The benefit of hindsight in observational science: Retrospective seismological observations

We show that interferometric theory allows recordings on a large variety of sensor types to be both spatially and temporally redatumed. Recordings of an energy source can thus be obtained at times before, during or after the period during which the sensor was physically installed. As a consequence, sensors in acoustic, elastic, electromagnetic, electrokinetic and a variety of other wavefield or diffusive environments may be deployed retrospectively, after an event of interest occurs and at locations chosen with the benefits of hind-sight: recordings of the event of interest can then be constructed post hoc. As an illustration, seismograms from two earthquakes are constructed on a seismometer deployed only after the earthquakesʹ seismic energy had completely dissipated. Bizarrely, a contributory component of such deterministic seismograms turns out to be ambient, random seismic noise. The seismograms obtained can be used to estimate seismic velocities in the vicinity of the seismometer, and provide independent information about the source phase (which is unavailable from the equivalent direct recordings). Thus, such retrospective observations provide novel information about both the earth and the energy source.