scholarly journals Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures

2013 ◽  
Vol 81 (3-4) ◽  
pp. 273-295 ◽  
Author(s):  
Illya M. Karabash
Keyword(s):  
Wave Equations ◽  
Inhomogeneous Media ◽  
Optimal Structures ◽  
D Wave

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

scholarly journals A New Construction for Scalar Wave Equations in Inhomogeneous Media

1997 ◽  
Vol 7 (9) ◽  
pp. 1071-1096 ◽  
Author(s):  
S. de Toro Arias ◽  
C. Vanneste
Keyword(s):  
Wave Equations ◽  
Inhomogeneous Media ◽  
Scalar Wave ◽  
New Construction

A low-dispersive method using the high-order stereo-modelling operator for solving 2-D wave equations

2017 ◽  
Vol 210 (3) ◽  
pp. 1938-1964 ◽  
Author(s):  
Jingshuang Li ◽  
Dinghui Yang ◽  
Hao Wu ◽  
Xiao Ma
Keyword(s):  
Wave Equations ◽  
High Order ◽  
D Wave

2.5-D wave equations and high‐frequency asymptotics

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 556-562 ◽  
Author(s):  
John W. Stockwell
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Wave Equations ◽  
Maximum Amplitude ◽  
Variable Density ◽  
Constant Density ◽  
Correction Factors ◽  
Wave Operators ◽  
Ray Series ◽  
D Wave

The need for modeling 3-D seismic data in a 2-D setting has motivated investigators to create so‐called 2.5-D modeling methods. One such method proposed by Liner involves the use of an approximate 2.5-D wave operator for constant‐density media. The traveltimes and amplitudes predicted by high‐frequency asymptotic ray series (WKBJ) analysis of the Liner 2.5-D wave equation match those predicted by Bleistein’s 2.5-D ray‐theoretic development in constant wavespeed media. However, high‐frequency analysis indicates that the Liner 2.5-D variable wavespeed equation will have a maximum amplitude error of ±35% in a linear c(z) model where the wavespeed doubles or halves from the beginning to the end of a raypath. These amplitudes are comparable to those produced by converting 2-D data to 2.5-D using correction factors of the type proposed by Emersoy and Oristaglio and Deregowski and Brown, with the exception being that the Liner equation lacks the half derivative waveform correction present in these operators. An alternate method of constructing 2.5-D wave operators based on the WKBJ analysis is proposed. This method permits variable density (acoustic) 2.5-D wave operators to be derived.

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