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Lawrence et al., 2012: DRAFT: JGR: Ambient Noise Numerical Evaluation found with traditional earthquake studies: This method provides reasonable geological and geophysical results from the scales of reservoirs [Weemstra et al., 2011a,b] to continents [Lawrence and Prieto, 2011]. Lin et al. [2011] confirmed that the NCFs amplitude decay with distance, or receiver separation, is conform to attenuation of the medium [see also Cupillard and Capdeville, 2010]. Nakahara [2012] showed that the expression above is approximately correct for small attenuation, providing a theoretical basis to estimate attenuation from the coherency of ambient noise records. With concerns on the ambient noise sources distribution, the accuracy of the NCF anelastic measurements is actively discussed. Weaver [2011; 2012] and Tsai [2011] suggest that NCF amplitudes highly depend on noise source distribution and that azimuthal averaging of coherency estimates may not be enough for retrieving reliable attenuation coefficients. Numerical simulations [Cupillard and Cadeville, 2010] and theoretical derivations [Tsai, 2011; Nakahara, 2012] corroborated that for uniformly distributed noise sources, NCF amplitude decays depend on the attenuation of the medium. Much of the debate regarding the recovery of attenuation from NCFs may largely depend on the different assumptions made regarding the intensity distribution of the ambient source field [Weaver, 2011]. We stress that the Earth’s ambient source field is not uniformly distributed; and rather that its origin varies spatially and temporally, depending on seasonal effects, proximity to the coast [e.g., Schulte-Pelkum et al., 2004; Stehly et al., 2006; Chevrot et al., 2007; Aster et al., 2008; Kedar et al., 2008; Ardhuin et al., 2011]. In practice, normalizing the ambient seismic field records and averaging of normalized correlations over time is thought to alleviate somewhat the strong directionality of the ambient seismic field. The ambient seismic field waveforms can be considered as a summation of displacements measured after propagation (with geometrical spreading and attenuation) from many sources. ,2 4 Marine Denolle 12/28/12 6:23 PM Comment: Here I am not mentioning “intrinsic” attenuation since the focusing/defocusing cancels out and i think that scattering plays a role in it. is that ok?
Lawrence et al., 2012: DRAFT: JGR: Ambient Noise Numerical Evaluation In this work, we present a numerical approach to express our understanding of estimated attenuation coefficients from the ambient seismic field and the effect of appropriate signal processing to reduce the effects of source directivity. We first build the synthetic ambient seismic field in a layered medium. We then compute synthetic coherencies (or spectrum of the NCFs) at all station pairs and compare with theoretical Bessel functions. We evaluate the impact of the noise-source and receiver distributions on attenuation measurements by numerically demonstrating that synthetic NCF amplitudes are consistent with the expected results from Prieto et al. [2009]. We show that for a wide range of noise source distributions we are able to recover accurate attenuation coefficients. We further show that the attenuation measured is sensitive to the local structure, instead of the path source-receiver. Analytical Framework Realistic ambient seismic field recorded at a given receiver can be considered as the sum of all wave fields propagating from all sources to the receiver. We assume a laterally homogenous medium with vertical only variations, and hence dispersive properties. For a single point-force source located at s with spectrum F, the displacement u recorded at location x is given by: where ω is the frequency, k is the wavenumber, t0 is the source time [Sánchez-Sesma and Campillo, 2006], α(ω) is the frequency-dependent attenuation coefficient, and rsx is the source-receiver distance. In cylindrical coordinates, this is a far-field approximation to the surface-wave displacement eigenfunction with attenuation incorporated as an exponential decay. As in Prieto et al. [2009], we consider only the vertical component of the Rayleigh waves. We follow the conventions in Sanchez-Sesma and Campillo [2006] with two receivers located at x and y, y taken at the origin, that record the displacement from a source , 3 5
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