Global-scale seismic interferometry: theory and numerical examples

Progress in the imaging of the mantle and core is partially limited by the sparse distribution of natural sources; the earthquake hypocenters are mainly along the active lithospheric plate boundaries. This problem can be approached with seismic interferometry. In recent years, there has been considerable progress in the development of seismic interferometric techniques. The term seismic interferometry refers to the principle of generating new seismic responses by cross‐correlating seismic observations at different receiver locations. The application of interferometric techniques on a global scale could create sources at locations where no earthquakes occur. In this way, yet unknown responses would become available for the application of travel‐time tomography and surface‐wave dispersion studies. The retrieval of a dense‐enough sampling of source gathers would largely benefit the application of reflection imaging. We derive new elastodynamic representation integrals for global‐scale seismic interferometry. The relations are different from other seismic interferometry relations for transient sources, in the sense that they are suited for a rotating closed system like the Earth. We use a correlation of an observed response with a response to which free‐surface multiple elimination has been applied to account for the closed system. Despite the fact that the rotation of the Earth breaks source‐receiver reciprocity, the seismic interferometry relations are shown to be valid. The Coriolis force is included without the need to evaluate an extra term. We synthesize global‐scale earthquake responses and use them to illustrate the acoustic versions of the new interferometric relations. When the sampling of real source locations is dense enough, then both the responses with and without free‐surface multiples are retrieved. When we do not take into account the responses from the sources in the direct neighborhood of the seismic interferometry‐constructed source location, the response with free‐surface multiples can still be retrieved. Even when only responses from sources at a certain range of epicentral distances are available, some events in the Green's function between two receiver locations can still be retrieved. The retrieved responses are not perfect, but the artefacts can largely be ascribed to numerical errors. The reconstruction of internal events – the response as if there was a source and a receiver on (major) contrasts within the model – could possibly be of use for imaging. With modelling it is possible to discover in which region of the correlation panel stationary phases occur that contribute to the retrieval of events. This knowledge opens up a new way of filtering out undesired events and of discovering whether specific events could be retrieved with a given source‐receiver configuration.