Lawrence et al., 2012: DRAFT: JGR: Ambient Noise Numerical ...
Lawrence et al., 2012: DRAFT: JGR: Ambient Noise Numerical ...
Lawrence et al., 2012: DRAFT: JGR: Ambient Noise Numerical ...
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<strong>Lawrence</strong> <strong>et</strong> <strong>al</strong>., <strong>2012</strong>: <strong>DRAFT</strong>: <strong>JGR</strong>: <strong>Ambient</strong> <strong>Noise</strong> Numeric<strong>al</strong> Ev<strong>al</strong>uation<br />
Most attempts that simplify this proof rely on significant assumptions and collapse to<br />
variations of equation 3 (e.g., equation 23 in Tsai [2011]). Under these assumptions, the<br />
NCF reve<strong>al</strong>s a strong dependence on source and receiver distributions [Tsai, 2011].<br />
Using the ambient seismic field displacement expressed in equation 8, the cross-<br />
spectrum for a receiver pair located in (x,y) becomes<br />
. 11<br />
Equation 11 obviously differs from equation 5 or 6. The coherency presented in equation<br />
9 then becomes<br />
Solving equation 12 an<strong>al</strong>ytic<strong>al</strong>ly is laborious and we turn to numeric<strong>al</strong> approaches to<br />
compute the coherencies.<br />
Numeric<strong>al</strong> solution:<br />
For numeric<strong>al</strong> c<strong>al</strong>culations, we discr<strong>et</strong>ize equation 8 with a finite number of sources<br />
per time window Ns,<br />
. 13<br />
The medium is later<strong>al</strong>ly homogeneous, and we assume Rayleigh-wave phase velocity<br />
C(ω) and attenuation α(ω) dispersions from Pri<strong>et</strong>o <strong>et</strong> <strong>al</strong>. [2009] for southern C<strong>al</strong>ifornia.<br />
We explore the impact of different source scenarios (distributions and spectra), receiver<br />
distributions to the estimates the coherency.<br />
Another widely discussed factor entering an<strong>al</strong>yses on Green’s function r<strong>et</strong>riev<strong>al</strong> is the<br />
role of incoherent noise sources such as site effects, electric<strong>al</strong> noise, wind, therm<strong>al</strong> effects,<br />
cultur<strong>al</strong> noise, micro-seismicity, and anything that can create vibrations well recorded at<br />
12<br />
8