Finite-difference computations of ultrasound wave propagation in bone

2008 ◽  
pp. 595-595
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Ultrasound Wave

scholarly journals Shear horizontal (SH) ultrasound wave propagation around smooth corners

Ultrasonics ◽  
2014 ◽  
Vol 54 (4) ◽  
pp. 997-1004 ◽  
Author(s):  
P.A. Petcher ◽  
S.E. Burrows ◽  
S. Dixon
Keyword(s):  
Wave Propagation ◽  
Ultrasound Wave ◽  
Shear Horizontal

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

Generalization of von Neumann analysis for a model of two discrete half-spaces: The acoustic case

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM35-SM46 ◽  
Author(s):  
Matthew M. Haney
Keyword(s):  
Wave Propagation ◽  
Numerical Model ◽  
Finite Difference ◽  
Stability Criterion ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Von Neumann ◽  
Transmission Coefficients ◽  
Strong Material ◽  
Von Neumann Analysis

Evaluating the performance of finite-difference algorithms typically uses a technique known as von Neumann analysis. For a given algorithm, application of the technique yields both a dispersion relation valid for the discrete time-space grid and a mathematical condition for stability. In practice, a major shortcoming of conventional von Neumann analysis is that it can be applied only to an idealized numerical model — that of an infinite, homogeneous whole space. Experience has shown that numerical instabilities often arise in finite-difference simulations of wave propagation at interfaces with strong material contrasts. These interface instabilities occur even though the conventional von Neumann stability criterion may be satisfied at each point of the numerical model. To address this issue, I generalize von Neumann analysis for a model of two half-spaces. I perform the analysis for the case of acoustic wave propagation using a standard staggered-grid finite-difference numerical scheme. By deriving expressions for the discrete reflection and transmission coefficients, I study under what conditions the discrete reflection and transmission coefficients become unbounded. I find that instabilities encountered in numerical modeling near interfaces with strong material contrasts are linked to these cases and develop a modified stability criterion that takes into account the resulting instabilities. I test and verify the stability criterion by executing a finite-difference algorithm under conditions predicted to be stable and unstable.

Finite difference forward modelling across the Tyrrhenian basin

2021 ◽  
Author(s):  
Chiara Nardoni ◽  
Luca De Siena ◽  
Fabio Cammarano ◽  
Elisabetta Mattei ◽  
Fabrizio Magrini
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Wave Attenuation ◽  
Software Tool ◽  
Seismic Wave Propagation ◽  
Tyrrhenian Sea ◽  
Forward Modelling ◽  
Crustal Thinning ◽  
Energy Leakage ◽  
Radiative Transfer Equations

<p>Strong lateral variations in medium properties affect the response of seismic wavefields. The Tyrrhenian Sea is ideally suited to explore these effects in a mixed continental-oceanic crust that comprises magmatic systems. The study aims at investigating the effects of crustal thinning and sedimentary layers on wave propagation, especially the reverberating (e.g., Lg) phases, across the oceanic basin. We model regional seismograms (600-800 km) using the software tool OpenSWPC (Maeda et al., 2017, EPS) based on the finite difference simulation of the wave equation. The code simulates the seismic wave propagation in heterogeneous viscoelastic media including the statistical velocity fluctuations as well as heterogeneous topography, typical of mixed settings. This approach allows to evaluate the role of interfaces and layer thicknesses on phase arrivals and direct and coda attenuation measurements. The results are compared with previous simulations of the radiative-transfer equations. They provide an improved understanding of the complex wave attenuation and energy leakage in the mantle characterizing the southern part of the Tyrrhenian Sea and the Italian peninsula. The forward modelling is to be embedded in future applications of attenuation, absorption and scattering tomography performed with MuRAT (the Multi-Resolution Attenuation Tomography code – De Siena et al. 2014, JVGR) available at https://github.com/LucaDeSiena/MuRAT.</p>

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