Centerless circular array method: Inferring phase velocities of Rayleigh waves in broad wavelength ranges using microtremor records

Author(s):  
Ikuo Cho ◽  
Taku Tada ◽  
Yuzo Shinozaki
1982 ◽  
Vol 72 (4) ◽  
pp. 1329-1349
Author(s):  
H. J. Patton

abstract Single-station measurements of Rayleigh-wave phase velocity are obtained for paths between the Nevada Test Site and the Livermore broadband regional stations. Nuclear underground explosions detonated in Yucca Valley were the sources of the Rayleigh waves. The source phase φs required by the single-station method is calculated for an explosion source by assuming a spherically symmetric point source with step-function time dependence. The phase velocities are used to analyze the Rayleigh waves of the Massachusetts Mountain earthquake of 5 August 1971. Measured values of source phase for this earthquake are consistent with the focal mechanism determined from P-wave first-motion data (Fischer et al., 1972). A moment-tensor inversion of the Rayleigh-wave spectra for a 3-km-deep source gives a horizontal, least-compressive stress axis oriented N63°W and a seismic moment of 5.5 × 1022 dyne-cm. The general agreement between the results of the P-wave study of Fischer et al. (1972) and this study supports the measurements of phase velocities and, in turn, the explosion source model used to calculate φs.


1964 ◽  
Vol 54 (2) ◽  
pp. 571-610
Author(s):  
George E. Backus

ABSTRACT If the averages of the reciprocal phase velocity c−1 of a given Rayleigh or Love mode over various great circular or great semicircular paths are known, information can be extracted about how c−1 varies with geographical position. Assuming that geometrical optics is applicable, it is shown that if c−1 is isotropic its great circular averages determine only the sum of the values of c−1 at antipodal points and not their difference. The great semicircular averages determine the difference as well. If c−1 is anisotropic through any cause other than the earth's rotation, even great semicircular averages do not determine c−1 completely. Rotation has negligible effect on Love waves, and if it is the only anisotropy present its effect on Rayleigh waves can be measured and removed by comparing the averages of c−1 for the two directions of travel around any great circle not intersecting the poles of rotation. Only great circular and great semicircular paths are considered because every earthquake produces two averages of c−1 over such paths for each seismic station. No other paths permit such rapid accumulation of data when the azimuthal variations of the earthquakes' radiation patterns are unknown. Expansion of the data in generalized spherical harmonics circumvents the fact that the explicit formulas for c−1 in terms of its great circular or great semicircular integrals require differentiation of the data. Formulas are given for calculating the generalized spherical harmonics numerically.


1993 ◽  
Vol 6 (2) ◽  
pp. 289-297 ◽  
Author(s):  
Guo-Ying Chen ◽  
Rong-Sheng Zeng ◽  
Francis T. Wu ◽  
Xiao-Lan Su

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1535-1551 ◽  
Author(s):  
Ikuo Cho ◽  
Taku Tada ◽  
Yuzo Shinozaki

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 radius, was on the order of a few meters.


1963 ◽  
Vol 53 (4) ◽  
pp. 741-764 ◽  
Author(s):  
M. Nafi Toksöz ◽  
Ari Ben-Menahem

Abstract Phase velocities of Love waves from five major earthquakes are measured over six great circle paths in the period range of 50 to 400 seconds. For two of the great circle paths the phase velocities of Rayleigh waves are also obtained. The digitized seismograph traces are Fourier analyzed, and the phase spectra are used in determining the phase velocities. Where the great circle paths are close, the phase velocities over these paths are found to be in very good agreement with each other indicating that the measured velocities are accurate and reliable. Phase velocities of Love waves over paths that lie far from each other are different, and this difference is consistent and much greater than the experimental error. From this it is concluded that there are lateral variations in the structure of the earth's mantle. One interpretation of this variation is that the mantle under the continents is different from that under the oceans, since the path with the highest phase velocities is almost completely oceanic. This interpretation, however, is not unique and variations under the oceans and continents are also possible. Group velocities are computed from the phase velocities and are also directly measured from the seismograms. The group-velocity curve of Love waves has a plateau between periods of 100 and 300 seconds with a shallow minimum at about 290 seconds. The sources of error in both Fourier analysis and direct time domain methods of phase velocity measurement are discussed.


