Amplitude analysis of isotropic P-wave reflections

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. C93-C103 ◽  
Author(s):  
Mirko van der Baan ◽  
Dirk Smit
Keyword(s):  
Plane Wave ◽  
Wave Reflection ◽  
P Wave ◽  
Background Information ◽  
Head Wave ◽  
Reflection Coefficients ◽  
Plane Wave Decomposition ◽  
Free Parameters ◽  
Time Offset ◽  
Wave Decomposition

The analysis of amplitude variation with offset (AVO) of seismic reflections is a very popular tool for detecting gas sands. It is assumed in AVO, however, that plane-wave reflection coefficients can be used directly to analyze amplitudes measured in the time-offset domain. This is not true for near-critical angles of reflection. Plane-wave reflection coefficients incorporate the contribution of the head wave. A plane-wave decomposition such as a proper [Formula: see text] transform must be applied to the seismic data for accurate analysis of reflection coefficients near critical angles. Amplitudes after plane-wave decomposition are related directly to the plane-wave reflection coefficients; geometric-spreading corrections are no longer required, and polarization effects of P-P reflections recorded on the [Formula: see text]-component are also removed. Conventional, linearized expressions for the isotropic P-P-wave reflection coefficient depend on contrasts in three parameters, and they require background information about average P-wave/S-wave velocity ratios. We derive a new reduced-parameter expression that depends only on two free parameters without loss of accuracy. No extra prior parameter information is needed either. The reduction in free parameters is achieved by explicitly incorporating P-wave moveout information. A new AVO strategy is developed that requires moveout analysis of three reflections: the target horizon, the reflections directly above and below the target horizon, and the amplitudes of the target horizon. The new AVO expression can be used in the time-offset domain for precritical arrivals and in the [Formula: see text] domain for precritical and critical reflections.

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.

Reflection coefficients in attenuative anisotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB193-WB202 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Plane Wave ◽  
Wave Reflection ◽  
Symmetry Plane ◽  
Anisotropic Media ◽  
P Wave ◽  
Substantial Contribution ◽  
Reflection Coefficients ◽  
Slowness Vector ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

Such reservoir rocks as tar sands are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here we study the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on transversely isotropic models with a vertical symmetry axis (VTI). Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation must be strong, with the quality factor [Formula: see text] not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-styleattenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost “isotropic” dependence on attenuation. Our formalism also helps evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes conventional amplitude-variation-with-offset (AVO) analysis inadequate for strongly attenuative media. For instance, an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PS-wave at normal incidence, even if both half-spaces have a horizontal symmetry plane. The developed linearized solutions can be used in AVO inversion for highly attenuative (e.g., gas-sand and heavy-oil) reservoirs.

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.

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

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.

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