# Localizing the First Interstellar Meteor with Seismometer Data
## 2 Method of Calculation
There were three peaks observed in the lightcurve of IM1, with separations of 0.101 s and 0.112 s in time, and 2.0 km and 2.3 km in altitude, between the first and second peaks, and second and third peaks, respectively. The meteor's direction of motion was perpendicular to the vector extending to AU MANU, so the x-y motion does not affect the timing of the acoustic transmission from the fireball to the seismometer. The maximum signal between 296 s and 297 s presumably corresponds to the third peak, because the signal from the third peak should have arrived earliest to AU MANU, given its relatively low altitude. It is also the strongest spike in the seismic signal; similarly, the third peak in the IM1 lightcurve was the most energetic. The altitude and temporal differences between the lightcurve peaks imply temporal separations for the acoustic maxima of \(\sim[(2\text{ km})/(\sqrt{3}\times 315\text{ m}/\text{s})]-0.101\text{ s}=3.57\text{ s}\) and \(\sim[(2.3\text{ km})/(\sqrt{3}\times 315\text{ m}/\text{s})]-0.112\text{ s}=4.11\text{ s}\) between the first and second peaks, and second and third peaks, respectively. Overall, this suggests that the maximum acoustic signatures associated with the second and first lightcurve peaks should arrive at 4.11 s and 7.68 s, respectively, after the signature associated with the third lightcurve peak. We illustrate this in Figure 2 as the gray lines overlaid onto the AU MANU seismic signal, which shows good agreement. Our model implies that the third peak in the lightcurve corresponds to an altitude of \(z=16.9\pm 0.9\text{ km}\), the second to an altitude of \(z=19.2\pm 0.9\text{ km}\), and the first to an altitude of \(z=21.2\pm 0.9\text{ km}\). The resulting ram pressures are \(244\pm 27\text{ MPa}\), \(183\pm 21\text{ MPa}\), and \(143\pm 16\text{ MPa}\), respectively. We use a numerical procedure to check if the derived values for \(r\) and \(z\) correctly describe the shape of the second packet. Note that this is a simple procedure that can be improved upon in the future by including factors such as atmospheric stratification or the gradient of sound speed. The procedure imagines the blast from the fireball as a singular spherical wave emitted \(z=16.9\pm 0.9\text{ km}\) above a point ocean surface \(r=83.9\pm 0.7\text{ km}\) away from the AU MANU seismometer, traveling at \(v=315\pm 2\text{ m s}^{-1}\). The spherical wave intersects the ocean surface at times \(t>(z/v_{a})\) in circles with radii \(r_{circ}=\arccos\left[(z/(v_{a}t))\right]\), carrying a fraction of the blast energy corresponding to the fraction of the spherical blast wave contacting the ocean surface, \(f\propto(2\pi r_{circ}\text{d}r_{circ})/(4\pi r^{2})\). We assume an angle-independent reflection coefficient and the amplitude does not matter for the probability distribution in Figure 2, given the arbitrary normalization. The procedure then considers each point on each ocean surface circle re-radiating, using the distance from the point to the AU MANU seismometer, \(s\), to derive the additional travel time \((s/v_{a})\) and the additional reduction in flux of \((4\pi s^{-2})\). For each possible path, the travel time from the fireball to the point on the ocean surface, and from the point on the ocean surface to the AU MANU seismometer, are summed, and the relative flux delivered to the AU MANU seismometer is tabulated. This allows the relative fluxes for all the paths with the arrival times within each time bin to be summed. The result is the relative amplitude for the simulated signal, assuming perfect reflection and no transmission losses, as a function of time. The simulated second packet provides a match to the rise, peak, and tail of the actual second packet, displayed in Figure 3. This match confirms the blast location parameters derived using Equations (1)-(3). We confirm the fireball location implied by AU MANU with the timing of the strong seismic signal, clearly distinct from background noise, detected by the AU COEN seismic station on 2014-01-08 18:23:53, presumably produced by the fireball.