Direct Solver in Cartesian and Generalized Coordinate Systems for Solving Rarefied Flows of Gases of Arbitrary Statistics

2013 ◽  
Author(s):  
Bagus Muljadi ◽  
Jaw-Yen Yang
Keyword(s):  
Coordinate Systems ◽  
Direct Solver ◽  
Rarefied Flows ◽  
Generalized Coordinate

Inline delayed-shot migration in tilted elliptical-cylindrical coordinates

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. S187-S197 ◽  
Author(s):  
Jeffrey Shragge ◽  
Guojian Shan
Keyword(s):  
Impulse Response ◽  
Seismic Data ◽  
Finite Difference Methods ◽  
Computational Cost ◽  
Coordinate Systems ◽  
Geologic Structure ◽  
Data Set ◽  
Implicit Finite Difference ◽  
Wavefield Extrapolation ◽  
Generalized Coordinate

Riemannian wavefield extrapolation, a one-way wave-equation method for propagating seismic data on generalized coordinate systems, is extended to inline delayed-shot migration using 3D tilted elliptical-cylindrical (TEC) coordinate meshes. Compared to Cartesian geometries, TEC coordinates are more conformal to the shape of inline delayed-source impulse response, which allows the bulk of wavefield energy to propagate at angles lower to the extrapolation axis, thus improving global propagation accuracy. When inline coordinate tilt angles are well matched to the inline source ray parameters, the TEC coordinate extension affords accurate propagation of both steep-dip and turning-wave components important for successfully imaging complex geologic structure. Wavefield extrapolation in TEC coordinates is no more complicated than propagation in elliptically anisotropic media and can be handled by existing implicit finite-difference methods. Impulse response tests illustrate the phase accuracy of the method and show that the approach is free of numerical anisotropy. Migration tests from a realistic 3D wide-azimuth synthetic derived from a field Gulf of Mexico data set demonstrate the imaging advantages afforded by the technique, including the improved imaging of steeply dipping salt flanks at a reduced computational cost.

Riemannian wavefield extrapolation: Nonorthogonal coordinate systems

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. T11-T21 ◽  
Author(s):  
Jeffrey Chilver Shragge
Keyword(s):  
Wave Propagation ◽  
Spherical Geometry ◽  
Coordinate Systems ◽  
Propagation Theory ◽  
Mesh Smoothing ◽  
Computational Overhead ◽  
Wavefield Extrapolation ◽  
2D And 3D ◽  
Smoothing Procedure ◽  
Generalized Coordinate

Riemannian wavefield extrapolation (RWE) is used to model one-way wave propagation on generalized coordinate meshes. Previous RWE implementations assume that coordinate systems are defined by either orthogonal or semiorthogonal geometry. This restriction leads to situations where coordinate meshes suffer from problematic bunching and singularities. Nonorthogonal RWE is a procedure that avoids many of these problems by posing wavefield extrapolation on smooth, but generally nonorthogonal and singularity-free, coordinate meshes. The resulting extrapolation operators include additional terms that describe nonorthogonal propagation. These extra degrees of complexity, however, are offset by smoother coefficients that are more accurately implemented in one-way extrapolation operators. Remaining coordinate mesh singularities are then eliminated using a differential mesh smoothing procedure. Analytic extrapolation examples and the numerical calculation of 2D and 3D Green’s functions for cylindrical and near-spherical geometry validate the nonorthogonal RWE propagation theory. Results from 2D benchmark testing suggest that the computational overhead associated with the RWE approach is roughly 35% greater than Cartesian-based extrapolation.

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