Radiation pattern of mantle Rayleigh waves and the source mechanism of the Hindu Kush earthquake of July 6, 1962

1965 ◽  
Vol 55 (5) ◽  
pp. 805-819 ◽  
Author(s):  
Ramesh Chander ◽  
James N. Brune
Keyword(s):  
Rayleigh Waves ◽  
Focal Depth ◽  
Point Sources ◽  
The Body ◽  
P Wave ◽  
Source Mechanism ◽  
Radiation Patterns ◽  
Wave Data ◽  
Hindu Kush ◽  
Double Couple

abstract The source mechanism of the Hindu Kush earthquake of July 6, 1962 (magnitude 634-7, focal depth 218 km) was studied by comparing the observed amplitude and phase radiation patterns of mantle Rayleigh waves of 150 sec and 200 sec period with theoretical radiation patterns of Rayleigh waves from single- and double-couple point sources, and by considering evidence from Love waves and the shape of P and S pulses. The solution for the source mechanism, which is consistent with all the body wave and surface wave data available for this earthquake, is a double couple acting as a step function in time, with nodal planes oriented as determined from P wave data. Since for waves with periods greater than about 5 sec, the source appears to be an ideal point source, the radius of the equivalent source volume is estimated to be less than 10 km. For Rayleigh waves of 150 sec period, the agreement between observed and theoretical phases (for the above source model) is greatly improved by assuming regional phase velocities instead of a uniform phase velocity for all areas. It is concluded that with the accuracy currently attainable, a study of Rayleigh waves alone cannot determine the source mechanism of an earthquake uniquely.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

Polar radiation patterns of P and SV waves in a multi-layered medium

1973 ◽  
Vol 63 (2) ◽  
pp. 529-547
Author(s):  
Tien-Chang Lee ◽  
Ta-Liang Teng
Keyword(s):  
Displacement Field ◽  
Layered Medium ◽  
Focal Depth ◽  
Focal Mechanisms ◽  
P Wave ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Double Couple ◽  
Spatial Coordinates ◽  
P And Sv Waves

abstract The displacement field in a multi-layered medium due to incident plane P or SV waves is formulated in terms of Haskell's layer matrices. Based on the reciprocity theorem, the far-field polar radiation patterns of single force, double force, single couple, double couple, and dilatation in a multi-layered medium can be obtained from the displacement field and its first derivatives with respect to the spatial coordinates. Numerical results for models of one layer overlying a half-space indicate that (1) the radiation patterns are sensitive to the variation of focal depth, (2) the layering has a more pronounced effect on SV-wave radiation patterns than on P-wave radiation patterns, (3) the radiation patterns become simpler as the wavelength increases, (4) polarity may reverse abruptly somewhere beyond the critical angle in SV-wave radiation patterns, (5) radiation may be discontinuous across interfaces for some assumed focal mechanisms applied slightly above and below the interfaces, and (6) no clearcut distinction among the various radiation patterns can be used to single out one type of the assumed focal mechanisms from the rest.

Radiation pattern of Rayleigh waves from a fault of arbitrary dip and direction of motion in a homogeneous medium

1963 ◽  
Vol 53 (3) ◽  
pp. 619-642
Author(s):  
N. A. Haskell
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Fault Plane ◽  
Cylindrical Wave ◽  
Point Sources ◽  
The Body ◽  
Wave Functions ◽  
Body Waves ◽  
Surface Boundary ◽  
Double Couple

Abstract Expressions for the displacements in the body waves radiated in an unbounded, homogeneous elastic medium by dipolar point sources of arbitrary orientation may be readily derived in Cartesian coordinates from formulae given by Love. The free-surface boundary conditions are, however, most conveniently expressed in terms of Sezawa's cylindrical wave functions. The necessary transformation between the two representations is provided by the Sommerfeld integral and others that may be derived from it by differentiations with respect to the radial and axial (vertical) coordinates. By this means the total radiation field (direct plus surface reflected) is expressed in terms of integrals of cylindrical wave functions. The Rayleigh wave component may then be separated out by calculating the residue at the Rayleigh pole of the integrand. The azimuthal dependence of the Rayleigh wave displacements appears as the sum of three terms, one independent of the azimuth angle, φ, another depending upon sin φ and cos φ, and a third depending upon sin 2φ and cos 2φ. The coefficients of these terms are functions of the direction cosines of the normal to the fault plane and the direction of the relative displacement vector in the fault plane. Equations are presented for sources of both single and double couple types. The effect of fault propagation with finite velocity over a finite distance may be included by multiplying these expressions by the finite source factor previously derived by Ben-Menahem. Polar plots of the amplitude and initial phase are presented for single and double-couple representations of a number of different types of faults. It is noted that for one certain orientation a shallow double-couple source generates no Rayleigh waves.

