Elastic wave modeling with free surfaces: Stability of long simulations

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 314-321 ◽  
Author(s):  
Stig Hestholm
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Surface Boundary ◽  
Wave Modeling ◽  
Propagation Modeling ◽  
Long Term Stability ◽  
Free Surface Boundary Condition ◽  
Wave Propagation Modeling

Three‐dimensional (3D) elastic wave propagation modeling in the velocity‐stress formulation using finite differences (FDs) have been investigated for a homogeneous medium covered by a representative, relatively steep surface topography consisting of a 1D square root function. This scenario using various numerical implementations is explored. The behavior with regard to stability of long simulations is expected to be indicative of each numerical implementation's robustness for other types of topographies/media. Employing various combinations of the FD order was found only to change the time of the first incidence of instability. On the other hand, nonequidistant grids in the horizontal and vertical directions are found to be extremely useful for long‐term stability of 3D wave propagation modeling with our free‐surface boundary condition for single‐valued topographies. In particular dz ≥ (3/2) dx is found completely stable for all tested vP/vS ratios. Such relationships of using dz > dx are also favorable for more accurate Rayleigh‐wave modeling. Setting the density equal to 1/10 of its interior value at one layer only at the surface is another simple means of achieving stability.

Brief review on PE method application to propagation channel modeling in sea environment

2012 ◽  
Vol 2 (1) ◽  
Author(s):  
Irina Sirkova
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Parabolic Equation ◽  
Initial Conditions ◽  
Channel Modeling ◽  
Radio Propagation ◽  
Propagation Channel ◽  
Tropospheric Propagation ◽  
Propagation Modeling ◽  
Wave Propagation Modeling

AbstractThis work provides an introduction to one of the most widely used advanced methods for wave propagation modeling, the Parabolic Equation (PE) method, with emphasis on its application to tropospheric radio propagation in coastal and maritime regions. The assumptions of the derivation, the advantages and drawbacks of the PE, the numerical methods for solving it, and the boundary and initial conditions for its application to the tropospheric propagation problem are briefly discussed. More details are given for the split-step Fourier-transform (SSF) solution of the PE. The environmental input to the PE, the methods for tropospheric refractivity profiling, their accuracy, limitations, and the average refractivity modeling are also summarized. The reported results illustrate the application of finite element (FE) based and SSF-based solutions of the PE for one of the most difficult to treat propagation mechanisms, yet of great significance for the performance of radars and communications links working in coastal and maritime zones — the tropospheric ducting mechanism. Recent achievements, some unresolved issues and ongoing developments related to further improvements of the PE method application to the propagation channel modeling in sea environment are highlighted.

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