scholarly journals A sloping‐boundary condition for PE calculations in range‐dependent acoustic media

1994 ◽  
Vol 95 (5) ◽  
pp. 2906-2907
Author(s):  
Gary H. Brooke ◽  
Philip M. Wort
Keyword(s):  
Boundary Condition ◽  
Acoustic Media

A SLOPING BOUNDARY CONDITION FOR EFFICIENT PE CALCULATIONS IN RANGE–DEPENDENT ACOUSTIC MEDIA

1996 ◽  
Vol 04 (01) ◽  
pp. 11-27 ◽  
Author(s):  
GARY H. BROOKE ◽  
DAVID J. THOMSON ◽  
PHILIP M. WORT
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Boundary Conditions ◽  
Standard Test ◽  
Numerical Results ◽  
Normal Displacement ◽  
Test Cases ◽  
Approximate Form ◽  
Acoustic Media ◽  
Horizontal Interface

The traditional one-way parabolic equation (PE) formulation for range-dependent layered acoustic media is modified to include effects associated with the boundary conditions along a sloping interface. Essentially, the boundary condition for continuity of the normal displacement along a sloping interface is cast in an approximate form which does not depend on range but does contain terms up to second order in the derivatives with respect to depth. The new sloping-boundary condition is then applied along an "equivalent" horizontal interface within each range-independent step of the PE. Numerical results obtained for standard test cases indicate that the sloping-boundary condition, incorporated into a one-way PE, maintains the efficiency yet improves the accuracy of forward predictions.

Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1813-1823 ◽  
Author(s):  
Bing Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Frequency Domain ◽  
Green's Function ◽  
Mixed Boundary ◽  
Waveform Inversion ◽  
Acoustic Medium ◽  
Model Parameters ◽  
Low Velocity ◽  
Acoustic Media

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] samples because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.

Interferometry by deconvolution: Part 1 — Theory for acoustic waves and numerical examples

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S115-S128 ◽  
Author(s):  
Ivan Vasconcelos ◽  
Roel Snieder
Keyword(s):  
Boundary Condition ◽  
Acoustic Waves ◽  
Time Function ◽  
Source Time Function ◽  
Field Quantity ◽  
Representation Theorems ◽  
Direct Wave ◽  
Wavefield Separation ◽  
Acoustic Media ◽  
Deconvolution Interferometry

Interferometry allows for synthesis of data recorded at any two receivers into waves that propagate between these receivers as if one of them behaves as a source. This is accomplished typically by crosscorrelations. Based on perturbation theory and representation theorems, we show that interferometry also can be done by deconvolutions for arbitrary media and multidimensional experiments. This is important for interferometry applications in which (1) excitation is a complicated source-time function and/or (2) when wavefield separation methods are used along with interferometry to retrieve specific arrivals. Unlike using crosscorrelations, this method yields only causal scattered waves that propagate between the receivers. We offer a physical interpretation of deconvolution interferometry based on scattering theory. Here we show that deconvolution interferometry in acoustic media imposes an extra boundary condition, which we refer to as the free-point or clamped-point boundary condition, depending on the measured field quantity. This boundary condition generates so-called free-point scattering interactions, which are described in detail. The extra boundary condition and its associated artifacts can be circumvented by separating the reference waves from scattered wavefields prior to interferometry. Three wavefield-separation methods that can be used in interferometry are direct-wave interferometry, dual-field interferometry, and shot-domain separation. Each has different objectives and requirements.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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