Single-scattering parabolic equation solutions for elastic media propagation, including Rayleigh waves

2012 ◽  
Vol 131 (2) ◽  
pp. 1131-1137 ◽  
Author(s):  
Adam M. Metzler ◽  
William L. Siegmann ◽  
Michael D. Collins
Keyword(s):  
Parabolic Equation ◽  
Rayleigh Waves ◽  
Single Scattering ◽  
Elastic Media

Energy‐conserving and single‐scattering parabolic equation solutions for elastic media

2003 ◽  
Vol 114 (4) ◽  
pp. 2428-2428
Author(s):  
Elizabeth T. Kusel ◽  
William L. Siegmann ◽  
Michael D. Collins ◽  
Joseph F. Lingevitch
Keyword(s):  
Parabolic Equation ◽  
Single Scattering ◽  
Elastic Media ◽  
Energy Conserving

scholarly journals Passive retrieval of Rayleigh waves in disordered elastic media

2005 ◽  
Vol 72 (4) ◽  
Author(s):  
Eric Larose ◽  
Arnaud Derode ◽  
Dominique Clorennec ◽  
Ludovic Margerin ◽  
Michel Campillo
Keyword(s):  
Rayleigh Waves ◽  
Elastic Media

scholarly journals EXTENSION OF THE PUFEM TO ELASTIC WAVE PROPAGATION IN LAYERED MEDIA

2012 ◽  
Vol 20 (02) ◽  
pp. 1240006 ◽  
Author(s):  
O. LAGHROUCHE ◽  
A. EL-KACIMI ◽  
J. TREVELYAN
Keyword(s):  
Finite Element Method ◽  
Elastic Wave ◽  
Rayleigh Waves ◽  
Partition Of Unity ◽  
Elastic Media ◽  
Elastic Wave Equation ◽  
Wave Problems ◽  
Numer Math ◽  
Basis Decomposition ◽  
Transmission And Reflection

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

A variable rotated parabolic equation for elastic media

2004 ◽  
Vol 115 (5) ◽  
pp. 2579-2579
Author(s):  
Donald A. Outing ◽  
William L. Siegmann ◽  
Michael D. Collins
Keyword(s):  
Parabolic Equation ◽  
Elastic Media

Time‐domain solutions for Rayleigh and Stoneley waves using the single‐scattering parabolic equation method.

2008 ◽  
Vol 124 (4) ◽  
pp. 2585-2585
Author(s):  
Adam M. Metzler ◽  
William L. Siegmann ◽  
Michael D. Collins ◽  
Robert A. Zingarelli ◽  
Stanley A. Chin‐Bing
Keyword(s):  
Parabolic Equation ◽  
Time Domain ◽  
Single Scattering ◽  
Equation Method ◽  
Stoneley Waves ◽  
Parabolic Equation Method

Seismo-Acoustic Benchmark Problems Involving Sloping Solid–Solid Interfaces and Variable Topography

2016 ◽  
Vol 24 (03) ◽  
pp. 1650019 ◽  
Author(s):  
Katherine Woolfe ◽  
Michael D. Collins ◽  
David C. Calvo ◽  
William L. Siegmann
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Parabolic Equation ◽  
Finite Element Model ◽  
Element Model ◽  
Single Scattering ◽  
Benchmark Problems ◽  
Scattering Approximation ◽  
Single Scattering Approximation ◽  
Variable Topography

The accuracy of the seismo-acoustic parabolic equation is tested for problems involving sloping solid–solid interfaces and variable topography. The approach involves approximating the medium in terms of a series of range-independent regions, using a parabolic wave equation to propagate the field through each region, and applying a single-scattering approximation to obtain transmitted fields across the vertical interfaces between regions. The accuracy of the parabolic equation method for range-dependent problems in seismo-acoustics was previously tested in the small slope limit. It is tested here for problems involving larger slopes using a finite-element model to generate reference solutions.

scholarly journals Parabolic Equation Modeling of Scholte Waves and Other Effects Along Sloping Fluid-Solid Interfaces

2021 ◽  
pp. 2050025
Author(s):  
Michael D. Collins ◽  
Adith Ramamurti
Keyword(s):  
Parabolic Equation ◽  
Fluid Layer ◽  
Solid Material ◽  
Single Scattering ◽  
Equation Modeling ◽  
Wide Range ◽  
Scholte Waves ◽  
Scholte Wave ◽  
Shear Speed ◽  
Low Shear

Several methods for handling sloping fluid–solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid–solid case is accurate for some problems but breaks down when the contrast across the interface is sufficiently large and when there is a Scholte wave. An approximate condition for conserving energy breaks down when a Scholte wave propagates along a sloping interface but otherwise performs well for a large class of problems involving gradual slopes, a wide range of sediment parameters, and ice cover. An approach based on treating part of the fluid layer as a solid with low shear speed is developed and found to handle Scholte waves and a wide range of sediment parameters accurately, but this approach needs further development. The variable rotated parabolic equation is not effective for problems involving frequent or continuous changes in slope, but it provides a high level of accuracy for most of the test cases, which have regions of constant slope. Approaches based on a coordinate mapping and on using a film of solid material with low shear speed on the rises of the stair steps that approximate a sloping interface are also tested and found to produce accurate results for some cases.

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