Note concerning non-double-couple source components from slip along surfaces of revolution

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.

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A teleseismic body-wave analysis of the May 1980 Mammoth Lakes, California, earthquakes

Bulletin of the Seismological Society of America ◽

10.1785/bssa0730020419 ◽

1983 ◽

Vol 73 (2) ◽

pp. 419-434

Author(s):

Jeffery S. Barker ◽

Charles A. Langston

Keyword(s):

Body Wave ◽

Moment Tensor ◽

Normal Fault ◽

Strike Slip ◽

Body Waves ◽

P Wave ◽

Moment Tensors ◽

Double Couple ◽

The Moment ◽

Mammoth Lakes

abstract Teleseismic P-wave first motions for the M ≧ 6 earthquakes near Mammoth Lakes, California, are inconsistent with the vertical strike-slip mechanisms determined from local and regional P-wave first motions. Combining these data sets allows three possible mechanisms: a north-striking, east-dipping strike-slip fault; a NE-striking oblique fault; and a NNW-striking normal fault. Inversion of long-period teleseismic P and SH waves for the events of 25 May 1980 (1633 UTC) and 27 May 1980 (1450 UTC) yields moment tensors with large non-double-couple components. The moment tensor for the first event may be decomposed into a major double couple with strike = 18°, dip = 61°, and rake = −15°, and a minor double couple with strike = 303°, dip = 43°, and rake = 224°. A similar decomposition for the last event yields strike = 25°, dip = 65°, rake = −6°, and strike = 312°, dip = 37°, and rake = 232°. Although the inversions were performed on only a few teleseismic body waves, the radiation patterns of the moment tensors are consistent with most of the P-wave first motion polarities at local, regional, and teleseismic distances. The stress axes inferred from the moment tensors are consistent with N65°E extension determined by geodetic measurements by Savage et al. (1981). Seismic moments computed from the moment tensors are 1.87 × 1025 dyne-cm for the 25 May 1980 (1633 UTC) event and 1.03 × 1025 dyne-cm for the 27 May 1980 (1450 UTC) event. The non-double-couple aspect of the moment tensors and the inability to obtain a convergent solution for the 25 May 1980 (1944 UTC) event may indicate that the assumptions of a point source and plane-layered structure implicit in the moment tensor inversion are not entirely valid for the Mammoth Lakes earthquakes.

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Radiation from supersonic faulting

Bulletin of the Seismological Society of America ◽

10.1785/bssa0610041009 ◽

1971 ◽

Vol 61 (4) ◽

pp. 1009-1012 ◽

Cited By ~ 1

Author(s):

J. C. Savage

Keyword(s):

Initial Point ◽

Step Function ◽

Fault Model ◽

Dislocation Segment ◽

Far Field ◽

Fault Propagation ◽

Unit Step ◽

Propagation Factor ◽

Double Couple ◽

Field Radiation

abstract The far-field radiation from a simple fault model is given by the radiation pattern associated with the appropriate strain nucleus (e.g., double couple) multiplied by a fault propagation factor. For a unilateral fault model the propagation factor is F ( c ; t ) = ζ bd [ H ( τ ) − H ( τ − ( L / ζ ) ( 1 − ( ζ / c ) cos ψ )) ] / ( 1 − ( ζ / c ) cos ψ ) where ξ is the velocity of fault propagation, b is the fault slip, d is the fault width, τ = t − r0/c, r0 is the distance of the observer from the initial point of faulting, c is the velocity of the seismic wave, H(τ) is the unit-step function, L is the length of the fault, and ψ the angle between r0 and the direction of fault propagation. This representation is valid for both subsonic and supersonic fault propagation. The latter case is important because Weertman (1969) has recently shown that spontaneous faulting may propagate at supersonic velocities. Because the propagation factor is always positive, the nodal planes for the radiation are the same as for the appropriate strain nucleus. Finally, it is shown by the application of this equation that the radiation from a screw dislocation segment is represented by the double-couple nucleus, not the compensated linear-vector dipole nucleus as recently suggested by Knopoff and Randall (1970).

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A least squares method for earthquake mechanism determination using S-wave data

Bulletin of the Seismological Society of America ◽

10.1785/bssa05406a2037 ◽

1964 ◽

Vol 54 (6A) ◽

pp. 2037-2047

Author(s):

Agustin Udias

Keyword(s):

Least Squares ◽

Statistical Evaluation ◽

Least Squares Method ◽

Numerical Approach ◽

Focal Mechanisms ◽

Least Square ◽

S Wave ◽

Double Couple ◽

Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

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Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

Bulletin of the Seismological Society of America ◽

10.1785/bssa0560040925 ◽

1966 ◽

Vol 56 (4) ◽

pp. 925-936 ◽

Cited By ~ 1

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.

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