On the Failure of Plane Wave Theory to Predict the Reflection of a Narrow Ultrasonic Beam

1952 ◽  
Vol 24 (3) ◽  
pp. 284-287 ◽  
Author(s):  
Marvin S. Weinstein
Keyword(s):  
Plane Wave ◽  
Wave Theory ◽  
Ultrasonic Beam

Dip selective 2-D multiple attenuation in the plane‐wave domain

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 264-274 ◽  
Author(s):  
Faqi Liu ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Plane Wave ◽  
Source Function ◽  
Real Data ◽  
Wave Theory ◽  
Geological Structure ◽  
Multiple Attenuation ◽  
Invariant Embedding ◽  
Free Data ◽  
Air Water Interface ◽  
Lateral Variations

In many geological settings, strong reflections at the air‐water interface contribute to most of the multiple energy in the recorded seismograms. Here, we describe a method for free‐surface multiple attenuation using a reflection operator model of a seismic record, derived using the well‐known invariant embedding technique. We implement this method in the 2-D plane‐wave domain, where lateral variation of the geological structure of the earth is taken into account by the coupling of different ray parameters. In situations where the lateral variations are smooth, the data are well compressed in the 2-D plane‐wave domain and the resultant bandlimited matrices significantly reduce the computation cost. One important feature of the proposed method is its flexibility, which allows for the removal of multiples from selected reflections. To generate multiple free data, wave‐theory‐based multiple attenuation methods attempt to estimate either the source function or the subsurface reflectivity. Our method takes advantage of both approaches, such that we initially predict multiple traveltime using the reflectivity approach and then seek a source function to predict the amplitudes. Synthetic and real data examples show that this method is stable and successful in attenuating the surface multiples.

The Plane-Wave Theory

1983 ◽  
pp. 7-12
Author(s):  
NORMAN K. GLENDENNING
Keyword(s):  
Plane Wave ◽  
Wave Theory

Transverse effects and noise in optical instabilities

1984 ◽  
Vol 313 (1525) ◽  
pp. 291-297 ◽  
Keyword(s):  
Plane Wave ◽  
Electric Field ◽  
Opposite Sign ◽  
Ring Cavity ◽  
Wave Theory ◽  
Radial Variation ◽  
Bistable System ◽  
Primary Role ◽  
Favourable Situation ◽  
Oscillatory Instabilities

We analyse the simplest model that describes the dynamics of a two-level, optically bistable system in a ring cavity, and incorporates a Gaussian radial variation of the electric field. We find that the most favourable situation to achieve self-pulsing instabilities is that of atomic and cavity detunings with opposite sign. The results are compared with those of plane-wave theory. We show that noise plays a primary role at the onset of self-oscillatory instabilities, and that its effects are governed by an equation formally identical to the Risken equation for the laser.

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