scholarly journals An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators

2012 ◽  
Vol 388 (2) ◽  
pp. 1090-1106 ◽  
Author(s):  
Ciprian Preda ◽  
Petre Preda ◽  
Cristina Praţa
Keyword(s):  
Evolution Operators

scholarly journals Gabor representations of evolution operators

2015 ◽  
Vol 367 (11) ◽  
pp. 7639-7663 ◽  
Author(s):  
Elena Cordero ◽  
Fabio Nicola ◽  
Luigi Rodino
Keyword(s):  
Evolution Operators

scholarly journals On some dichotomy concepts with different growth rates for evolution operators in Banach spaces

2015 ◽  
Vol 53 (2) ◽  
pp. 133-150
Author(s):  
Nicolae Marian Seimeanu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Growth Rates ◽  
Real Numbers ◽  
Evolution Operators

Abstract This paper treats three concepts of (h, k)-dichotomy and their correspondents in the uniform cases. The connections between them are established through examples and counterexamples presented on the Banach space of square-summable sequences of real numbers.

scholarly journals Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

1998 ◽  
Vol 93 (3/4) ◽  
pp. 981-999 ◽  
Author(s):  
Predrag Cvitanović ◽  
C. P. Dettmann ◽  
Ronnie Mainieri ◽  
Gábor Vattay
Keyword(s):  
Perturbation Theory ◽  
Stochastic Evolution ◽  
Trace Formulas ◽  
Evolution Operators ◽  
Weak Noise ◽  
Noise Perturbation

Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Iury Araújo ◽  
Murillo Nascimento ◽  
Jesse Costa ◽  
Alan Souza ◽  
Jörg Schleicher
Keyword(s):  
Anisotropic Medium ◽  
Mathematical Formulation ◽  
Hamiltonian Formulation ◽  
Anisotropic Media ◽  
Low Rank ◽  
Direct Access ◽  
S Wave ◽  
Evolution Operators ◽  
Individual Parameter ◽  
Reflection Data

We present a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudo-acoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudo-acoustic evolution operators. Therefore it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information like its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudo-acoustic anisotropic media.

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