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 relative errors in the order of a percent which may affect monitoring results, especially where smaller relative velocity variations (smaller than 10(-3) for some applications) are investigated. Finally, we see that correlation of coda waves helps mitigate the effects of a nonisotropic field, hence making the estimation of traveltime quite stable irrespective of the source distribution.