scholarly journals Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation

2013 ◽  
Vol 29 (6) ◽  
pp. 065007 ◽  
Author(s):  
Tuncay Aktosun ◽  
Vassilis G Papanicolaou
Keyword(s):  
Wave Equation ◽  
Wave Speed ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Symmetric Variable

Isospectral sets for transmission eigenvalue problem

2020 ◽  
Vol 28 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Sergey A. Buterin
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Wave Speed ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Constructive Methods ◽  
Transmission Eigenvalue ◽  
Symmetric Variable ◽  
Transmission Eigenvalue Problem

AbstractWe consider the boundary value problem {R(a,q)}: {-y^{\prime\prime}(x)+q(x)y(x)=\lambda y(x)} with {y(0)=0} and {y(1)\cos(a\sqrt{\lambda})=y^{\prime}(1)\frac{\sin(a\sqrt{\lambda})}{\sqrt{% \lambda}}}. Motivated by the previous work [T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question: how does one characterize isospectral sets corresponding to problem {R(1,q)}? In this paper applying constructive methods we answer the above question.

The Influence of Variable-Speed Waveforms on Vibration Suppression in Time-Varying Speed Cutting

2013 ◽  
Vol 690-693 ◽  
pp. 2514-2518
Author(s):  
Juan Cong ◽  
Yun Wang ◽  
Wei Na Yu
Keyword(s):  
Wave Speed ◽  
Vibration Suppression ◽  
Sine Wave ◽  
Time Varying ◽  
Variable Speed ◽  
Suppression Effect ◽  
Speed Variation ◽  
Input And Output ◽  
System Input ◽  
Better Than

Through the research on the change of system input and output energy in time-varying speed cutting, the influence of variable-speed waveforms on vibration suppression effect in time-varying speed cutting is quantitatively analyzed in this paper. A conclusion can be drawn that sine wave speed variation is better than triangle wave speed variation in vibration suppression.

scholarly journals ADMM-based multiparameter wavefield reconstruction inversion in VTI acoustic media with TV regularization

2019 ◽  
Vol 219 (2) ◽  
pp. 1316-1333 ◽  
Author(s):  
H S Aghamiry ◽  
A Gholami ◽  
S Operto
Keyword(s):  
Wave Equation ◽  
Wave Speed ◽  
Homogeneous Model ◽  
Waveform Inversion ◽  
Search Space ◽  
Bound Constraints ◽  
The North ◽  
Tv Regularization ◽  
Acoustic Media ◽  
Suitable Framework

SUMMARYFull waveform inversion (FWI) is a nonlinear waveform matching procedure, which suffers from cycle skipping when the initial model is not kinematically accurate enough. To mitigate cycle skipping, wavefield reconstruction inversion (WRI) extends the inversion search space by computing wavefields with a relaxation of the wave equation in order to fit the data from the first iteration. Then, the subsurface parameters are updated by minimizing the source residuals the relaxation generated. Capitalizing on the wave-equation bilinearity, performing wavefield reconstruction and parameter estimation in alternating mode decomposes WRI into two linear subproblems, which can be solved efficiently with the alternating-direction method of multiplier (ADMM), leading to the so-called iteratively refined WRI (IR–WRI). Moreover, ADMM provides a suitable framework to implement bound constraints and different types of regularizations and their mixture in IR–WRI. Here, IR–WRI is extended to multiparameter reconstruction for vertical transverse isotropic (VTI) acoustic media. To achieve this goal, we first propose different forms of bilinear VTI acoustic wave equation. We develop more specifically IR–WRI for the one that relies on a parametrization involving vertical wave speed and Thomsen’s parameters δ and ϵ. With a toy numerical example, we first show that the radiation patterns of the virtual sources generate similar wavenumber filtering and parameter cross-talks in classical FWI and IR–WRI. Bound constraints and TV regularization in IR–WRI fully remove these undesired effects for an idealized piecewise constant target. We show with a more realistic long-offset case study representative of the North Sea that anisotropic IR–WRI successfully reconstruct the vertical wave speed starting from a laterally homogeneous model and update the long wavelengths of the starting ϵ model, while a smooth δ model is used as a passive background model. VTI acoustic IR–WRI can be alternatively performed with subsurface parametrizations involving stiffness or compliance coefficients or normal moveout velocities and η parameter (or horizontal velocity).

scholarly journals Wave equation on spherically symmetric Lorentzian metrics

2011 ◽  
Vol 52 (6) ◽  
pp. 063511 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
Ahmad Y. Al-Dweik ◽  
A. H. Kara ◽  
M. Karim ◽  
F. D. Zaman
Keyword(s):  
Wave Equation ◽  
Spherically Symmetric ◽  
Lorentzian Metrics
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