scholarly journals Plane-wave decomposition into P and S waves using dispersion relationship for three component and three dimensional reflection seismic data

2011 ◽  
Vol 64 (2) ◽  
pp. 139-152 ◽  
Author(s):  
Yutaka Okano ◽  
Hitoshi Mikada ◽  
Kyosuke Onishi ◽  
Tada-Nori Goto
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
Three Dimensional ◽  
S Waves ◽  
Reflection Seismic ◽  
Plane Wave Decomposition ◽  
Dispersion Relationship ◽  
Wave Decomposition

A plane‐wave decomposition for elastic wave fields applied to the separation of P‐waves and S‐waves in vector seismic data

Geophysics ◽  
1986 ◽  
Vol 51 (2) ◽  
pp. 419-423 ◽  
Author(s):  
A. J. Devaney ◽  
M. L. Oristaglio
Keyword(s):  
Plane Wave ◽  
Elastic Wave ◽  
Seismic Data ◽  
Seismic Profile ◽  
P Waves ◽  
Wave Fields ◽  
S Waves ◽  
Plane Wave Decomposition ◽  
Wave Decomposition ◽  
Seismic Measurements

We describe a method to decompose a two‐dimensional (2-D) elastic wave field recorded along a line into its longitudinal and transverse parts, that is, into compressional (P) waves and shear (S) waves. Separation of the data into P-waves and S-waves is useful when analyzing vector seismic measurements along surface lines or in boreholes. The method described is based on a plane‐wave expansion for elastic wave fields and is illustrated with a synthetic example of an offset vertical seismic profile (VSP) in a layered elastic medium.

scholarly journals Denoising Directional Room Impulse Responses with Spatially Anisotropic Late Reverberation Tails

2020 ◽  
Vol 10 (3) ◽  
pp. 1033 ◽  
Author(s):  
Pierre Massé ◽  
Thibaut Carpentier ◽  
Olivier Warusfel ◽  
Markus Noisternig
Keyword(s):  
Plane Wave ◽  
Gaussian Noise ◽  
Three Dimensional ◽  
Microphone Arrays ◽  
Impulse Responses ◽  
Noise Floor ◽  
Surround Sound ◽  
Plane Wave Decomposition ◽  
Spherical Microphone Arrays ◽  
Wave Decomposition

Directional room impulse responses (DRIR) measured with spherical microphone arrays (SMA) enable the reproduction of room reverberation effects on three-dimensional surround-sound systems (e.g., Higher-Order Ambisonics) through multichannel convolution. However, such measurements inevitably contain a nondecaying noise floor that may produce an audible “infinite reverberation effect” upon convolution. If the late reverberation tail can be considered a diffuse field before reaching the noise floor, the latter may be removed and replaced with an extension of the exponentially-decaying tail synthesized as a zero-mean Gaussian noise. This has previously been shown to preserve the diffuse-field properties of the late reverberation tail when performed in the spherical harmonic domain (SHD). In this paper, we show that in the case of highly anisotropic yet incoherent late fields, the spatial symmetry of the spherical harmonics is not conducive to preserving the energy distribution of the reverberation tail. To remedy this, we propose denoising in an optimized spatial domain obtained by plane-wave decomposition (PWD), and demonstrate that this method equally preserves the incoherence of the late reverberation field.

On plane‐wave decomposition: Alias removal

Geophysics ◽  
1989 ◽  
Vol 54 (10) ◽  
pp. 1339-1343 ◽  
Author(s):  
S. C. Singh ◽  
G. F. West ◽  
C. H. Chapman
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Time Distance ◽  
P Domain ◽  
Wave Decomposition ◽  
Rapid Modeling

The delay‐time (τ‐p) parameterization, which is also known as the plane‐wave decomposition (PWD) of seismic data, has several advantages over the more traditional time‐distance (t‐x) representation (Schultz and Claerbout, 1978). Plane‐wave seismograms in the (τ, p) domain can be used for obtaining subsurface elastic properties (P‐wave and S‐wave velocities and density as functions of depth) from inversion of the observed oblique‐incidence seismic data (e.g., Yagle and Levy, 1985; Carazzone, 1986; Carrion, 1986; Singh et al., 1989). Treitel et al. (1982) performed time migration of plane‐wave seismograms. Diebold and Stoffa (1981) used plane‐wave seismograms to derive a velocity‐depth function. Decomposing seismic data also allows more rapid modeling, since it is faster to compute synthetic seismograms in the (τ, p) than in the (t, x) domain. Unfortunately, the transformation of seismic data from the (t, x) to the (τ, p) domain may produce artifacts, such as those caused by discrete sampling, of the data in space.

