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

Geophysics ◽  
2004 ◽  
Vol 69 (6) ◽  
pp. 1535-1551 ◽  
Author(s):  
Ikuo Cho ◽  
Taku Tada ◽  
Yuzo Shinozaki
Keyword(s):  
Rayleigh Waves ◽  
Vertical Component ◽  
Field Tests ◽  
Spectral Ratio ◽  
New Method ◽  
Phase Velocities ◽  
Seismic Sensors ◽  
Time Histories ◽  
Theoretical Considerations ◽  
Incoherent Noise

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.

Miniature array analysis of microtremors

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. KS13-KS23 ◽  
Author(s):  
Ikuo Cho ◽  
Shigeki Senna ◽  
Hiroyuki Fujiwara
Keyword(s):  
Urban Areas ◽  
Rayleigh Waves ◽  
Evaluation Method ◽  
Vertical Component ◽  
Test Site ◽  
Observation Point ◽  
Shallow Subsurface ◽  
Phase Velocities ◽  
Time Required ◽  
Array Analyses

We suggest observing microtremors by using a miniature array consisting of vertical-component seismometers that are placed at the center and on the circumference of a circle with a radius of several tens of centimeters, for identifying the phase velocities of Rayleigh waves with wavelengths exceeding several tens or a hundred meters. We present, as tools for the analysis, a set comprised of the analysis methods for the phase velocity and the evaluation method for the analysis limit, which were recently developed by the authors on the basis of a rigorous theory derived by generalizing a spatial autocorrelation method. We conducted miniature-array observations using four or six servo-type seismometers, JU-215 manufactured by Hakusan Corporation, at about 50 observation points throughout a test site and urban areas in Tsukuba City and its surroundings, which have various topographical and geologic environments. The time required from arrival at an observation point to retrieval averaged about 30 min. We could determine the phase velocities of Rayleigh waves with wavelengths of 40 and 100 m at 91% and 51% of all the observation points, respectively. Miniature array analyses can significantly improve the mobility of observation to infer shallow subsurface velocity structures to the depth of several tens of meters.

Residual dispersion measurement—a new method of surface-wave analysis

1972 ◽  
Vol 62 (1) ◽  
pp. 129-139
Author(s):  
A. Dziewonski ◽  
J. Mills ◽  
S. Bloch
Keyword(s):  
Rayleigh Waves ◽  
Love Wave ◽  
Absolute Error ◽  
New Method ◽  
Transverse Motion ◽  
Period Range ◽  
Phase Velocities ◽  
Dispersion Measurement ◽  
Order Of Magnitude ◽  
Velocity Changes

Abstract Measurements of group velocities by means of band-pass filtering lead to systematic errors when group in velocity changes rapidly with frequency. A new method hereafter referred to as “residual dispersion measurement” avoids this difficulty by transforming the signal prior to the filtering. An observed seismogram is cross-correlated with a theoretical seismogram in which the dispersion approximates the observed dispersion within a few per cent. Dispersion of the resulting pulse can be measured with a much higher precision, since du/dω has been reduced by at least an order of magnitude. In addition, the method can be employed iteratively to obtain a greater precision of measurement. The dispersion of mantle Rayleigh waves is measured from a sum of 48 auto-correlograms of the recordings of the Alaskan earthquake of March 28, 1964. Group and phase velocities are obtained for order numbers between 0S9 and 0S47. It is estimated that the absolute error of the group-velocity measurement does not exceed 0.015 km/sec. The analysis of a sum of 13 auto-correlograms of horizontal component seismograms with predominantly transverse motion reveals that the fundamental-mode Love-wave data may be contaminated by higher torsional modes. Comparison of several sets of average Love-wave phase velocities shows a discrepancy of the order of 0.4 per cent in the period range from 350 to 170 sec. The corresponding figure for Rayleigh waves is less by at least an order of magnitude.

Quantification of Effects of Ridge and Valley Topography on the Rayleigh Wave Characteristics

2018 ◽  
Vol 12 (03) ◽  
pp. 1850007 ◽  
Author(s):  
J. P. Narayan ◽  
A. Kumar
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Large Scale ◽  
Research Work ◽  
Vertical Component ◽  
Staggered Grid ◽  
Long Span ◽  
Shape Ratio ◽  
Day By Day ◽  
Ridge And Valley

The effects of ridge and valley on the characteristics of Rayleigh waves are presented in this paper. The research work carried out has been stimulated by the day by day increase of long-span structures in the hilly areas which are largely affected by the spatial variability in ground motion caused by the high-frequency Rayleigh waves. The Rayleigh wave responses of the considered triangular and elliptical ridge and valley models were computed using a fourth-order accurate staggered-grid viscoelastic P-SV wave finite-difference (FD) program. The simulated results revealed very large amplification of the horizontal component and de-amplification of the vertical component of Rayleigh wave at the top of a triangular ridge and de-amplification of both the components at the base of the triangular valley. The observed amplification of both the components of Rayleigh wave in front of elliptical valley was larger than triangular valley models. A splitting of the Rayleigh wave wavelet was inferred after interaction with ridge and valley. It is concluded that the large-scale topography acts as a natural insulator for the surface waves and the insulating capacity of the valley is more than that of a ridge. This insulation phenomenon is arising due to the reflection, diffraction and splitting of the surface wave while moving across the topography. It is concluded that insulating potential of the topography for the Rayleigh waves largely depends on their shape and shape-ratio.

