Taku Tada

A new method to determine phase velocities of Rayleigh waves from microseisms

We have developed a new method to determine phase velocities from the vertical component of microseisms recorded with an array of seismic sensors spaced around the circumference of a circle. We calculate two different time histories by taking the average of the seismograms with differing sets of weights for the sensor stations. The spectral ratio of these two time histories contains no information on the arrival directions or on the amplitudes of the incoming waves but depends solely on the phase velocities of the arriving modes.Theoretical considerations indicate that the effects of directional aliasing caused by the use of a finite number of sensors in the field implementation of our method are small in most situations except for short wavelengths. The presence of incoherent noise limits the efficacy of our method for long wavelengths. In field tests using arrays of three seismic sensors, we obtained appropriate estimates of phase velocities in the wavelength range from 5r to 30r where r, the array radi...

Beyond the SPAC Method: Exploiting the Wealth of Circular-Array Methods for Microtremor Exploration

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.