On: “Comparison of plane‐wave decomposition and slant stacking of point‐source seismic data” by Rakesh Mithal and Emilio E. Vera (GEOPHYSICS, 52, 1631–1638, December 1987)

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 378-379 ◽  
Author(s):  
Douglas W. McCowan
Keyword(s):  
Data Analysis ◽  
Plane Wave ◽  
Point Source ◽  
Seismic Data ◽  
Stratified Media ◽  
Cylindrically Symmetric ◽  
Plane Wave Decomposition ◽  
Source Radiation ◽  
Wave Decomposition ◽  
Slant Stacking

Mithal and Vera give the impression that the correct cylindrically symmetric slant stack (e.g., Chapman, 1981; Harding, 1985; Brysk and McCowan, 1986a) needed to represent point‐source radiation in vertically stratified media is both expensive and unnecessary in ordinary data analysis.

Reply by the authors to Douglas W. McCowan

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 379-379 ◽  
Author(s):  
Rakesh Mithal ◽  
Emilio E. Vera
Keyword(s):  
Plane Wave ◽  
Point Source ◽  
Seismic Data ◽  
Wave Reflection ◽  
Suitable Alternative ◽  
Plane Wave Decomposition ◽  
Main Emphasis ◽  
Source Data ◽  
Wave Decomposition ◽  
Slant Stacking

In his discussion, McGowan directs his attention exclusively to which method should be used to produce a plane-wave decomposition of point-source seismic data. Although the choice of method is an important point, it was not the main emphasis of our paper which, as its title indicates, was the comparison between plane-wave decomposition (cylindrical slant stacking) and simple slant stacking. We demonstrated the differences between these two processes and clearly indicated the necessity of using cylindrical slant stacking in order to get the correct plane-wave reflection response of point-source data. McGowan criticizes our method because it makes use of the standard asymptotic approximation of the Bessel function [Formula: see text] and considers only outward traveling waves. In our paper we acknowledged that these simplifications do not produce accurate results for ray parameters near zero and explicitly mentioned the method of Brysk and McGowan (1986) as a suitable alternative to deal with this problem.

Plane‐wave decomposition of seismograms

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1375-1401 ◽  
Author(s):  
Sven Treitel ◽  
P. R. Gutowski ◽  
D. E. Wagner
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
Angle Of Incidence ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Predictive Deconvolution ◽  
Seismic Recording ◽  
Wave Decomposition ◽  
Slant Stacking

A point‐source seismic recording can be decomposed into a set of plane‐wave seismograms for arbitrary angles of incidence. Such plane‐wave seismograms possess an inherently simple structure that make them amenable to existing inversion methods such as predictive deconvolution. Implementation of plane‐wave decomposition (PWD) takes place in the frequency‐wavenumber domain under the assumption of radial symmetry. This version of PWD is equivalent to slant stacking if allowance is made for the customary use of linear recording arrays on the surface of a three‐dimensional medium. An imaging principle embodying both kinematic as well as dynamic characteristics allows us to perform time migration of the plane‐wave seismograms. The imaging procedure is implementable as a two‐dimensional filter whose independent variables are traveltime and angle of incidence.

