Constructing new seismograms from old earthquakes: retrospective seismology at multiple length scales

If energy emitted by a seismic source such as an earthquake is recorded on a suitable backbone array of seismometers, source-receiver interferometry (SRI) is a method that allows those recordings to be projected to the location of another target seismometer, providing an estimate of the seismogram that would have been recorded at that location. Since the other seismometer may not have been deployed at the time at which the source occurred, this renders possible the concept of “retrospective seismology” whereby the installation of a sensor at one period of time allows the construction of virtual seismograms as though that sensor had been active before or after its period of installation. Here we construct such virtual seismograms on target sensors in both industrial seismic and earthquake seismology settings, using both active seismic sources and ambient seismic noise to construct SRI propagators, and on length scales ranging over 5 orders of magnitude from ∼40 m to ∼2500 km. In each case we compare seismograms constructed at target sensors by SRI to those actually recorded on the same sensors. We show that spatial integrations required by interferometric theory can be calculated over irregular receiver arrays by embedding these arrays within 2-D spatial Voronoi cells, thus improving spatial interpolation and interferometric results. The results of SRI are significantly improved by restricting the backbone receiver array to include approximately those receivers that provide a stationary-phase contribution to the interferometric integrals. Finally, we apply both correlation-correlation and correlation-convolution SRI and show that the latter constructs fewer nonphysical arrivals