scholarly journals Approximate Cloaking for the Full Wave Equation via Change of Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 1894-1924 ◽  
Author(s):  
Hoai-Minh Nguyen ◽  
Michael S. Vogelius
Keyword(s):  
Wave Equation ◽  
Change Of Variables ◽  
Full Wave

scholarly journals Generalized impedance boundary conditions for strongly absorbing obstacle: The full wave equation

2015 ◽  
Vol 25 (10) ◽  
pp. 1927-1960 ◽  
Author(s):  
Hoai-Minh Nguyen ◽  
Linh Viet Nguyen
Keyword(s):  
Wave Equation ◽  
Three Dimensions ◽  
Impedance Boundary ◽  
Change Of Variables ◽  
Full Wave ◽  
Time Harmonic ◽  
Time Regime ◽  
Frequency Regime ◽  
The Difference ◽  
The Time Domain

This paper is devoted to the study of the generalized impedance boundary conditions (GIBCs) for a strongly absorbing obstacle in the time regime in two and three dimensions. The GIBCs in the time domain are heuristically derived from the corresponding conditions in the time harmonic regime. The latter is frequency-dependent except the one of order 0; hence the formers are non-local in time in general. The error estimates in the time regime can be derived from the ones in the time harmonic regime when the frequency dependence is well controlled. This idea is originally due to Nguyen and Vogelius [Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807] for the cloaking context. In this paper, we present the analysis to the GIBCs of orders 0 and 1. To implement the ideas in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807], we revise and extend the work of Haddar, Joly, and Nguyen, [Generalized impedance boundary condition for scattering by strongly absorbing obstacles: the scalar case, Math. Models Methods Appl. Sci.15 (2005) 1273–1300], where the GIBCs were investigated for a fixed frequency in three dimensions. Even though we heavily follow the strategy in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807], our analysis on the stability contains new ingredients and ideas. First, instead of considering the difference between solutions of the exact model and the approximate model, we consider the difference between their derivatives in time. This simple idea helps us to avoid the machinery used in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variables, SIAM J. Math. Anal.44 (2012) 769–807] concerning the integrability with respect to frequency in the low frequency regime. Second, in the high frequency regime, the Morawetz multiplier technique used in [H.-M. Nguyen and M. S. Vogelius, Approximate cloaking for the full wave equation via change of variable, SIAM J. Math. Anal.44 (2012) 769–807] does not fit directly in our setting. Our proof makes use of a result by Hörmander in [Lp estimates for (pluri-) subharmonic functions, Math. Scand.20 (1967) 65–78]. Another important part of the analysis in this paper is the well-posedness in the time domain for the approximate problems imposed with GIBCs on the boundary of the obstacle, which are non-local in time.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Randomized HSS acceleration for full-wave-equation depth stepping migration

2014 ◽  
Author(s):  
Lina Miao* ◽  
Polina Zheglova ◽  
Felix J. Herrmann
Keyword(s):  
Wave Equation ◽  
Full Wave

scholarly journals Numerical treatment of the spatio-temporal electromagnetic beam-wave packet

2017 ◽  
Vol 68 (2) ◽  
pp. 109-116
Author(s):  
L’ubomír Šumichrast ◽  
Jaroslav Franek
Keyword(s):  
Numerical Simulation ◽  
Wave Equation ◽  
Wave Packet ◽  
Paraxial Approximation ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Beam Wave ◽  
Electromagnetic Beam ◽  
Full Wave ◽  
Spatio Temporal

Abstract Propagation of a two-dimensional spatio-temporal electromagnetic beam wave is analysed. In parabolic (paraxial) approximation the exact analytical results for a spatio-temporal Gaussian impulse can be obtained. For solution of the full wave equation the numerical simulation has to be used. The various facets of this simulation are discussed here.

Gulf of Suez acquisition design using 2D and 3D full wave equation simulation

2003 ◽  
Author(s):  
Dana Jurick ◽  
Jeff Codd ◽  
Fatmir Hoxha ◽  
Julia Naumenko ◽  
David Kessler
Keyword(s):  
Wave Equation ◽  
Gulf Of Suez ◽  
Full Wave ◽  
2D And 3D

Numerical Solution of Full-Wave Equation With Mode Coupling

Radio Science ◽  
1966 ◽  
Vol 1 (8) ◽  
pp. 957-970 ◽  
Author(s):  
Yuji Inoue ◽  
Samuel Horowitz
Keyword(s):  
Wave Equation ◽  
Numerical Solution ◽  
Mode Coupling ◽  
Full Wave
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