Analysis of data, recorded on March 8th 2014 at the Comprehensive Nuclear-Test-Ban Treaty Organisation's hydroacoustic stations off Cape Leeuwin Western Australia, and at Diego Garcia, reveal unique pressure signatures that could be associated with objects impacting at the sea surface, such as falling meteorites, or the missing Malaysian Aeroplane MH370. To examine the recorded signatures, we carried out experiments with spheres impacting at the surface of a water tank, where we observed almost identical pressure signature structures. While the pressure structure is unique to impacting objects, the evolution of the radiated acoustic waves carries information on the source. Employing acoustic-gravity wave theory we present an analytical inverse method to retrieve the impact time and location. The solution was validated using field observations of recent earthquakes, where we were able to calculate the eruption time and location to a satisfactory degree of accuracy. Moreover, numerical validations confirm an error below 0.02% for events at relatively large distances of over 1000 km. The method can be developed to calculate other essential properties such as impact duration and geometry. Besides impacting objects and earthquakes, the method could help in identifying the location of underwater explosions and landslides.