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

Abstract

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.

On the Nature of Higher‐Order Ambient Seismic Field Correlations

“…Though SRI is also suitable for extracting the Green's function between a virtual source and a receiver (Curtis & Halliday, ), it has been mostly used to bridge a real source and a receiver, which combines two independent wavefields: the ambient noise wavefield and the wavefield excited from the target source. While the Green's functions from the target source, either active (e.g., Duguid et al, ) or passive (e.g., Entwistle et al, ), are unbiased, it ensures that SRI sees fewer artifacts in the ultimate results.…”

Empirical Green's Function Retrieval Using Ambient Noise Source‐Receiver Interferometry

“…The EGFs obtained from the interreceiver interferometry are used as propagators to project the energy from the virtual source (e.g., permanent station S) to the target receiver (e.g., temporary station A; Figure 2a). In a canonical setting of SRI that involves an earthquake source (e.g., Entwistle et al, 2015), the second step of SRI conducts cross correlation between earthquake recordings from the real source to a set of backbone receivers and the EGFs from the virtual source to the same set of backbone receivers (i.e., propagators constructed with interreceiver interferometry). Then summation is performed over all backbone receivers to complete the intersource interferometry.…”

“…We employ two stacking schemes in the calculation of C 2 functions, including linear and weighted stacking. We follow the weighted stacking method proposed by Entwistle et al (2015) and discretize the approximate stationary phase region using Voronoi tessellation. The spatial distribution of the Voronoi cell is determined by the location of the virtual sources.…”

“…The application of SRI has been mostly focusing on exploration or engineering scale experiments (e.g., Duguid et al, 2011;King & Curtis, 2012;Löer et al, 2013;Ravasi et al, 2014;Vasconcelos, 2013). Recently, the development of SRI in earthquake seismology enables a form of "retrospective" seismology (Curtis et al, 2012), whereby one can reconstruct the virtual seismograms at old or new station locations before or after the occurrence of earthquakes, as long as the recordings are made using a few qualified backbone stations (Curtis et al, 2012;Entwistle et al, 2015). As importantly, the application of SRI is not restricted to earthquake sources.…”

Relating source-receiver interferometry to an inverse-scattering series to derive a new method to estimate internal multiples

“…The latter of the three methods, SRI, has been subject to increasing interest due to its close relationship to seismic imaging methods and the new perspective it provides on nonlinear imaging schemes and so-called extended images (Vasconcelos et al, 2010;Fleury and Vasconcelos, 2012;Ravasi and Curtis, 2013;Ravasi et al, 2014). Other applications of SRI include ground-roll removal in land-based exploration seismology (Duguid et al, 2011), construction of underside reflections from borehole recordings (Poliannikov, 2011), retrospectively observing seismograms from old earthquakes in seismology Entwistle et al, 2015), suppression of nonphysical reflections in standard interferometry (King and Curtis, 2012), and prediction of multiply diffracted events and identification of scattering paths Löer et al, 2015). We focus on this last application and show that by considering multiple reflected scattering paths, a new method is obtained to predict internal multiples in reflection seismic data.…”