Stable plane-wave decomposition and spherical-wave reconstruction: applications to converted S-mode separation and trace interpolation

1984 ◽  
Vol 15 (4) ◽  
pp. 265-265
Author(s):  
J. J. Cabrera ◽  
S. Levy
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Stable Plane ◽  
Plane Wave Decomposition ◽  
Mode Separation ◽  
Wave Decomposition

Stable plane‐wave decomposition and spherical‐wave reconstruction: Applications to converted S-mode separation and trace interpolation

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1915-1932 ◽  
Author(s):  
J. Julian Cabrera ◽  
Shlomo Levy
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Vertical Displacement ◽  
Hankel Transform ◽  
Displacement Component ◽  
Common Source ◽  
Plane Wave Decomposition ◽  
Mode Separation ◽  
Wave Decomposition ◽  
Discrete Integration

Plane‐wave decomposition of the vertical displacement component of a spherical‐wave field corresponding to a compressional point source is solved as a set of inverse problems. The solution method utilizes the power and stability of Backus and Gilbert (smallest and flattest) model‐construction techniques, and achieves computational efficiency through the use of analytical solutions to the involved integrals. The theory and algorithms developed in this work allow stable and efficient reconstruction of spherical‐wave fields from a relatively sparse set of their plane‐wave components. Comparison of the algorithms with discrete integration of the Hankel transform shows very little or no advantage for the transformation from the time‐distance (t-x) domain to the intercept time‐angle of emergence (τ-γ) domain if the seismograms are equisampled spatially. However, when the observed seismograms are not equally spaced or the transformation τ-γ to t-x is performed, the proposed schemes are superior to the discrete integration of the Hankel transform. Applicability of the algorithms to reflection seismology is demonstrated by means of the solution of the problem of trace interpolation, and also that of the separation of converted S modes from other modes presented in common‐source gathers. In both cases the application of the algorithms to a set of synthetic reflection seismograms yields satisfactory results.

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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