Use of the slant stack for geologic or geophysical map lineament analysis

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1774-1778 ◽  
Author(s):  
Robert S. Pawlowski
Keyword(s):  
Plane Wave ◽  
Radon Transform ◽  
Seismic Data ◽  
Seismic Events ◽  
Seismic Data Processing ◽  
Coherent Noise ◽  
Plane Wave Decomposition ◽  
Lineament Analysis ◽  
The Individual ◽  
Wave Decomposition

The slant‐stack technique (also known as Radon transform, τ-p transform, and plane‐wave decomposition) used in seismic data processing for discriminating between and separating seismic events of differing dips (or moveout) is applied here to the problem of geologic or geophysical map lineament analysis. The latter problem is analogous to the seismic coherent noise problem in the sense that lineaments associated with one geologic event or episode are often underprinted by the lineaments of preceding geologic disturbances and overprinted by the lineaments of subsequent disturbances. Consequently, it can be difficult to distinguish between the individual lineament sets.

Comparison of plane‐wave decomposition and slant stacking of point‐source seismic data

Geophysics ◽  
1987 ◽  
Vol 52 (12) ◽  
pp. 1631-1638 ◽  
Author(s):  
Rakesh Mithal ◽  
Emilio E. Vera
Keyword(s):  
Phase Shift ◽  
Plane Wave ◽  
Point Source ◽  
Bessel Function ◽  
Seismic Data ◽  
Weighting Function ◽  
Real Data ◽  
Plane Wave Decomposition ◽  
Wave Decomposition ◽  
Slant Stacking

The plane‐wave decomposition and slant stacking of point‐source seismic data are not identical processes; they are, however, related. We have found that the algorithm for slant stacking can be used for plane‐wave decomposition if we apply a weighting function (depending on frequency and offset, and including a π/4 phase shift) before slant stacking, and a p-dependent correction after the slant stacking. This procedure requires only a small extra effort to incorporate the geometrical spreading and phase shift not accounted for by the slant stacking. In this process we use the asymptotic approximation for the zeroth‐order Bessel function. This approximation reduces the number of computations significantly, but it is valid only for ωpx greater than 2 or 3. Using this approximation, we have been able to obtain the correct plane‐wave decomposition of expanding spread profile data for ray parameters as low as 0.03 s/km; for smaller p, the exact Bessel function should be used. We have performed model studies to compare plane‐wave decomposition and slant stacking. Using a possible velocity model for the North Atlantic Transect (NAT) expanding spread profile (ESP 5), we computed synthetic seismograms at a 50 m spacing using the reflectivity method, and then computed the plane‐wave decomposition and slant stacks of these seismograms. On comparing these with the exact τ-p seismograms for this model, we found that the waveforms, the frequency content, and the amplitudes were exactly reproduced in the plane‐wave decomposition, but were significantly different in the slant stacks. We also computed the plane‐wave decomposition and slant stacks of real data (NAT ESP 5). The results in this case show that the amplitudes of deep crustal arrivals in plane‐wave decomposition are higher than in slant stacks, and therefore these arrivals can be identified much better in the plane‐wave decomposition.

Direct mapping of seismic data to the domain of intercept time and ray parameter—A plane‐wave decomposition

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 255-267 ◽  
Author(s):  
Paul L. Stoffa ◽  
Peter Buhl ◽  
John B. Diebold ◽  
Friedemann Wenzel
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Beam Forming ◽  
Reflection And Refraction ◽  
Plane Wave Decomposition ◽  
Direct Mapping ◽  
Marine Seismic ◽  
Wave Decomposition ◽  
Ray Parameter

Marine seismic data recorded as a function of source‐receiver offset and traveltime are mapped directly to the domain of intercept or vertical delay time and horizontal ray parameter. This is a plane‐wave decomposition based on beam forming of wide‐aperture seismic array data to determine automatically the loci of coherent seismic reflection and refraction events. In this computation, semblance, in addition to the required slowness or horizontal ray parameter stack, is found for linear X — T trajectories across subarrays. Subsequently, semblance is used to derive a windowing filter that is applied to the slowness stack to determine the points of stationary phase and eliminate aliasing. The resulting filtered slowness stacks for multiple subarrays can then be linearly transformed and combined according to ray parameter, range, and time. The resulting function of intercept time and horizontal ray parameter offers significant computational and interpretational advantages for the case of horizontal homogeneous layers and leads directly to the derivation of a detailed velocity‐depth function.

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