1968 ◽  
Vol 58 (3) ◽  
pp. 1021-1034 ◽  
Author(s):  
S. Bloch ◽  
A. L. Hales

abstract A number of new techniques have been developed for the determination of phase velocities from the digitized seismograms from pairs of stations. One of these techniques is to Fourier analyze the sum (or difference) of the two seismograms after time shifting in steps to correspond to steps in phase velocity. The amplitude of the summed seismogram is a maximum for any particular period when both seismograms are in phase at that period. Another method is to pass both seismograms through a narrow bandpass digital filter centered at various periods and form the cross product of the filtered seismograms, after time shifting. The average of the resultant time series is a maximum when the two signals are in phase. The computer output is a matrix consisting of amplitudes or averages as a function of phase velocity and period. The phase velocity dispersion is determined from the contoured matrix. Using these techniques, interstation phase velocities of Rayleigh waves have been determined for the “World Wide Network Standard Stations” at Pretoria, Bulawayo and Windhoek. The method using cross-products is the most efficient.


2020 ◽  
Author(s):  
Zongbo Xu

One uses seismic interferometry (SI) to recover Green's functions (i.e. impulse response) from ambient seismic recordings and estimate surface-wave phase velocities to investigate subsurface structure. This method has been commonly used in the last 20 years because this method only utilizes ambient seismic recordings from seismic stations/sensors and does not rely on traditional seismic sources (e.g. earthquakes or active sources). SI assumes that the ambient seismic wavefield is isotropic, but this assumption is rarely met in practice. We demonstrate that, with linear-array spatial sampling of an anisotropic ambient seismic wavefield, SI provides a better estimate of Rayleigh-wave phase velocities than another commonly used ambient seismic method, the refraction microtremor (ReMi) method. However, even SI does not work in some extreme cases, such as when the out-of-line sources are stronger than the inline sources. This is because the recovered Green's functions and surface-wave phase velocity estimations from SI are biased due to the anisotropic wavefield. Thus, we propose to use multicomponent data to mitigate this bias. The multicomponent data are vertical (Z) and radial (R) components, where the R direction is parallel to a line or great circle path between two sensors. The multicomponent data can deal with the extreme anisotropic source cases, because the R component is more sensitive to the in-line sources than the out-of-line sources, while the Z component possesses a constant sensitivity to sources in all directions. Estimation of source distributions (i.e. locations and strengths) can aid correction of the bias in SI results, as well as enable the study of natural ambient seismic sources (e.g. microseism). We use multicomponent seismic data to estimate ambient seismic source distributions using full-waveform inversion. We demonstrate that the multicomponent data can better constrain the inversion than only the Z component data, due to the different source sensitivities between the Z and R components. When applying the inversion to field data, we propose a general workflow which is applicable for different field scales and includes vertical and multicomponent data. We demonstrate the workflow with a field data example from the CO2 degassing in Harstouˇsov, Czech Republic. We also apply the workflow to the seismic recordings in Antarctica during February 2010 and estimate the primary microseism source distributions. The SI results include both direct and coda waves. While using the direct waves in investigating subsurface structure and estimating source distributions, one can utilize the coda waves to monitor small changes in the subsurface. The coda waves include multiply-scattered body and surface waves. The two types of waves possess different spatial sensitivities to subsurface changes and interact each other through scattering. We present a Monte Carlo simulation to demonstrate the interaction in an elastic homogeneous media. In the simulation, we incorporate the scattering process between body and Rayleigh waves and the eigenfunctions of Rayleigh waves. This is a first step towards a complete modelling of multiply-scattered body and surface waves in elastic media.


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