Zero‐offset reflections from a curved interface

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 50-53 ◽  
Author(s):  
Bjørn Ursin
Keyword(s):  
Stationary Phase ◽  
Simple Formula ◽  
Inhomogeneous Media ◽  
Ray Theory ◽  
Approximate Computation ◽  
Kirchhoff Approximation ◽  
Complicated Structure ◽  
Zero Offset ◽  
Ray Methods ◽  
Curved Interface

Dynamic ray theory is used to compute the reflection response from a curved surface when the source and receiver are located at the same point. This response has also been computed by Cohen and Bleistein from the Helmholtz formula using the Kirchhoff approximation and the method of multidimensional stationary phase. The same approximation has been derived by Hilterman, and it may also be computed from a simple formula given by Hubral. Ray methods may be applied to the approximate computation of the reflection response from inhomogeneous media with complicated structure. This is not so easily done with methods based on the Kirchhoff approximation of the Helmholtz integral.

Axisymmetric Elastic Waves Excited by a Point Source in a Plate

1982 ◽  
Vol 49 (4) ◽  
pp. 821-836 ◽  
Author(s):  
R. L. Weaver ◽  
Yih-Hsing Pao
Keyword(s):  
Point Source ◽  
Stationary Phase ◽  
Elastic Plate ◽  
Elastic Waves ◽  
Normal Modes ◽  
Integral Transforms ◽  
Far Field ◽  
Exact Results ◽  
Ray Theory ◽  
Vertical Step

The response of an infinite elastic plate to dynamic loading is presented by the method of superposition of normal modes, a method particularly appropriate in the intermediate and far field. The method is compared with the method of integral transforms. Explicit expressions are given for the case of loading by a concentrated vertical step force. These expressions are evaluated numerically over a range of distances from 4 to 40 plate thicknesses. The numerical results are compared with qualitative stationary phase analyses and with the exact results of generalized ray theory.

Modeling and Analysis of Monostatic Seafloor Reverberation from Bottom Consisting of Two Slopes

2014 ◽  
Vol 22 (02) ◽  
pp. 1450005 ◽  
Author(s):  
Youngmin Choo ◽  
Woojae Seong ◽  
Wooyoung Hong
Keyword(s):  
Continental Shelf ◽  
Cross Sections ◽  
Propagation Model ◽  
Ray Theory ◽  
Kirchhoff Approximation ◽  
Spectral Form ◽  
Modeling And Analysis ◽  
Scattering Cross ◽  
Scattering Strength ◽  
Scattering Cross Sections

An incoherent reverberation from a continental shelf was simulated using a propagation model based on ray theory combined with several scattering strength formulas. The concept of an N × 2D reverberation model is used to consider azimuthal and radial dependent bottom. For verification of the reverberation model, the result is compared to consensus solutions of problem XI in Reverberation Modeling Workshop I (RMW I). Subsequently, the model is applied to one of data-inspired problems in Reverberation Modeling Workshop II (RMW II). Scattering strength formulas based on the Kirchhoff approximation (KA) and small slope approximation (SSA) are adapted to be applicable to a von Karman roughness spectral form. The monostatic reverberations on the continental shelf are observed at 200 Hz and 1600 Hz for various scattering cross-sections. The results with SSA scattering cross-section are examined to analyze the features of continental shelf reverberation depending on the sound speed profile and bottom slope, and they are found to affect both the pattern and level of reverberations.

Paraxial ray methods for anisotropic inhomogeneous media

2007 ◽  
Vol 55 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Tijmen Jan Moser ◽  
Vlastislav Červený
Keyword(s):  
Inhomogeneous Media ◽  
Paraxial Ray ◽  
Ray Methods

Elastic-wavefield interferometry using P-wave source VSPs at the Wamsutter field, Wyoming

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. Q27-Q36 ◽  
Author(s):  
James Gaiser ◽  
Ivan Vasconcelos ◽  
Rosemarie Geetan ◽  
John Faragher
Keyword(s):  
Stationary Phase ◽  
Wave Velocity ◽  
P Wave ◽  
Phase Point ◽  
S Wave ◽  
Wave Source ◽  
S Waves ◽  
Wave Splitting ◽  
Zero Offset ◽  
Tube Wave

In this study, elastic-wavefield interferometry was used to recover P- and S-waves from the 3D P-wave vibrator VSP data at Wamsutter field in Wyoming. S-wave velocity and birefringence is of particular interest for the geophysical objectives of lithology discrimination and fracture characterization in naturally fractured tight gas sand reservoirs. Because we rely on deconvolution interferometry for retrieving interreceiver P- and S-waves in the subsurface, the output fields are suitable for high-resolution, local reservoir characterization. In 1D media where the borehole is nearly vertical, data at the stationary-phase point is not conducive to conventional interferometry. Strong tube-wave noise generated by physical sources near the borehole interfere with S-wave splitting analyses. Also, converted P- to S-wave (PS-wave) polarity reversals occur at zero offset and cancel their recovery. We developed methods to eliminate tube-wave noise by removing physical sources at the stationary-phase point and perturbing the integration path in the integrand based on P-wave NMO velocity of the direct-arrival. This results in using nonphysical energy outside a Fresnel radius that could not have propagated between receivers. To limit the response near the stationary-phase point, we also applied a weighting condition to suppress energy from large offsets. For PS-waves, a derivative-like operator was applied to the physical sources at zero offset in the form of a polarity reversal. These methods resulted in effectively recovering P-wave dipole and PS-wave quadrupole pseudosource VSPs. The retrieved wavefields kinematically correspond to a vertical incidence representation of reflectivity/transmissivity and can be used for conventional P- and S-wave velocity analyses. Four-component PS-wave VSPs retrieve S-wave splitting in transmitted converted waves that provide calibration for PS-wave and P-wave azimuthal anisotropy measurements from surface-seismic data.

Nonspecular reflections from a curved interface

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1203-1214 ◽  
Author(s):  
J. Schleicher ◽  
P. Hubral ◽  
M. Tygel
Keyword(s):  
Observation Point ◽  
Ray Theory ◽  
Seismic Section ◽  
Specular Reflections ◽  
Nonspecular Reflection ◽  
Incident Plane ◽  
Inflection Points ◽  
Arbitrary Velocity ◽  
Curved Interface ◽  
Complex Rays

If an incident wavefield hits a curved interface that possesses certain inflection points, there may exist “nonspecular” events in the reflected field that cannot be explained by real ray theory. The magnitude of such events can reach the order of the specular ones and can be expressed in terms of specular reflections at certain points on the analytic continuation of the interface. In fact, specular reflected “complex rays,” connecting complex reflection points with the observation point, are used to explain such events. Previous results obtained for acoustic calculations, involving an incident plane wave and a perfectly soft reflector, are extended to arbitrary velocity and density contrasts, as well as to an incident far‐field cylindrical wavefield. Moreover, the agreement between analytic results and independent computations using a finite‐differences scheme is shown. It confirms the existence of nonspecular reflections. The interpreter of a seismic section should, therefore, be aware of not attributing a subsurface interface to a nonspecular reflection, e.g., at a flank of a saltdome.

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