{'fraction_non_alphanumeric': 0.016202203499675955, 'fraction_numerical': 0.0038885288399222295, 'mean_word_length': 5.74235807860262, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The azimuthal dependence of Rayleigh wave ellipticity in a slightly anisotropic medium


 A recent study analysed the Rayleigh wave ellipticity obtained by ambient noise cross-correlation in periods of 8–20 s, and observed the Rayleigh wave ellipticity is backazimuth-dependent with a 180° periodicity in the contiguous United States. However, the azimuthal anisotropic parameters have not been inverted to depths, and the comparison with other seismic results has not been possible so far, partially due to the lack of related theoretical investigations. Here, we first derive explicit formulation to relate the period-dependent backazimuthal Rayleigh wave ellipticity with the depth-dependent azimuthal wave speed variation in a slightly anisotropic medium based on the variational principle; by carefully examining relations among different parametrizations of a horizontally transverse isotropic medium, we then express the final formulation in terms of Crampin’s notation. The formulation is verified by comparison with the results of anisotropic propagator matrix technique. Tests show the backazimuth-dependent Rayleigh wave ellipticity provides complementary information on anisotropic parameters in addition to the widely used phase velocity. A simple application of the derived formulation to real data in North America is also provided. Our formulation can be regarded as an extension of the classic work on azimuthal-dependent phase velocity, and helps to quantitatively explain the backazimuth-dependent Rayleigh wave ellipticity.