We explore the wealth of alternative methods for inferring phase velocities of Rayleigh waves using vertical-component seismograms of microtremors from a circular array of seismic sensors, which are formulable along the extension of the popularly used spatial autocorrelation (SPAC) method. Four such methods are illustrated here: the centerless circular-array (CCA) method, the Henstridge methods of the zeroth and first orders (the H0 and H1 methods, respectively), and what we tentatively call the fifth (V) method.
Different methods of phase velocity estimation have different wavelength ranges of good resolution. Implementation to field data from two sites reveals that the traditional SPAC method and the H0 method are both capable of producing reasonable estimates of Rayleigh-wave phase velocities within a relatively narrow range on the short-wavelength side, whereas the H1 method is valid in a relatively narrow range on the long-wavelength side. The CCA and V methods both remain valid over a very broad range of wavelengths, the upper limit extending as far up as several 10s of times the array radius. Use of a noise-compensation technique can further prolong the maximum resolvable wavelength of the CCA method.
We also illustrate the field performance of circle phase methods, which give, without recourse to the conventional frequency-wavenumber analysis, estimates for the principal arrival directions of Rayleigh waves on the basis of circular-array seismograms of microtremors.