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

Abstract

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 signals are reconstructed, in particular for the purpose of estimating traveltime from correlations. We present in this study a way to quantify effects of a non-isotropic noise 1 field by estimating the arrival time error due to a particular non-isotropic 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 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 non-isotropic field, hence making the estimation of traveltime quite stable irrespective of the source distribution.2

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

“…Finally, the phase of the symmetric part of the cross-correlation, that is, [ C S ], is largely unaffected by the non-uniformity of P(θ ). This suggests that phase velocity measurements may give results that only slightly deviate from the 'real' phase velocity and is in line with the data analyses by Gouédard et al (2008) and Froment et al (2010).…”

“…Our results show that multiple scattering mitigates the effect of the source distribution on the amplitude of the cross-correlation; this has been shown for the phase of the cross-correlation previously (Froment et al 2010;Sens-Schönfelder & Wegler 2011). Specifically, we show that the spatially and azimuthally averaged cross-spectrum decays exponentially in case of a purely elastic scattering medium illuminated uniformly from all angles.…”

Arrival angle anomalies of Rayleigh waves observed at a broadband array: a systematic study based on earthquake data, full waveform simulations and noise correlations

“…The detailed processing that lead to these correlation functions can be found in Boué et al (2014). The use of one year of continuous data, and the symmetric part (stack of the positive and negative lag time) of the correlation functions strongly reduced potential bias due to uneven noise source distributions (Froment et al 2010;Kimman & Trampert 2010). In total, 593 stations were used (i.e.…”

Characterization of ambient seismic noise near a deep geothermal reservoir and implications for interferometric methods: a case study in northern Alsace, France

“…Using the work of Weaver et al (2009) andFroment et al (2010), we estimate the theoretical phase shifts predicted by a given azimuthal distribution of the noise energy (ADNE). We find that a simple synthetic ADNE made of two Gaussian functions centered at 150°and 300°(the principal back azimuths of the noise directivity observed in Figure 3) reproduces the main features (sinusoidal shape and amplitudes) of the phase shifts measured on real data.…”

“…The consequences of violating these assumptions have been studied theoretically and numerically using synthetic data (Weaver et al 2009;Froment et al 2010). Although the seismic noise distribution on Earth is rarely homogeneous in time and space, the CCFs approximate Green's functions correctly if the inter-station distances are long and the azimuthal distribution of the noise is smooth.…”