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caustic curves

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Series: Society of Exploration Geophysicists Geophysics Reprint Series
Published: 01 January 2016
EISBN: 9781560803232
... being a caustic curve of diffraction. If a circle replaces the ellipse the shadow from the point of tangency is directed toward the Arago spot at the center of the circular shadow. (See No. 18.) If the disc and straight-edge be now rotated about an axis in their plane figures like Plate II...
FIGURES
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...
Image
(upper <b>curve</b>) 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
Series: Society of Exploration Geophysicists Open File
Published: 01 January 2001
DOI: 10.1190/1.9781560801771.ch25
EISBN: 9781560801771
... quasi-S slowness surfaces frequently arise in naturally occurring anisotropy, and curved reflecting boundaries and other heterogeneities lead to a profusion of caustics. Therefore, encountering this problem is quite likely in practical exploration geophysics using shear-wave imaging...
FIGURES
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
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)
Journal Article
Journal: Geophysics
Published: 12 April 2010
Geophysics (2010) 75 (2): S81-S93.
... equation. On the other hand, the ray method suffers from so-called caustic problems, which means exactly that if the rays associated with the wave-propagation problem under investigation either touch a focal surface in three dimensions (or a focal curve in two dimensions) or traverse a focal point...
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Series: Society of Exploration Geophysicists Geophysics Reprint Series
Published: 01 January 2016
EISBN: 9781560803232
... of the involute of a circle, when the diffraction figure was identical with the generating circle which was, of course, the evolute of the edge of the shadow. A series of photographs of elliptical shadows show that the diffraction caustics are not continuous curves. The changes of detail and of color...
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Journal Article
Journal: Geophysics
Published: 01 August 1987
Geophysics (1987) 52 (8): 1065-1073.
... that simplifies and stabilizes the calculations of inverse Fourier transforms.We compare reflection seismograms computed using the Gaussian beam-summation method with those calculated by finite differences. Two simple models are used. The first is a continuous curved interface separating an elastic layer from...
Journal Article
Published: 01 December 1983
Bulletin of the Seismological Society of America (1983) 73 (6A): 1637-1653.
... are larger for stations in the central region and smaller for stations near the edge. Waveforms and amplitudes can change drastically between two nearby stations due to caustics and geometric focusing for different paths. It is found, for the particular basin geometry and velocity contrast used...
Series: SEPM Special Publication
Published: 01 January 1976
DOI: 10.2110/pec.76.24.0024
EISBN: 9781565761544
... wave rays (Chao and Pierson, 1972) has been applied to the interpretation of such wave phenomena as curved caustics (over the shelf-edge canyons and ridge and swale bathymetry) and straight caustics (over deep channels off the mouths of Delaware and Chesapeake Bays); (6) this information is then used...
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
Journal Article
Journal: Geophysics
Published: 01 January 1992
Geophysics (1992) 57 (1): 39-50.
...W. A. Schneider; Kurt A. Ranzinger; A. H. Balch; Curtis Kruse Abstract Curved-ray tomographic traveltime inversion, reverse-time migration and various other seismic modeling applications require the calculation of traveltime and raypath information throughout a two- or three-dimensional medium...
Series: Society of Exploration Geophysicists Geophysics Reprint Series
Published: 01 January 2016
EISBN: 9781560803188
... of curved reflectors, nonplanar wave fronts, and finite frequencies. The proposed method is capable of producing complex wave phenomenas, such as caustics, edge diffractions, and head waves. Seismograms modeled for even simple models reveal significant errors implicit in the plane-wave approximation...
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Journal Article
Journal: Geophysics
Published: 23 August 2007
Geophysics (2007) 72 (5): SM19-SM34.
... of the plane-wave coefficients widely used in conventional seismic modeling, even for the case of curved reflectors, nonplanar wavefronts, and finite frequencies. The proposed method is capable of producing complex wave phenomenas, such as caustics, edge diffractions, and head waves. Seismograms modeled...
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Journal Article
Journal: Geophysics
Published: 01 July 1988
Geophysics (1988) 53 (7): 903-907.
... distance.Synthetic gathers of reflections from a single plane-stratified layer with and without the random lateral inhomogeneities produce an amplitude anomaly which is related to the random occurrence of a caustic; limit theorems for stochastic differential equations provide a theory. Theoretical curves, giving...
Journal Article
Published: 01 June 1983
Bulletin of the Seismological Society of America (1983) 73 (3): 765-780.
...Jia-Ju Lee; Charles A. Langston abstract A three-dimensional ray method is used to compute three components of ground motion for complex structures involving curved boundaries. The method of principal curvature is developed to compute geometrical spreading of rays. This method, commonly used...
Journal Article
Journal: Geophysics
Published: 26 August 2010
Geophysics (2010) 75 (4): S139-S150.
...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...
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Series: Society of Exploration Geophysicists Geophysics Reprint Series
Published: 01 January 2016
EISBN: 9781560803188
... including diffraction by edges and vertices is described. A generalization of ihe concept of edge waves for caustic situations is given the method of superposition of edge,tip waves. The result of such a generalization no longer supplements the geometrical seismic description, but completely replaces il...
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