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.

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.

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.

Efficient angle-domain common-image gathers using Cauchy-condition-based polarization vectors

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S69-S77 ◽  
Author(s):  
Xiongwen Wang ◽  
Jianliang Qian ◽  
Huazhong Wang
Keyword(s):  
Plane Wave ◽  
Model Building ◽  
Computational Cost ◽  
Decomposition Algorithm ◽  
Reverse Time ◽  
Imaging Condition ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Imaging Result ◽  
Wave Decomposition

Because angle-domain common-image gathers (ADCIGs) from reverse time migration (RTM) are capable of obtaining the correct illumination of a subsurface geologic structure, they provide more reliable information for velocity model building, amplitude-variation versus angle analysis, and attribute interpretation. The approaches for generating ADCIGs mainly consist of two types: (1) indirect approaches that convert extended image gathers into ADCIGs and (2) direct approaches that first obtain propagating angles of wavefronts and then map the imaging result to the angle domain. In practice, however, generation of ADCIGs usually incurs high computational cost, poor resolution, and other drawbacks. To generate efficient ADCIGs using RTM methods, we have introduced a novel approach to obtain polarization vectors — directions of particle motion — from the Cauchy wavefield (CWF) and an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. The CWF is a wavefield constructed from the Cauchy condition of the wave equation at any given time, and it only contains negative frequencies of the original wavefield so that the polarization vector is obtained from the local CWF in the wavenumber domain. With polarization vectors at our disposal, we have further developed an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. Numerical examples have indicated that the new approach is able to handle complex wave phenomenon and has advantages in illuminating subsurface structure.

Comparison of methods for extracting ADCIGs from RTM

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S89-S103 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan ◽  
Huimin Guan
Keyword(s):  
Plane Wave ◽  
Low Noise ◽  
Direction Vector ◽  
Reverse Time ◽  
Imaging Condition ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Local Plane ◽  
Local Shift ◽  
Wave Decomposition

Methods for extracting angle-domain common-image gathers (ADCIGs) during 2D reverse-time migration fall into three main categories; direction-vector-based methods, local-plane-wave decomposition methods, and local-shift imaging condition methods. The direction-vector-based methods, which use either amplitude gradients or phase gradients, cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time; however, the ADCIGs from the direction-vector-based methods have the highest angle resolution. A new direction-vector-based method using instantaneous phase gradients in space and time gives the same propagation directions and ADCIGs as those obtained by the Poynting vector or polarization vector based methods, where amplitudes are large. Angles calculated by the phase gradients have larger uncertainties at smaller amplitudes, but they do not significantly degrade the ADCIGs because they contribute only small amplitudes. The local-plane-wave decomposition and local-shift imaging condition methods, implemented either by a Fourier transform or by a slant stack transform, can handle overlapping events, and produce very similar angle gathers. ADCIGs from both methods depend on the local window size in which the transforms are done. In small local windows, both methods produce ADCIGs with low noise, but also with low angle resolution; in large windows, they have high angle resolution, but contain smeared artifacts.

A fast algorithm for plane-wave decomposition

1985 ◽  
Author(s):  
Julian Cabrera ◽  
Shlomo Levy ◽  
Kerry Stinson
Keyword(s):  
Plane Wave ◽  
Fast Algorithm ◽  
Plane Wave Decomposition ◽  
Wave Decomposition
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