Generalised receiver functions and seismic interferometry

Classical seismological receiver functions are correlational or deconvolutional combinations of vertical and horizontal component seismometer recordings of earthquake waves that focus information on near-receiver subsurface Earth structure and properties. We show that seismic interferometry can be thought of as a generalisation of receiver functions analysis to cases where recordings at pairs of receivers are considered simultaneously, and where either the same or different component recordings are combined. Further, seismic interferometry uses any of deconvolution, convolution and cross-correlation, and energy from either impulsive or random noise sources. We show both how receiver functions can logically be extended to a new, convolutional form, and that the now little-used correlational form of receiver functions contains more intuitive information than previously realised.Seismic interferometry has provided other extraordinary extensions to seismologists’ arsenal. Passive noise recordings can be converted into seismograms from virtual (imagined) earthquakes that in turn can be used to image the real Earth. Active sources (e.g., earthquakes or man-made sources) can be redatumed into new, virtual sources elsewhere, or can be converted into virtual sensors (seismometers) that record seismograms from other real earthquakes, man-made sources or noise sources that occur either in the future or in the past. And the ability to construct virtual sources and sensors at desired times and locations (rather than having to wait for earthquake sources that occur at uncontrollable locations) promises more repeatable monitoring of changes in Earth subsurface properties over time. Indeed, so-called coda wave interferometry offers unprecedented accuracy in detecting such changes. Finally, existing theoretical extensions to other regimes such as electromagnetic, electrokinetic and diffusive energy propagation may lead to future revolutions in other domains of science.