Uniform high-frequency approximations of the square root Helmholtz operator symbol

Fishman, Louis; Gautesen, A. K.; Sun, Zhiming

doi:10.1016/s0165-2125(97)00018-8

Cited by 36 publications

(86 citation statements)

References 32 publications

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“…After solving the parabolic equation (13), we use (15) as the boundary condition when solving the Helmholtz equation in Ω H , and then we use (16) as the initial condition for solving the parabolic equation (14) in Ω P , i.e., the incoming wave is passed from parabolic region to the Helmholtz region and the back scattered wave is passed correspondingly.…”

Section: Conditionmentioning

confidence: 99%

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Efficient numerical simulation for long range wave propagation

Huang

Papanicolaou

Sølna

et al. 2006

Journal of Computational Physics

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We develop an efficient algorithm for simulating wave propagation over long distances with both weak and strong scatterers. In domains with weak heterogeneities the wave field is decomposed into forward propagating and back scattered modes using two coupled parabolic equations. In the region near strong scatterers, the Helmholtz equation is used to capture the strong scattering events. The key idea in our method is to combine these two regimes using a combined domain decomposition and wave decomposition method. A transparent interface condition is derived to couple these two regions together. Numerical examples show that the simulated field is close to the field obtained using the full Helmholtz equation in the whole domain.

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Section: Conditionmentioning

confidence: 99%

“…The construction of several explicit, uniform asymptotic approximations of the square root Helmholtz operator are given in [14]. A re-formulation based on the Dirichlet-to-Neumann (DtN) map has also been derived in [16] and [17,18].…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical simulation for long range wave propagation

Huang

Papanicolaou

Sølna

et al. 2006

Journal of Computational Physics

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“…In our approach, Tα is taken to be a Fourier integral operator (Duistermaat, 1996) where the subscript α is called the operator symbol and is a mathematical function of position, wavenumber, and frequency that describes the physics of the propagating waves. In principle, it is possible to find exact symbols for highly complex lateral velocity variations (Fishman et al, 1997), which describe all internal scattering as well as primary transmitted waves. Here we are concerned with more approximate expressions and in particular we begin with the explicit form for equation 1 known as the locally homogeneous approximation (Fishman et al, 1997) Ψ…”

Section: Generalized Pspimentioning

confidence: 99%

“…In principle, it is possible to find exact symbols for highly complex lateral velocity variations (Fishman et al, 1997), which describe all internal scattering as well as primary transmitted waves. Here we are concerned with more approximate expressions and in particular we begin with the explicit form for equation 1 known as the locally homogeneous approximation (Fishman et al, 1997) Ψ…”

Section: Generalized Pspimentioning

confidence: 99%

Stabilizing explicit frequency‐space migration using local WKBJ operators

Hogan

Margrave

2006

SEG Technical Program Expanded Abstracts 2006

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SummaryWe introduce a new operator for explicit wavefield extrapolation. We modify the commonly used locally homogeneous wavefield extrapolator to include a local vertical gradient, whose purpose is simply to enhance operator stability when spatially localized. The locally homogeneous operator assumes that wavefield extrapolation across a single depth step can be done with straight raypaths using the assumed constant velocity at the output point. Such operators can produce excellent seismic images but the straight ray assumption means that their spatial aperture is infinite, which leads to instability when the operator is localized by spatial windowing. Adjusting the operator to accommodate a suitably chosen positive vertical velocity gradient causes raypath curvature which naturally limits the operator within a finite aperture. The required modification to the locally homogeneous operator is essentially a WKBJstyle integrated phase. The resulting operator has a finite aperture and is sufficiently stable when localized to be used in an explicit depth migration scheme. We demonstrate operator fidelity with excellent images of the Marmousi model.

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“…This gives a non-local one-way wave operator asymptotically correct in both the high frequency and high wave number limit. A more careful decomposition is proposed in [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

The Bremmer series for a multi-dimensional acoustic scattering problem

Gustafsson

2000

J. Phys. A: Math. Gen.

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Uniform high-frequency approximations of the square root Helmholtz operator symbol

Cited by 36 publications

References 32 publications

Efficient numerical simulation for long range wave propagation

Efficient numerical simulation for long range wave propagation

Stabilizing explicit frequency‐space migration using local WKBJ operators

The Bremmer series for a multi-dimensional acoustic scattering problem

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