter with corner frequencies of 0.5 and 19 Hz.

Array measurements enable the detection of signal on the basis of coherency. A coherent signal can be detected by evaluating the Fisher ratio. The Fisher ratio is a statistical measure of signal-to-noise ratio (snr) and describes the signal likelihood. The usage of arrays also enables the characterization of an event in terms of back azimuth and apparent sound speed. The apparent sound speed is the horizontal fraction of the true sound speed as measured by the planar array. The higher the apparent sound speed, the more vertical incident the infrasonic wave is. An infinite apparent sound speed means that all microbarometers measured the coherent wave at the same time, thus the energy came from right above the array. The apparent sound speed equals the true sound speed in case of far-field sources because of the wind gradient in the atmosphere.
In Figure 2 the results are shown of the array data processing. The Fisher ratio is plotted in the lower frame as function of time. The Fisher ratio increases around the time of the event indicating that a coherent infrasonic wave travelled over DBN. The plane could be followed for more than 2 minutes. The apparent sound speed also increases during the passage of the plane as can be seen in the second frame. This implies that the plane nearly flew over the array. The back azimuth, in the third frame, clearly shows a moving source. The plane flew from 40 to 190 degrees, i.e. from the East towards the South relative to the array location. In the top the best beam is plotted, this beam is the sum of the time shifted traces. The time shift is calculated for the event characteristics corresponding to the maximum Fisher ratio, that is 114 deg and 811 m/s as indicated by the purple circles.

Figure 2: Results of the array data processing on the basis of Fisher ratio. The time axis is the same for all four frames. The lower frame gives the Fisher ratio, the middle two frames give the resolved apparent sound speed and back azimuth corresponding to the calculated Fisher ratio. The top frame gives the best beam corresponding the the higher Fisher ratio.

The object is moving as follows from the variation in time of the back azimuth and apparent sound speed. Analysis of the data in the slowness domain shows the displacement of the plane with time as shown in this animation.

Is there a model that can explain the observed values for back azimuth and apparent sound speed? A simple model can explain the observation, this model is valid for a plane flying with a constant speed at a fixed height. In Figure 3 the blue curves show the result. The blue curves follow from the model for a plane flying at a height of 7 km with a speed of 500 km/h. The closest horizontal distance of approach to DBN is 3 km. There is a strong similarity between te observations, dots, and the model, blue curves. Therefore, the plane has been localized and could be identified with available flight records.

Figuur 3: The blue curves follow from a simple model model for a plane flying at a height of 7 km with a speed of 500 km/h. The closest horizontal distance of approach to DBN is 3 km.

Infrasonic wave propagation is in first order dependent on the wind and temperature structure of the atmosphere. Both down wind and a high temperature are favourable conditions for wave propagation. Furthermore, a temperature inversion, increasing temperature with height, can cause infrasonic to bend back towards the earth's surface. Models for wind and temperature are assembled by the European Center for Medium range Weather Forcasting (ECMWF), among others based on KNMI balloon measurements. Figure 3 gives the wind and temperature profiles for 2003, August 18 at 00h00 GMT in the vicinity of De Bilt.

Figure 4: Wind and temperature profiles for 2003, 18 August on 00h00 GMT near De Bilt.

The atmospheric trajectories of infrasound can be modeled with raytracing. The model in Figure 3 server as input model for the raytracing algorithm. The modeled and measured sound intensity can be compared to validate the model. Figure 5 shows how the rays, in white, travel from the airplane to DBN. The airplane is located at at height of 7 km, see the blue rectangle. DBN is situated at 3 km distance and is given by the red triangle. The coloured atmospheric layers represent the effective sound speed. The effective sound speed is the temperature dependent sound speed including the component of the wind in the direction from source to receiver.

Figure 5: The atmospheric trajectories of the infrasound from the airplane at 7 km height, blue rectangle, to DBN at a distance of 3 km, red triangle. Zoom in for a closer look around DBN.

Figure 6 gives the traveltime of the infrasonic waves as function of the distance. It takes the infrasound from the airplane 25 seconds to travel to DBN at its closest approach of 3 km. The sound intensity decreases with distance. Infrasound can at least be measured up to a distance of 30 km. This maximum distance highly depends on the state of the atmosphere.

Figure 6: Traveltime of the infrasonic energy towards the earth's surface.

September 2003
Läslo Evers