Accounting for limited spatial aperture in the waveform inversion of p-τ seismograms

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 452-457 ◽  
Author(s):  
S. L. Dobbs ◽  
C. R. Wilson ◽  
M. M. Backus
Keyword(s):  
Plane Wave ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Fundamental Property ◽  
Seismic Arrays ◽  
Plane Wave Decomposition ◽  
Iterative Inversion ◽  
Wave Decomposition ◽  
Parameter Dependent ◽  
Ray Parameter

The finite length of seismic arrays results in smeared estimates of the plane‐wave decomposition of the recorded wave field. The smearing is a fundamental property of plane‐wave decomposition; it can be reduced but not eliminated. If not accounted for, this smearing can have a significant effect upon the waveform inversion of plane‐wave seismograms. This paper illustrates the effects of limited spatial aperture on the plane‐wave decomposition and demonstrates that these truncation artifacts can be described by a linear ray parameter‐dependent filter. Experiments with synthetic data indicate that including the effects of limited aperture in the forward model of an iterative inversion produces a stable inversion result without significantly reducing the information content of the data. The method is illustrated with synthetic data derived for an earth consisting of elastic, isotropic, flat layers.

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.

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.

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.

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