Characteristics of long-period microtremors and their applicability in exploration of deep sedimentary layers

1994 ◽  
Vol 84 (6) ◽  
pp. 1831-1841 ◽  
Author(s):  
Hiroaki Yamanaka ◽  
Masayuki Takemura ◽  
Hiroshi Ishida ◽  
Masanori Niwa
Keyword(s):  
Rayleigh Waves ◽  
Ground Motions ◽  
Spectral Ratio ◽  
Northwestern Part ◽  
Trial And Error ◽  
Sediment Thickness ◽  
Short Term ◽  
Subsurface Structures ◽  
Long Period ◽  
Good Agreement

Abstract Applicability of long-period microtremors in inferring subsurface structure is examined using measurements of microtremors in the northwestern part of the Kanto Plain in Japan. Short-term continuous measurements of long-period microtremors at both sediment and basement sites were taken. A spectral peak at a period of 4 to 5 sec is stable with time, while peaks at periods less than 2 sec are time variant, suggesting a variation of microtremor sources. However, it was found that the spectral ratio between vertical and horizontal microtremors (ellipticity) at each site is stable with time. Good agreement was found between ellipticities of microtremors at the sediment site and those computed for Rayleigh waves in which the structure of the sediments beneath the site was taken into account. We also found that the ellipticities of Rayleigh waves in earthquake ground motions were consistent with those of the microtremors. These comparisons provide strong evidence that long-period microtremors in the area studied consist mainly of Rayleigh waves. The ellipticity of microtremors was investigated by observing microtremors at temporary observation sites in the Kanto Plain where the sediment thickness varied from 0 to 1 km. The subsurface structures were deduced by trial-and-error fitting of observed ellipticities with theoretical ellipticities that were calculated assuming Rayleigh waves. These results show that ellipticity of long-period microtremors is effective for deducing structure from microtremor data at a single site.

Measurements of Rayleigh-wave phase velocities in Nevada: Implications for explosion sources and the Massachusetts Mountain earthquake

1982 ◽  
Vol 72 (4) ◽  
pp. 1329-1349
Author(s):  
H. J. Patton
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Moment Tensor ◽  
Test Site ◽  
P Wave ◽  
Stress Axis ◽  
Phase Velocities ◽  
Wave Phase ◽  
Single Station ◽  
Source Phase

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.

Strain, tilt, and rotation associated with strong ground motion in the vicinity of earthquake faults

1982 ◽  
Vol 72 (5) ◽  
pp. 1717-1738 ◽  
Author(s):  
Michel Bouchon ◽  
Keiiti Aki
Keyword(s):  
Ground Motion ◽  
Rotational Velocity ◽  
Near Field ◽  
Strike Slip ◽  
Phase Velocities ◽  
Crustal Structures ◽  
Time Histories ◽  
San Fernando ◽  
Earthquake Faults ◽  
Strong Ground

abstract In the absence of near-field records of differential ground motion induced by earthquakes, we simulate the time histories of strain, tilt, and rotation in the vicinity of earthquake faults embedded in layered media. We consider the case of both strike-slip and dip-slip fault models and study the effect of different crustal structures. The maximum rotational motion produced by a buried 30-km-long strike-slip fault with slip of 1 m is of the order of 3 × 10−4 rad while the corresponding rotational velocity is about 1.5 × 10−3 rad/sec. A simulation of the San Fernando earthquake yields maximum longitudinal strain and tilt a few kilometers from the fault of the order of 8 × 10−4 and 7 × 10−4 rad. These values being small compared to the amplitude of ground displacement, the results suggest that most of the damage occurring in earthquakes is caused by translation motions. We also show that strain and tilt are closely related to ground velocity and that the phase velocities associated with strong ground motions are controlled by the rupture velocity and the basement rock shearwave velocity.

Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semi-circular paths

1964 ◽  
Vol 54 (2) ◽  
pp. 571-610
Author(s):  
George E. Backus
Keyword(s):  
Spherical Harmonics ◽  
Rayleigh Waves ◽  
Seismic Station ◽  
Great Circle ◽  
Explicit Formulas ◽  
Phase Velocities ◽  
Rapid Accumulation ◽  
Generalized Spherical Harmonics ◽  
Geographical Position ◽  
The Difference

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.

scholarly journals A NEW METHOD OF PERFORMING FIELD TRIALS

1969 ◽  
Vol 28 (1) ◽  
pp. 22-34
Author(s):  
Bernardo G. Capó
Keyword(s):  
Field Experiments ◽  
Field Tests ◽  
Field Trials ◽  
New Method ◽  
Numerical Example ◽  
Fertilizer Experiment ◽  
Treatment Experiment

A new method of performing field experiments with relatively small numbers of treatments is described. The requirement to be fulfilled by the layouts of such field tests is specified and examples of possible designs for a 5-treatment experiment are illustrated. The theory of the procedure of calculation is discussed and a numerical example of said calculations is furnished in connection with the interpretation of a fertilizer experiment performed with cotton.

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