The cross correlation of ambient signal allows seismologists to collect data even in the absence of seismic events. “Seismic interferometry” shows that the cross correlation of simultaneous recordings of a random wavefield made at two locations is formally related to the impulse response between those locations. This idea has found many applications in seismology, as a growing number of dense seismic networks become available: cross‐correlating long seismic records, the Green's function between instrument pairs is “reconstructed” and used, just like the seismic recording of an explosion, in tomography, monitoring, etc. These applications have been accompanied by theoretical investigations of the relationship between noise cross correlation and the Green's function; numerous formulations of “ambient noise” theory have emerged, each based on different hypotheses and/or analytical approaches. The purpose of this study is to present most of those approaches together, providing a comprehensive overview of the theory. Understanding the specific hypotheses behind each Green's function recipe is critical to its correct application. Hoping to guide nonspecialists who approach ambient noise theory for the first time, we treat the simplest formulation (the stationary‐phase approximation applied to smooth unbounded media) in detail. We then move on to more general treatments, illustrating that the “stationary‐phase” and “reciprocity theorem” approaches lead to the same formulae when applied to the same scenario. We show that a formal cross correlation/Green's function relationship can be found in complex, bounded media and for nonuniform source distributions. We finally provide the bases for understanding how the Green's function is reconstructed in the presence of scattering obstacles.

Phase velocities derived from ambient-noise cross-correlation are compared with phase velocities calculated from cross-correlations of waveform recordings of teleseismic earthquakes whose epicentres are approximately on the station–station great circle. The comparison is conducted both for Rayleigh and Love waves using over 1000 station pairs in central Europe. We describe in detail our signal-processing method which allows for automated processing of large amounts of data. Ambient-noise data are collected in the 5–80 s period range, whereas teleseismic data are available between about 8 and 250 s, resulting in a broad common period range between 8 and 80 s. At intermediate periods around 30 s and for shorter interstation distances, phase velocities measured from ambient noise are on average between 0.5 per cent and 1.5 per cent lower than those observed via the earthquake-based method. This discrepancy is small compared to typical phase-velocity heterogeneities (10 per cent peak-to-peak or more) observed in this period range.We nevertheless conduct a suite of synthetic tests to evaluate whether known biases in ambient-noise cross-correlation measurements could account for this discrepancy; we specifically evaluate the effects of heterogeneities in source distribution, of azimuthal anisotropy in surface-wave velocity and of the presence of near-field, rather than far-field only, sources of seismic noise. We find that these effects can be quite important comparing individual station pairs. The systematic discrepancy is presumably due to a combination of factors, related to differences in sensitivity of earthquake versus noise data to lateral heterogeneity. The data sets from both methods are used to create some preliminary tomographic maps that are characterized by velocity heterogeneities of similar amplitude and pattern, confirming the overall agreement between the two measurement methods.

We apply two different algorithms to measure surface wave phase velocity, as a function of frequency, from seismic ambient noise recorded at pairs of stations from a large European network. The two methods are based on consistent theoretical formulations, but differ in the implementation: one method involves the time-domain cross-correlation of signal recorded at different stations; the other is based on frequency-domain cross-correlation, and requires finding the zero-crossings of the real part of the cross-correlation spectrum. Furthermore, the time-domain method, as implemented here and in the literature, practically involves the important approximation that interstation distance be large compared to seismic wavelength. In both cases, cross-correlations are ensemble-averaged over a relatively long period of time (1 yr). We verify that the two algorithms give consistent results, and infer that phase velocity can be successfully measured through ensemble-averaging of seismic ambient noise, further validating earlier studies that had followed either approach. The description of our experiment and its results is accompanied by a detailed though simplifed derivation of ambient-noise theory, writing out explicitly the relationships between the surface wave Green’s function, ambient-noise cross-correlation and phase and group velocities.

The Reykjanes Geothermal System (RGS) is a high‐temperature geothermal system located on the Reykjanes peninsula, a transtensional plate‐boundary zone located on the southwestern tip of Iceland. The area is characterized by high seismicity, recent volcanism, and high‐temperature geothermal fields. We use seismic noise records from April 2014 to August 2015 to study stress changes and potential deformation of the subsurface caused by injection and production operations at RGS through seismic interferometry. We retrieve continuous time series of waveform similarity values and seismic velocity changes during this period. The S‐transform of the similarity values allows us to clearly identify three variations in the mechanical properties of the Reykjanes peninsula related to rapid changes of RGS production. In addition, we observe a slow seismic velocity decrease of 0.36%/year in the reservoir due to the water deficit and seasonal variations associated with the energy production demand.

We applied seismic interferometry to data from an ocean-bottom survey offshore Norway and found that ambient seismic noise can be used to constrain subsurface attenuation on a reservoir scale. By crosscorrelating only a few days of recordings by broadband ocean bottom seismometers, we were able to retrieve empirical Green’s functions associated with surface waves in the frequency range between 0.2 and 0.6 Hz and acoustic waves traveling through the sea water between 1.0 and 2.5 Hz. We discovered that the decay of these surface waves cannot be explained by geometrical spreading alone and required an additional loss of energy with distance. We quantified this observed attenuation in the frequency domain using a modified Bessel function to describe the cross-spectrum in a stationary field. We averaged cross-spectra of equally spaced station couples and sorted these azimuthally averaged cross-spectra with distance. We then obtained frequency-dependent estimates of attenuation by minimizing the misfit of the real parts to a damped Bessel function. The resulting quality factors as function of frequency are indicative of the depth variation of attenuation and correlated with the geology in the survey area.