# Probing the atmosphere with sound waves

Summer is a quiet time for both the University of Reading and the town itself. The buzzing that fills campus during term time is gone, the population decreases and activities are reduced. Some people find it relaxing – I find it boring and lethargic.  There is an exception to this quietness which occurs during the August Bank Holiday weekend. Any music aficionado knows this is the time when the annual Reading and Leeds Festival takes place. Thousands of people from all around the UK descend into our town to inhabit a patch of land next to the Thames for three days and enjoy some of their favourite bands, as well as some other excesses…

During my seven years in Reading, I have indulged myself with attending the festival four times. In each of these occasions, I have had a similar conversation with my colleagues when we were back at work the day after the Bank Holiday Monday. First, they hypothesize that I was the oldest person in the whole festival (not true, but it is accurate to say that I am too old to camp and instead I go home each day). Second, they state that at night they could hear the music all the way to their houses. I found the latter comment interesting given what I had experienced. Let me explain: there have been days in which I was not interested in the headliner act and hence I left the festival while the music was still playing. In each occasion, I remember walking away from the festival and noticing the music fading progressively until it was gone. So how could other people hear it at their homes when these were further away from the stage? The answer, not obvious to me at first, is that there were some sound waves that were ‘jumping’ over me.

Figure 1: Simple representation of the reflection of a vertically propagating wave in the atmosphere. The sound wave (yellow line) departs from a source (S) at the surface, reaches a maximum height (Zmax) and it is reflected back towards the surface where it can be detected in a receiver (R). The cross-winds that the wave-front encounters make it seem to come from a false source in a slightly different direction than the real source.

To understand my explanation, we need to think about the way sound travels from the loud-speakers around and above the stage. Without going into the specifics of the type of loud-speaker (there are lots), the sound waves can be transmitted in both the horizontal and vertical directions (you can see a classical illustration of how spherical sound waves work in the youtube link in the references). At the end of the night, as I walked away from the source, the sound waves coming horizontally in my direction were attenuated by the medium (air) and obstacles, and hence I stopped hearing the music. What about those waves with a vertical component? Figure 1 answers this: the yellow line represents the path of these waves. They travel up to some maximum height until they are reflected back towards the surface. The attenuation over that path is different from the attenuation of the horizontal propagating wave (in the case I am discussing it is less). So, the people in town were receiving a sound-wave that had been reflected in an upper level and still had enough intensity. It also helped that is was night-time and not day-time (at night the conditions are more prone for reflection/refraction, but that is another issue).

Figure 2: Vertical sensitivities for the infra-sound waves generated by the detonation of old ammunition in Finland and detected in Norway. The horizontal axis is the time; we indicate the year but not the exact time of detonation. The vertical axis is height. Notice that most infra-sound waves reach about 40km in height.

Why am I telling this story? Because lately, I have been using the behaviour I just described as a tool to probe the winds in the stratosphere (roughly between 12 to 50 km in the mid-latitudes). Finland has a lot of old ammunition, mainly from the Cold War, that it is trying to get rid of. Therefore, every summer the Finnish army performs a series of controlled detonations at a remote location during the course of several days. These explosions produce infra-sound waves (waves below 20 Hz which cannot be detected by the human ear). Some of them follow a path with a vertical component, they reach a maximum level and they are reflected back to the surface where they are detected, about 10 minutes after the explosion, in a station in Norway. This station is about 178 km due north from the explosion site and it has quite powerful micro-barometers which are able to measure precisely the pressure variations caused by the infrasound waves. I have some enthusiastic colleagues in the Norway Seism Array (NORSAR) who have shared these observations with me. Figure 2 shows a model-based reconstruction of the maximum height the waves reach for explosion events from 2001 to 2018. There are different numbers of detonations per year, which is why the horizontal axis looks irregular. Notice that most of the waves reach about 40 km in height, and some up to 60 km.

So how do I probe the atmosphere with these waves? As the waves travel through the atmosphere they are affected by several atmospheric conditions: winds, humidity, etc. In particular, the presence of cross-winds (i.e. winds perpendicular to the direction of the wavefront) can shift the detection angle of the waves when they reach the ground. Hence the waves appear to have come from a false source in the direction of the blue line in Figure 1. Since I know the exact location of the source, the time it took for the waves to be detected, and the shift angle towards the apparent source, I can deduce some values for the cross-winds each infrasound wave encountered, including those in upper levels of the atmosphere. In order to solve this estimation problem, I use techniques from inverse problems and data assimilation which I will not discuss in this post; I only mention that I use an implementation of the ensemble Kalman filter.

It is quite difficult to measure winds in the stratosphere, hence any source of information is valuable and this includes the strategy discussed here. There are other sources of infrasound waves that we can exploit around the world, and some of them are natural! For instance, the ocean swell in a spot near Iceland is a natural producer of infra-sound waves. So, we could use this hot-spot to probe the winds between that location and the same receiver in Norway, or many other receiving stations at the moment. At the moment I am participating in a collaborative project with some people from different institutions in Europe to solve this problem.

Reference:

#### Extract of Sound Waves And Their Sources (1933), you can see a classical illustration of how spherical sound waves work in this animation.

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