Body wave radiation patterns from elementary sources within a half space

1967 ◽  
Vol 57 (4) ◽  
pp. 657-674
Author(s):  
I. N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Body Wave ◽  
Point Sources ◽  
The Body ◽  
Wave Radiation ◽  
Seismic Sources ◽  
Vertical Force ◽  
Radiation Patterns ◽  
Double Couple

abstract The known expressions for the polar radiation patterns due to a horizontal or a vertical force, applied at a point within a uniform half space, are used to obtain the body wave radiation patterns from several other elementary seismic sources. Polar radiation patterns from seven elementary line sources, i.e., horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation, center of ratation, and double couple without moment, are first derived. Similar point sources in the three-dimensional space are also considered and the corresponding polar as well as azimuthal radiation patterns are obtained for P, SV, and SH waves. The results obtained include the effect of finite depth of the source below the free surface. Some of the results of Burridge et al for double-couple type seismic sources near a free surface are reproduced in a simple manner. For the elementary point sources considered here, the azimuthal radiation patterns for a uniform half-space are found to be identical with those for an infinite homogeneous medium. However the polar radiation patterns appear to be profoundly affected by the proximity of the free surface.

Focal mechanism and source depth of earthquakes from body- and surface-wave data

1971 ◽  
Vol 61 (5) ◽  
pp. 1369-1379 ◽  
Author(s):  
Nezihi Canitez ◽  
M. Nafi Toksöz
Keyword(s):  
Surface Wave ◽  
Body Wave ◽  
Source Parameters ◽  
Focal Depth ◽  
Spectral Ratio ◽  
The Body ◽  
Spectral Ratios ◽  
Motion Data ◽  
Wave Data ◽  
Surface Wave Data

abstract The determination of focal depth and other source parameters by the use of first-motion data and surface-wave spectra is investigated. It is shown that the spectral ratio of Love to Rayleigh waves (L/R) is sensitive to all source parameters. The azimuthal variation of the L/R spectral ratios can be used to check the fault-plane solution as well as for focal depth determinations. Medium response, attenuation, and source finiteness seriously affect the absolute spectra and introduce uncertainty into the focal depth determinations. These effects are nearly canceled out when L/R amplitude ratios are used. Thus, the preferred procedure for source mechanism studies of shallow earthquakes is to use jointly the body-wave data, absolute spectra of surface waves, and the Love/Rayleigh spectral ratios. With this procedure, focal depths can be determined to an accuracy of a few kilometers.

Spectral and magnitude characteristics of anomalous Eurasian earthquakes

1977 ◽  
Vol 67 (2) ◽  
pp. 463-478
Author(s):  
So Gu Kim ◽  
Otto W. Nuttli
Keyword(s):  
Focal Mechanism ◽  
Rayleigh Waves ◽  
Main Shock ◽  
Focal Depth ◽  
P Wave ◽  
Wave Spectra ◽  
P Waves ◽  
Aftershock Sequences ◽  
Short Period ◽  
Amplitude Spectra

Abstract A number of main shock-aftershock sequences in the Eurasian interior contain some aftershocks whose mb:MS values are close to those of underground explosions. This paper is concerned with a study of the amplitude spectra of the P waves and Rayleigh waves for earthquakes of those main shock-aftershock sequences. It is found that for any given sequence studied, there is little if any variation in focal depth or focal mechanism. This rules out variations in these quantities as being the cause of anomalous mb:MS values. A study of the P-wave spectra establishes that one or both of the corner periods of anomalous earthquakes are smaller than those of non-anomalous earthquakes of the same moment. Thus the cause of anomalous mb:MS values of the earthquakes studied is a relative enrichment of the short-period portion of the spectrum of the anomalous events, which cannot be attributed to focal depth or focal mechanism.

