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 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.

scholarly journals Geodynamics of the Wadati-Benioff zone earthquakes: The 2004 Sumatra earthquake and other great earthquakes

2007 ◽  
Vol 46 (1) ◽  
pp. 19-50
Author(s):  
Giancarlo Scalera
Keyword(s):  
Large Scale ◽  
Volcanic Eruptions ◽  
P Wave ◽  
Wave Radiation ◽  
Benioff Zone ◽  
Great Earthquakes ◽  
2004 Sumatra Earthquake ◽  
Vertical Fault ◽  
Double Couple ◽  
New Interpretation

The displacement of the Earth’s instantaneous rotation pole – observed at ASI of Matera, Italy – the seismic data (USGS) in the two days following the main shock, the high frequency P-wave radiation, the geomorphologic data, and the satellite data of uplift/subsidence of the coasts (IGG) converge toward a new interpretation of the Great Sumatran earthquake (TU=26 December 2004 - 00h 58m, Lat=3.3°N, Lon=95.8°E, H=10 km, M=9.3) based on the second conjugate – nearly vertical – CMT fault plane solution. In a non-double-couple treatment that considers non-negligible non-elastic contributions to the earthquake phenomena, only a nearly vertical fault can explain both high values of seismic moment and the ?3.0 mas (?10 cm) polhody displacement toward an azimuth exactly opposite to the epicentre azimuth. Case-histories of great earthquakes are then reviewed to highlight the overall analogies. The similarity of the vertical displacements shown by these earthquakes (Chile 1960, Alaska 1964, ...) leads to a common interpretation necessitating resort to a prevailing uprising of lithospheric material. This interpretation is supported by the inspection of the irregularities of the hypocentre distribution along the Wadati-Benioff zones. Moreover, in the case of great South American earthquakes, a volcanic eruptions-earthquakes correlation is clearly recognisable. A thorough revision of the pure elastic rebound model of great earthquakes occurrence and a complete overcoming of the large scale subduction concept is then needed.

scholarly journals Velocity contrast across the San Andreas fault in central California: Small-scale variations from P-wave nodal plane distortion

1977 ◽  
Vol 67 (6) ◽  
pp. 1565-1576
Author(s):  
Karen C. McNally ◽  
Thomas V. McEvilly
Keyword(s):  
Fault Zone ◽  
Fault Plane ◽  
San Andreas Fault ◽  
P Wave ◽  
Wave Radiation ◽  
Small Scale ◽  
Depth Range ◽  
Radiation Patterns ◽  
Central California ◽  
San Andreas

abstract Systematic variations in P-wave radiation patterns, evident in a data set of 400 central California earthquakes, have been analyzed for variations in velocity contrast across the San Andreas fault zone. Vertical strike-slip faulting characterizes the region, with radiation patterns well constrained by the dense local seismographic station network. A discontinuity in crustal velocity occurs across the San Andreas fault. The distribution of systematically inconsistent first motions indicates that first arrivals observed along the fault plane within the northeastern block have followed refracted paths through the higher velocity crustal rocks to the southwest, retaining P-wave polarities characteristic of the quadrant of origin, and thus appearing reversed. A simple geometrical interpretation, with P waves refracted at the fault plane near the focus, yields the velocity contrast across the fault zone; the distribution of hypocenters allows its mapping in time and space. The velocity contrast so determined ranges up to 15 per cent, for a depth range of 1 to 10 km. The observed pattern of contrast values is coherent, with the greatest contrast related apparently in space, and possibly in time, to the larger earthquakes occurring on the fault. We suggest the phenomenon reflects changes in stress state at the fault and, by virtue of its ease of measurement, offers a new and valuable technique in earthquake studies.

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.

The effect of the earthquake radiation pattern on mb—A study using aftershocks in the 1976 Gazli sequence

1998 ◽  
Vol 88 (2) ◽  
pp. 523-530 ◽  
Author(s):  
David Bowers ◽  
Alan Douglas
Keyword(s):  
Radiation Pattern ◽  
Analysis Of Variance ◽  
Wave Amplitude ◽  
Focal Mechanisms ◽  
P Wave ◽  
Radiation Coefficient ◽  
Short Period ◽  
Double Couple ◽  
Earthquake Mechanism ◽  
Scalar Moment

Abstract We use published focal mechanisms to estimate radiation coefficients to four short-period arrays recording teleseismic P from 38 aftershocks in the 1976 Gazli, Uzbekistan, earthquake sequence. We divide the observed P-wave amplitude by its radiation coefficient to estimate the P-wave amplitude that would be observed if it was from the maximum of the double-couple radiation pattern. We use this new P-wave amplitude to calculate a P-wave magnitude, mCb, that is independent of the P-radiation pattern if the focal mechanisms are without error. Analysis of variance shows that the random error in mCb is reduced relative to that in the original P-wave magnitudes mCb and that this reduction is statistically significant at the 11% level. Further, analysis of variance demonstrates that the radiation coefficients calculated from the focal mechanisms contain error but that this error is probably not large enough to mask the detection of the radiation effect in mOb. Published averages of the logarithm of P-radiation coefficients allow an assessment of the differences in network-averaged mb due to the radiation pattern of point earthquake and explosion sources. Network-averaged mb from a vertical strike-slip earthquake can differ from an explosion of similar scalar moment by as much as 1.0 m.u. (magnitude units). However, this difference can be as little as 0.2 m.u. if the earthquake mechanism is 30° dip slip. We argue that, if mb is required to be independent of the earthquake mechanism, the most appropriate network average is mCb − 0.48.

scholarly journals Body‐wave radiation patterns and AVO in transversely isotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1409-1425 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Reflection Coefficient ◽  
Radiation Pattern ◽  
Transversely Isotropic ◽  
P Wave ◽  
Wave Radiation ◽  
Reflection Coefficients ◽  
Radiation Patterns ◽  
Avo Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

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.

Aftershocks of the February 21, 1973 Point Mugu, California earthquake

1976 ◽  
Vol 66 (6) ◽  
pp. 1931-1952
Author(s):  
Donald J. Stierman ◽  
William L. Ellsworth
Keyword(s):  
Fault Zone ◽  
Main Shock ◽  
Fault Plane ◽  
Body Wave ◽  
P Wave ◽  
Fault System ◽  
Wave Radiation ◽  
Fault Plane Solutions ◽  
Complex Deformation ◽  
Transverse Ranges

abstract The ML 6.0 Point Mugu, California earthquake of February 21, 1973 and its aftershocks occurred within the complex fault system that bounds the southern front of the Transverse Ranges province of southern California. P-wave fault plane solutions for 51 events include reverse, strike slip and normal faulting mechanisms, indicating complex deformation within the 10-km broad fault zone. Hypocenters of 141 aftershocks fail to delineate any single fault plane clearly associated with the main shock rupture. Most aftershocks cluster in a region 5 km in diameter centered 5 km from the main shock hypocenter and well beyond the extent of fault rupture estimated from analysis of body-wave radiation. Strain release within the imbricate fault zone was controlled by slip on preexisting planes of weakness under the influence of a NE-SW compressive stress.

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

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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