Rayleigh wave H / V amplitude ratio measurement using multicomponent ambient noise cross-correlations , and its relationship to Vp / Vs

The promise of passive seismology has increasingly been realized in recent years. Given the expense in installing and maintaining these seismic networks, it is important to extract as much information from the measurements as possible. In this context, the ellipticity or H/V amplitude ratio of Rayleigh waves can prove to be a valuable observable in ambient noise seismology due to its potential for constraining VP structure, an advantage over group and phase-velocity dispersion, which are primarily sensitive to VS . However, the suitability of the Rayleigh H/V ratio in noise-based studies depends on the accurate interpretation of measurements made on multi-component ambient-noise cross-correlations. We present a synthetic study that critically examines such measurements – commonly interpreted in terms of the Rayleigh H/V ratio – for realistic scenarios of spatially distributed and non-uniform noise sources. Using the Rayleigh-wave Green’s function in a laterally homogeneous medium, we rigorously model multi-component cross-correlation for arbitrary noise-source distributions and extract from them standard estimates of the H/V ratio. Variation of these measurements with VP is studied empirically by brute-force simulation. We find that the measurements depart significantly from the theoretical Rayleigh wave H/V for the medium in 1 Malkoti, Datta & Hanasoge question, when noise sources are strongly directional or anisotropic. However, the sensitivity to VP structure is comparable to that of the classic Rayleigh wave H/V. We also propose a new measurement for cross-correlations that has slightly greater sensitivity to VP . Finally, uncertainty analysis on synthetic tests suggests that the ellipticity measurements can robustly resolve the Vp structure in the presence of noise (up to 10%). The primary utility of this method in scenarios when the noise level in the measured cross-correlations is significant (& 20%), is in being able to discern between different classes of models.


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In this study we do not invoke Green's function interpretations for noise-correlation 57 signals; instead we model these signals rigorously for arbitrary spatial distributions of 58 noise sources (Section 2). To our knowledge, no previous study that models cross-59 correlations in this manner has analysed the Rayleigh H/V measurement in detail.

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Through a series of synthetic tests, we quantify the dependence of this measurement on 61 the anisotropy of noise-source distribution, as well as on model V P , to assess its utility in  i.e. we write S(ξ, ω) = P (ω)σ(ξ). These three simplifications lead to the expression: The evaluation of eq. (2) is still a three-step process in general, based on the invocation Hence C pq is computed as follows. First, we obtain the z-component of impulse response where all symbols follow the Aki and Richards (2002) notation and r = x 2 + y 2 . The Equivalently, one may write The equivalence between eqs.(6) and (5) is seen from eq. (4), when the x, y axes are 122 oriented along the radial and transverse directions respectively (e.g. Fig. 1). Since the 123 second index in the Green's tensor G ij refers to the source orientation, eq. (6) asserts 124 that η is a medium property, independent of whether the source (point-force) is vertical 125 or radial.

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In the case of CCs, most studies define the Rayleigh H/V ratio analogously to eq. Green's function holds, the two CC measurements, Γ R and Γ Z , correspond to virtual 130 sources oriented radially and vertically, respectively: Here, f represents the operations applied to the CCs to obtain robust measurements.

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In this study, we 1) Determine the envelope of the cross-correlation signal, 2) Pick its 133 maximum value on the causal and anti-causal branches, 3) Average the two values thus 134 obtained. 135 We note that the interpretation of Γ R or Γ Z as the Rayleigh wave H/V ratio (right 136 side of eq. (7)) is supported in this study by the fact that the CCs are constructed 137 from Rayleigh waves alone. The superscript of these ratios in eq. (7) represents the (2), we estimate that it should be related to η 2 : 3 Simulations 144 We perform a suite of simulations designed to empirically assess the sensitivity of H/V 145 measurements to V p structure, as well as gross geometrical features of the noise-source   are cosine tapered to zero over an additional 5 • at both ends.

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The five source-distribution models utilized for the simulations are shown in Fig. 2.

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4 Analysis and results 188 We start by examining the CC obtained for each of the noise-source distributions in 189 Earth model M 0 (Fig. 3) . The effect of anisotropic source distributions is readily  Table 1.

Measurements with added synthetic noise
Since our aim in this study is to assess the sensitivity of H/V measurements to V P , where α is the desired signal to noise ratio and k is a scaling factor to bring the noise  Table 1.

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This helps us evaluate the efficacy of measurements based on the thresholds given by 233 η DR for Γ R and Γ Z , and by η 2 DR for Γ. We infer two things from the observed values.

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First, meaningful measurements can only be made for up to 15% random Gaussian noise.

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Beyond this noise level, the uncertainties in CC-derived H/V ratios exceed the η DR or 236 η 2 DR thresholds. Second, noise has a lower impact on Γ in comparison to Γ R and Γ Z , 237 due to its larger dynamic range.   5 Discussion and conclusions 239 We have presented a synthetic study that critically examines measurements commonly