Body‐wave radiation patterns and AVO in anisotropic media

1993 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Body Wave ◽  
Anisotropic Media ◽  
Wave Radiation ◽  
Radiation Patterns

Body wave radiation patterns from force applied within a half space

1966 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Half Space ◽  
Body Wave ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Numerical Results ◽  
Wave Radiation ◽  
Far Field ◽  
Radiation Patterns ◽  
Sh Waves ◽  
Vertical Displacements

abstract Expressions are derived for the horizontal and vertical displacements at an arbitrary depth within a homogeneous, isotropic, elastic half space when plane harmonic P, SV or SH waves are incident at any given angle. On the basis of the reciprocity theorem, these expressions represent also the far-field polar radiation patterns of P, SV and SH waves due to horizontal and vertical forces applied at a point within the half space. Numerical results for a few selected values of depth are shown for a solid half space.

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.

Average body-wave radiation coefficients

1984 ◽  
Vol 74 (5) ◽  
pp. 1615-1621
Author(s):  
David M. Boore ◽  
John Boatwright
Keyword(s):  
High Frequency ◽  
Body Wave ◽  
Strike Slip ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
S Wave ◽  
P Waves ◽  
Effective Radiation ◽  
Average Body

Abstract Averages of P- and S-wave radiation patterns over all azimuths and various ranges of takeoff angles (corresponding to observations at teleseismic, regional, and near distances) have been computed for use in seismological applications requiring average radiation coefficients. Various fault orientations and averages of the squared, absolute, and logarithmic radiation patterns have been considered. Effective radiation patterns combining high-frequency direct and surfacere-flected waves from shallow faults have also been derived and used in the computation of average radiation coefficients at teleseismic distances. In most cases, the radiation coefficients are within a factor of 1.6 of the commonly used values of 0.52 and 0.63 for the rms of P- and S-wave radiation patterns, respectively, averaged over the whole focal sphere. The main exceptions to this conclusion are the coefficients for P waves at teleseismic distances from vertical strike-slip faults, which are at least a factor of 2.8 smaller than the commonly used value.

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.

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 Slip heterogeneity, body-wave spectra, and directivity of earthquake ruptures

1994 ◽  
Vol 37 (6) ◽  
Author(s):  
P. Bernard ◽  
A. Herrero
Keyword(s):  
Rise Time ◽  
Green's Functions ◽  
Green’S Functions ◽  
Body Wave ◽  
Kinematic Model ◽  
Wave Number ◽  
Wave Radiation ◽  
Wave Spectra ◽  
Directivity Effect ◽  
Directivity Factor

We present a broadband kinematic model based on a self-similar k-square distribution of the coseismic slip, with an instantaneous rise-time and a constant rupture velocity. The phase of the slip spectrum at high wave number is random. This model generates an ?-squared body-wave radiation, and a particular directivity factor C2d scaling the amplitude of the body-wave spectra, where Cd is the standard directivity factor. Considering the source models with a propagating pulse and a finite rise-time, we assume that within the slipping band, the rupture has some random character, with small scale rupture in various directions. With such a model, the pulse cannot be resolved, and the directivity factor is still C2d at low frequency; at periods shorter than the rise-time, however, the directivity effect drops to much smaller rms values. This frequency dependent directivity effect, which is expected to be the strongest for sites located in the direction of rupture, was evidenced for the Landers 1992 earthquake, leading to a 2 to 3 s rise-time of the slip pulse. This kinematic model can be used with more refined theoretical Green's functions, including near-field terms and surface waves, or with empirical Green's functions, for generating realistic broadband records in the vicinity of moderate to large earthquakes, in a frequency range relevant for engineering applications (0 Hz to about 20 Hz).

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.

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