Ajay Malkoti , Arjun Datta , Shravan M. Hanasoge 

The promise of passive seismology has increasingly been realized in recent years. Given the expense in installing and maintaining seismic station 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 complimentary sensitivity to subsurface structure, compared to phase and group-velocity dispersion, as well as its potential for constraining Vp structure in addition 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 measurements commonly interpreted as the Rayleigh wave H/V ratio, under realistic scenarios of spatially distributed and non-uniform noise sources. Using the surface wave terms of Green's function in a laterally homogeneous medium, we rigorously model multi-component cross-correlations for arbitrary noise-source distributions and extract from them standard estimates of the H/V ratio. Variation of these measurements as a function of 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 question, when noise sources are strongly directional or anisotropic. Love waves, if present in the cross correlations, also have the potential to significantly bias interpretation. Accurate interpretation of the H/V ratio measurement thus rests on carefully modelling these effects. 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 simplistic interpretations of Rayleigh wave ellipticity are only effective (in resolving Vp structure) when the Love-wave contamination is negligible and measurement uncertainties are less than 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.