Radiation patterns of body waves due to the seismic dislocation occurring in an anisotropic source medium

1981 ◽  
Vol 71 (1) ◽  
pp. 37-50
Author(s):  
Ichiro Kawasaki ◽  
Toshiro Tanimoto
Keyword(s):  
Body Waves ◽  
Wave Radiation ◽  
Seismic Moment Tensor ◽  
Radiation Patterns ◽  
Nodal Lines ◽  
Seismic Dislocation ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
Anisotropic Source ◽  
Seismic Body Waves

abstract We investigate body force equivalents for a seismic dislocation occurring in an anisotropic source medium and study radiation patterns of seismic body waves resulting from them. The point source representation of the equivalent body forces is obtained following a result of Kosevich (1962, 1965). Green's tensor for an anisotropic medium is calculated using a far-field approximate method by Kosevich and Natsik (1964). Radiation patterns of seismic body waves are obtained by a straightforward convolution operation on the equivalent forces with the approximate Green's tensor. The seismic dislocation occurring in an anisotropic source medium is equivalent in general to the sum of three orthogonal dipole forces with different magnitudes, for which the seismic moment tensor has a nonzero trace. Because of the third dipole force which never appears for an isotropic medium, a significant distortion of the radiation patterns occurs in a direction near the null vector. Nodal lines of P-wave radiation patterns are separated into isolated loops and/or secondary nodal lines appear. In directions where group velocity differs from the corresponding phase velocity, the effect of the medium transfer response on the polarities of body waves seems to be larger than that in other directions. The combination of the effects of source forces and medium transfer response distorts the radiation pattern.

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.

SEISMIC RECIPROCITY

Geophysics ◽  
1959 ◽  
Vol 24 (4) ◽  
pp. 681-691 ◽  
Author(s):  
Leon Knopoff ◽  
Anthony F. Gangi
Keyword(s):  
Scalar Product ◽  
Point Sources ◽  
Simple Experiment ◽  
Reciprocity Relations ◽  
Green's Tensor ◽  
Vector Case ◽  
Green’S Tensor

The reciprocity relationship describing the relations among the fields resulting from the interchange of point sources and receivers may be extended to the seismic case. Seismic reciprocity can be described either in terms of the scalar product of the vectors representing the excitation of the source and the field at the receiver, or in terms of a Green’s tensor describing these two quantities. Theoretical reciprocity relations give no information concerning reciprocity in the cases for which the scalar product vanishes. A simple experiment in the vector case demonstrates that reciprocity is not obtained when the scalar product of the two vectors vanishes.

A kinematic self-similar rupture process for earthquakes

1994 ◽  
Vol 84 (4) ◽  
pp. 1216-1228 ◽  
Author(s):  
A. Herrero ◽  
P. Bernard
Keyword(s):  
Stress Drop ◽  
Numerical Models ◽  
Kinematic Model ◽  
Body Waves ◽  
Partial Slip ◽  
Wave Radiation ◽  
Similar Process ◽  
Dislocation Model ◽  
Radiation Spectra ◽  
Self Similar

Abstract The basic assumption that the self-similarity and the spectral law of the seismic body-wave radiation (e.g., ω-square model) must find their origin in some simple self-similar process during the seismic rupture led us to construct a kinematic, self-similar model of earthquakes. It is first assumed that the amplitude of the slip distribution high-pass filtered at high wavenumber does not depend on the size of the ruptured fault. This leads to the following “k-square” model for the slip spectrum, for k > 1/L: Δ~uL(k)=CΔσμLk2, where L is the ruptured fault dimension, k the radial wavenumber, Δσ the mean stress drop, μ the rigidity, and C an adimensional constant of the order of 1. The associated stress-drop spectrum, for k > 1/L, is approximated by Δ~σL(k)=ΔσLk. The rupture front is assumed to propagate on the fault plane with a constant velocity v, and the rise time function is assumed to be scale dependent. The partial slip associated to a given wavelength 1/k is assumed to be completed in a time 1/kv, based on simple dynamical considerations. We therefore considered a simple dislocation model (instantaneous slip at the final value), which indeed correctly reproduces this self-similar characteristic of the slip duration at any scale. For a simple rectangular fault with isochrones propagating in the x direction, the resulting far-field displacement spectrum is related to the slip spectrum as u˜(ω)=FΔ~u(kx=1Cdωv,ky=0), where the factor F includes radiation pattern and distance effect, and Cd is the classical directivity coefficient 1/[1 − v/c cos (θ)]. The k-square model for the slip thus leads to the ω-square model, with the assumptions above. Independently of the adequacy of these assumptions, which should be tested with dynamic numerical models, such a kinematic model has several important applications. It may indeed be used for generating realistic synthetics at any frequency, including body waves, surface waves, and near-field terms, even for sites close to the fault, which is often of particular importance; it also provides some clues for estimating the weighting factors for the empirical Green's function methods. Finally, the slip spectrum may easily be modified in order to model other power-law decay of the radiation spectra, as well as composite earthquakes.

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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