Radiation pattern of surface waves from point sources in a multi-layered medium

1964 ◽  
Vol 54 (1) ◽  
pp. 377-393 ◽  
Author(s):  
N. A. Haskell
Keyword(s):  
Radiation Pattern ◽  
Rayleigh Waves ◽  
Homogeneous Medium ◽  
Previous Treatment ◽  
Point Sources ◽  
Wave Radiation ◽  
Arbitrary Orientation ◽  
Double Couple ◽  
Single Force ◽  
Force Dipole

abstract A previous treatment of the radiation pattern of Rayleigh waves from single and double couple point sources of arbitrary orientation in a semi-infinite homogeneous medium is generalized to the case of a medium composed of an arbitrary number of parallel homogeneous layers by the use of layer matrices. Source coefficients are given for a single force, a force dipole without torque, a single couple, and a double couple without torque, all for arbitrary orientation vectors, and also for a spherically symmetrical compressional source. For the simplest case permitting the existence of Love waves, a single finite layer over a semi-infinite medium, expressions for the Love wave radiation pattern are given explicitly in a form comparable to that previously given for Rayleigh waves in the homogeneous case.

Inversion of 3D VSP P‐wave data for local anisotropy: A case study

2003 ◽  
Author(s):  
Petr Jílek ◽  
Brian Hornby ◽  
Amal Ray
Keyword(s):  
P Wave ◽  
Local Anisotropy ◽  
Wave Data

Dense surface seismic data confirm non-double-couple source mechanisms induced by hydraulic fracturing

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. KS207-KS217 ◽  
Author(s):  
Jeremy D. Pesicek ◽  
Konrad Cieślik ◽  
Marc-André Lambert ◽  
Pedro Carrillo ◽  
Brad Birkelo
Keyword(s):  
Hydraulic Fracturing ◽  
Seismic Data ◽  
P Wave ◽  
Source Modeling ◽  
Moment Tensors ◽  
Amplitude Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Models ◽  
Favorable Conditions

We have determined source mechanisms for nine high-quality microseismic events induced during hydraulic fracturing of the Montney Shale in Canada. Seismic data were recorded using a dense regularly spaced grid of sensors at the surface. The design and geometry of the survey are such that the recorded P-wave amplitudes essentially map the upper focal hemisphere, allowing the source mechanism to be interpreted directly from the data. Given the inherent difficulties of computing reliable moment tensors (MTs) from high-frequency microseismic data, the surface amplitude and polarity maps provide important additional confirmation of the source mechanisms. This is especially critical when interpreting non-shear source processes, which are notoriously susceptible to artifacts due to incomplete or inaccurate source modeling. We have found that most of the nine events contain significant non-double-couple (DC) components, as evident in the surface amplitude data and the resulting MT models. Furthermore, we found that source models that are constrained to be purely shear do not explain the data for most events. Thus, even though non-DC components of MTs can often be attributed to modeling artifacts, we argue that they are required by the data in some cases, and can be reliably computed and confidently interpreted under favorable conditions.

Direct shear-wave seismic survey in Sanhu area, Qaidam Basin, west China

2022 ◽  
Vol 41 (1) ◽  
pp. 47-53
Author(s):  
Zhiwen Deng ◽  
Rui Zhang ◽  
Liang Gou ◽  
Shaohua Zhang ◽  
Yuanyuan Yue ◽  
...  
Keyword(s):  
Shear Wave ◽  
Reservoir Characterization ◽  
Qaidam Basin ◽  
P Wave ◽  
Data Sets ◽  
Direct Shear ◽  
Subsurface Structure ◽  
S Wave ◽  
West China ◽  
Wave Data

The formation containing shallow gas clouds poses a major challenge for conventional P-wave seismic surveys in the Sanhu area, Qaidam Basin, west China, as it dramatically attenuates seismic P-waves, resulting in high uncertainty in the subsurface structure and complexity in reservoir characterization. To address this issue, we proposed a workflow of direct shear-wave seismic (S-S) surveys. This is because the shear wave is not significantly affected by the pore fluid. Our workflow includes acquisition, processing, and interpretation in calibration with conventional P-wave seismic data to obtain improved subsurface structure images and reservoir characterization. To procure a good S-wave seismic image, several key techniques were applied: (1) a newly developed S-wave vibrator, one of the most powerful such vibrators in the world, was used to send a strong S-wave into the subsurface; (2) the acquired 9C S-S data sets initially were rotated into SH-SH and SV-SV components and subsequently were rotated into fast and slow S-wave components; and (3) a surface-wave inversion technique was applied to obtain the near-surface shear-wave velocity, used for static correction. As expected, the S-wave data were not affected by the gas clouds. This allowed us to map the subsurface structures with stronger confidence than with the P-wave data. Such S-wave data materialize into similar frequency spectra as P-wave data with a better signal-to-noise ratio. Seismic attributes were also applied to the S-wave data sets. This resulted in clearly visible geologic features that were invisible in the P-wave data.

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