Some Auckland residents reported houses shaking and a noise similar to an explosion between 4pm and 5pm on Wednesday, June 18.
The sounds most likely came from the Kaipara Bombing Range at the top of Muriwai Beach.
But hearing these explosions strongly from 50km away in Albany and Stanmore Bay is unusual.
Watch: Air Force's bombing runs
How did the sound travel over these distances?
Sound will normally spread out in all directions horizontally and upwards from the source.
This means the sound intensity rapidly decreases with distance from an explosion.
We generally measure sound intensity using decibels, or dB, to allow for the ear's ability to hear extremely faint sounds right up to jet engine loudness.
A car 10m away would have a sound intensity of about 70dB.
Nearby thunder might have a sound intensity level of 100 dB, but if it is twice as far away the intensity will only be 94dB.
This intensity decrease with distance means that an explosion at Kaipara, heard 400 m away as a very sharp loud explosion of perhaps 12 dB, would 60 km away sound no louder than a car.
But this does not allow for the fact that the atmosphere can act as a "sound lens", when the sound path bends and focusses, just like light going through a glass lens.
For this to happen, there has to be a change in the speed of sound.
Two things affect the speed of sound: air temperature and wind speed.
If either the temperature or the wind speed increases with height, then the sound speed is higher further up, and this makes the sound bend down towards the ground.
However, temperature usually decreases with height - it's colder up a mountain - and on Wednesday, June 18, the air temperature decreased two to three deg C every 1000m of altitude.
So the most likely explanation for the focussing of sound in the downwind direction, 60km away, is that the wind speed increased with height.
Another factor is important.
The sound which bends, or refracts, travels in a shallow curved path above the ground and will combine with sound which just skims over the ground.
The travel distance for these two paths is different, and the combination from the two sound paths can lead to cancellation at some distances and twice as much amplitude at other distances.
This means that there will be an intermediate range over which not much is heard, and further out from the source - the 50-60 km to Albany and Stanmore Bay - there will be an arc in the downwind direction where more intense sound is heard.
Still further away, there will again be a sound shadow zone.
But this alone is not enough to explain being able to hear loud sounds as far away as Stanmore Bay, because sound initially spreads out in all directions from the explosion.
For example, if the wind speed increases with height, then the sound going in the upwind direction will bend upwards and be lost into the higher altitudes. This means there must have been something else going on.
One possibility is a "low level jet" (LLJ) of faster air.
This could act as a duct for the sound, collecting together sound going outwards and upwards from the explosion and sending it down the jet, much like laser light down an optical fibre.
A LLJ could last a few hours, and they are quite common.
The wind speeds at Whenuapai at noon showed no change in wind speed over the lowest km of height, but the balloon sounding at midnight did show wind speed increasing with height, so it is possible a LLJ existed in the mid-afternoon.
Incidentally, it is a common misconception that sound will be reflected off cloud, as suggested in the New Zealand Herald article, or that sound travels further in fog.
In practice, cloud droplets have no effect and humidity only has a very tiny influence.
Most likely this misconception comes from movies in which fog horns from boats are heard eerily in fog.
Of course the fog might arise from a cold surface, which would cause downward refraction of sound, as described above.