Berenice Froment

Estimation of the effect of nonisotropically distributed energy on the apparent arrival time in correlations

Correlations of random seismic noise are now widely used to retrieve the Green’s function between two points. Whereas this technique provides useful results in tomography and monitoring studies, it is mainly limited by an uneven distribution of noise sources. In that case, theoretical requirements are not completely fulfilled and we may wonder how reliable the reconstructed signals are, in particular for the purpose of estimating traveltime from correlations. This study finds a way to quantify effects of a nonisotropic noise field by estimating the arrival-time error resulting from a particular nonisotropic distribution of recorded wave intensity. Our study is based on a theoretical prediction of this bias and we successfully test the theory by comparing the theoretical expectation to real measurements from seismic-prospecting data. In particular, we distinguish between the effects of source distribution and the effects of medium heterogeneity between the sources and the region of receivers. We find relat...

On the correlation of non-isotropically distributed ballistic scalar diffuse waves

Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Greens function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed them. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and tomographically constructed impressive maps of seismic wave velocity. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The error, in apparent travel time, due to non-isotropic specific intensity is evaluated here in a limit of large receiver-receiver separation and for the case in which the source of the noise is in the far field of both receivers. It is shown that the effect is small, even for cases in which one might have considered the anisotropy to be significant, and even for station pairs separated by as little as one or two wavelengths. A formula is derived that permits estimations of error and corrections to apparent travel time. It is successfully compared to errors seen in synthetic waveforms.

Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise

Analysis of long-range correlation of the microseisms has been shown to provide reliable measurements of surface wave speeds that can be used for seismic imaging and monitoring. In the case of an even distribution of noise sources, it has been theoretically demonstrated that the correlation is the exact Greens function, including all types of waves. This method is limited in its application by the actual source distribution. In practice, the azimuthal distribution of energy flux of the noise is dominated by some particular directions resulting in a clear azimuthal dependence of the quality of the reconstruction of Rayleigh waves, with a poor reconstruction in some azimuths. To solve this problem, we use noise correlations measured on the entire network. We consider two stations, A and B, for which the Rayleigh waves could not be discerned in the in the correlation of continuous records of ambient noise. We computed all correlations between the station A (respectively B) and all the 150 other stations located at regional distances. Theoretically, these virtual seismograms contain direct waves and coda, although they are clearly contaminated by the influence of the imperfect ambient noise field and most are inadequate for direct analysis. We used these correlation functions as equivalents to seismograms produced by sources acting at the 150 stations locations and recorded in A (respectively B). We select time windows in those virtual seismograms that correspond to coda and compute correlations between them. This metacorrelation is found to exhibit the surface wave part of the Greens function that was not visible in the raw correlation of ambient noise. We illustrate the legitimacy of the reconstruction by comparison with raw noise correlations. This procedure can be used to assess seismic velocity between stations, even in presence of a directive and poorly oriented ambient noise. The result shows that in spite of the small signal-to-noise ratios often seen in correlations of ambient noise, especially at large lag time corresponding to coda, their codas are better equipartitioned than was the ambient noise upon which they were based. They are therefore presumably multiply scattered and contain information on both direct surface waves and also on more complex travel paths.

Correlation of nonisotropically distributed ballistic scalar diffuse waves in two dimensions.

Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Greens function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed this. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and constructed impressive tomographic maps of seismic wave velocity, and even detected fractional secular changes in seismic wave speed at a level of 0.0001. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The usual wave field used in long‐period seismology is due to distant ocean storms and is, even in the presence of scattering, not isotropic. Here an asymptotic evaluation of the effect, on apparent travel time in a correlation waveform, is made of nonisotropic distributions of ba...