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caustics

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Journal Article
Journal: Geophysics
Published: 14 January 2005
Geophysics (2005) 70 (1): S1-S17.
... in the presence of caustics and illustrate it with three examples: dip moveout (DMO), azimuth moveout (AMO), and offset continuation. This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator...
FIGURES | View All (14)
Series: Society of Exploration Geophysicists Open File
Published: 01 January 2001
DOI: 10.1190/1.9781560801771.ch24
EISBN: 9781560801771
... Abstract The morphology of rays and wavefronts generated by a point source in a vertically heterogeneous TI elastic medium is studied. The qSV rays form two conoidal caustics with vertices at the source. A generic ray touches 0, 1 or both caustics successively. In the latter case the KMAH...
Series: Society of Exploration Geophysicists Open File
Published: 01 January 2001
DOI: 10.1190/1.9781560801771.ch25
EISBN: 9781560801771
... Abstract Abstract It is well known from asymptotic ray theory that the complex wave amplitude along a ray undergoes a phase shift every time the ray touches a caustic surface. If the slowness surface associated with the propagation of this ray is not convex, which is possible for quasi-shear...
FIGURES
Journal Article
Published: 01 October 1981
Bulletin of the Seismological Society of America (1981) 71 (5): 1445-1461.
..., is shown to be more generally valid and just as simple to compute. In addition, it is shown that the phase shift due to caustics is intimately related to the occurrence of turning points along the ray. An expression is derived explicitly relating this phase shift to the number of turning points...
Journal Article
Published: 01 December 1974
Bulletin of the Seismological Society of America (1974) 64 (6): 1733-1742.
...David P. Hill abstract Body waves that form an internal caustic attain a±π/2 phase shift in the vicinity of the point where the ray touches the caustic. This phase shift distorts a pulse propagating along the ray into its allied function. Asymptotic and numerically exact solutions for a particular...
Journal Article
Published: 01 December 1993
Bulletin of the Seismological Society of America (1993) 83 (6): 1835-1854.
...S. Houard; J. L. Plantet; J. P. Massot; H. C. Nataf Abstract The purpose of this paper is 2-fold. It is first a continuation of the study of Massot and Rocard (1982) on the amplitude variations of the core waves near the PKP caustic, for French nuclear explosions in the South Pacific recorded...
Image
M  s   O     isochrons and rays in case of <b>caustics</b>. (a)      M  s   O     ...
in > Geophysics
Published: 26 August 2010
Figure 6. M s O isochrons and rays in case of caustics. (a) M s O isochron for two-way traveltime t 0 = 4.72 s; (b) conventional CO isochron (thick gray curve) and isochron ray (thick black curve) in the image space corresponding to slice h = 0
Image
Conventional CO isochrons and an isochron ray in the presence of <b>caustics</b>. ...
in > Geophysics
Published: 26 August 2010
Figure 7. Conventional CO isochrons and an isochron ray in the presence of caustics. Gray curves — CO isochrons as intersection of M s O isochron surfaces with h = 0 plane. They correspond to two-way time t 0 = 2 , 3.8, and 4.7 s (from top to bottom
Image
Model 3. Development of head-wave <b>caustics</b> for different values of     Δ  z...
in > Geophysics
Published: 23 August 2007
Figure 9. Model 3. Development of head-wave caustics for different values of Δ z : (a) Δ z = 0.005 km , (b) Δ z = 0.02 km , (c) Δ z = 0.04 km , and (d) Δ z = 0.08 km .
Journal Article
Journal: Geophysics
Published: 12 April 2010
Geophysics (2010) 75 (2): S81-S93.
..., but break down in cases when a complex velocity structure gives rise to the appearance of caustics. Ray methods also have difficulties in correctly handling the different branches of the wavefront that result from wave propagation through a caustic. On the other hand, migration methods based on the two-way...
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Journal Article
Journal: Geophysics
Published: 01 January 2001
Geophysics (2001) 66 (2): 413-418.
... describing the wavefield. These integrals are similar to oscillatory integrals in the frequency domain. This description is uniformly valid near caustics, allowing the calculation of higher order terms of the ray series approximation. Practical use of the technique is illustrated by several examples which...
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Journal Article
Published: 01 February 1997
Bulletin of the Seismological Society of America (1997) 87 (1): 164-173.
... that the hyperbolic function performs accurately, particularly when a wave front is only smoothly bent, but there exists a tolerance range for the value of the coefficient. Outside this range, errors of caustic type or pseudocaustic type arise. Because the range is limited, and because it changes for different...
Journal Article
Published: 01 February 1996
Bulletin of the Seismological Society of America (1996) 86 (1A): 159-171.
...Jörg Schlittenhardt Abstract The GRF (Gräfenberg) seismic array in Germany is located at epicentral distances immediately before the PKP caustic B generated by underground nuclear explosions on the French atolls Mururoa and Fangataufa in the South Pacific. I use the large-amplitude PKP waveforms...
Journal Article
Published: 01 April 1992
Seismological Research Letters (1992) 63 (2): 161-167.
...R. B. Herrmann Abstract In order to illustrate wave propagation concepts of ray theory, breakdown of ray theory at caustics, the formation of caustics, free oscillations, and the mode-ray duality, elastic wave propagation in a homogeneous, isotropic fluid sphere is considered. The analytical...
Image
labpse  seismic stations are red (noncaustic) and yellow (<b>caustic</b>) diamonds...
Published: 01 February 2006
Figure 1. labpse seismic stations are red (noncaustic) and yellow (caustic) diamonds. Events used in this study are displayed as focal mechanisms. Those events that had no focal mechanism available are located within clusters of events with focal mechanisms. Event numbering goes as increasing
Image
(upper curve) Averaged spectral ratios for the <b>caustic</b> events (17–22) measu...
Published: 01 February 2006
Figure 9. (upper curve) Averaged spectral ratios for the caustic events (17–22) measured at station 11 divided by average spectra over stations 1–6. The smooth curve is a fit of the caustic equation (10) to the data. The lower curve is the averaged spectral ratios for the noncaustic events
Image
Turning of the set of bicharacteristics in phase space. At the <b>caustic</b> poin...
in > Geophysics
Published: 01 January 2002
F IG . 7. Turning of the set of bicharacteristics in phase space. At the caustic point x 0 , the set of bi-characteristics has a vertical tangent direction.
Image
The synthetic signal within the vicinity of a cusp <b>caustic</b>. The signal shap...
in > Geophysics
Published: 01 January 2001
F IG . 5. The synthetic signal within the vicinity of a cusp caustic. The signal shape is given at distances 0.75, 0.15, and 0 wavelengths away from the caustic. (a) The signal shape computed using the standard ray method. (b) The signal shape computed using the uniform representation
Image
—X-ray diffraction analyses of <b>Caustic</b> Lignite, Bit-Lube, Aktaflo-S, Barite...
Published: 01 April 1981
FIG. 1 —X-ray diffraction analyses of Caustic Lignite, Bit-Lube, Aktaflo-S, Barite A, and Barite B.
Series: Society of Exploration Geophysicists Geophysics Reprint Series
Published: 01 January 2016
EISBN: 9781560803232
.... In such a case the diffraction figure consists of two caustics. These are illustrated in No. 8. When the cone was reversed so that the apex was turned away from the point source, no adjustment whatever was capable of producing a true Arago spot. The nearest approach to a circular spot was crescent shaped...
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