# Localizing the First Interstellar Meteor with Seismometer Data
## 2 Method of Calculation  
We use the National Weather Service's Global Ensemble Forecast System model atmospheric profile (pressure as a function of temperature) for the DoD-reported fireball location, \((-1.3^{\circ},147.6^{\circ})\) at the time of 8 January 2014 17:05:34 (private communication, [PERSON] and [PERSON], 27 April 2022). We compute the sequential altitude differences as \(dz=H(dP/P)\), where \(H=(RT/g)\) is the scale height, \(R\) is the gas constant, \(g\) is the gravitational acceleration, \(T\) is the temperature as a function of pressure \(P\), and \(dP\) are the sequential pressure differences. The sound speed as a function of temperature is given by \(v_{a}=331.3\) m s\({}^{-1}\)\([1+(T/546.3\) C\(])\). For this particular atmospheric profile, the sound speed as a function of altitude \(z\) can be expressed as \(v_{a}=(347.2-\frac{1861_{\rm s}}{\rm km})\) m s\({}^{-1}\). The geometric setup is shown in Figure 1 and the AU MANU seismic signal that appears to correspond to the fireball (with the three directions of the seismometer added in quadrature, and the overall signal normalized to unity) is displayed in Figure 2. We conservatively regard a packet of seismic energy that appears a few minutes before the one shown in Figure 2 as background noise because there is no clear mechanism by which a signal from the fireball would arrive at the AU MANU sensor so quickly and, given the prevalence of apparent seismic activity in the hours before and after the fireball, it is consistent with background noise. For the isolated seismic signal from AU MANU, we require the first arrival of air-mediated sound waves from the fireball to occur at a delay of 270.5-271.5 s, with the green region in Figure 2 corresponding to where the signal rises above the noise threshold. This implies sound waves traversing the shortest path in between the blast and the seismometer, a distance of \(\sqrt{r^{2}+z^{2}}\), where \(z\) is the altitude of the fireball above the ocean surface and \(r\) is the horizontal separation of the fireball from the seismometer. Similarly, we require the peak amplitude of the air-mediated sound waves to occur at a delay of 296-297 s (within the orange region), corresponding to the apparent peak in the signal. To first order, this should correspond to sound waves that traveled a distance of roughly \(r+(z/\sqrt{3})\) in the air (note that we use this approximation for the analytical derivation, but then verify the fit numerically). Figure 1: Schematic showing the geometry of the meteor fireball and the seismometer. Sound rays can travel directly through the air or reflect off of the surface of the ocean. The illustrated paths are not meant to be accurate depictions of individual sound waves, and the symbol designating the seismometer does not indicate its height. By summing over the different paths, we are able to fit the recorded sound signal for particular values of the horizontal distance (\(r\)) and altitude above sea level (\(z\)). Figure 2: AU MANU seismic signal as a probability function of counts normalized to a unit area. The green region (270.5–271.5 s after the fireball) indicates the constraint for the arrival of the air-mediated sound waves, and the orange region (296–297 s after the fireball) illustrates the constraint for the peak signal produced by the air-mediated sound waves. The first, second, and third gray lines correspond to the first, second, and third peaks in the IM1 light curve [2]. We solve for the following constraints:  
\[\text{Sound speed} :v=(347.2-\frac{1.861z}{\text{km}})\text{ m s}^{-1} \tag{1}\] \[\text{Signal arrival} :270.5\text{ s}<\frac{\sqrt{r^{2}+z^{2}}}{v_{a}}<271.5\text{ s}\] (2) \[\text{Signal maximum} :296\text{ s}<\frac{r+z/\sqrt{3}}{v_{a}}<297\text{ s}, \tag{3}\]  
and find that this yields a ground distance \(r=83.9\pm 0.7\text{ km}\) and an altitude of \(z=16.9\pm 0.8\text{ km}\). Both values are consistent with the DoD-provided measurements of the fireball's 3D location.