A hybrid grid finite difference method for acoustic wave propagation in tilted orthorhombic media

2012 ◽  
Author(s):  
Chunlei Chu
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Method ◽  
Acoustic Wave Propagation ◽  
Hybrid Grid

The role and application of entropy terms for acoustic wave modeling by the finite‐difference method

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1457-1465 ◽  
Author(s):  
M. A. Dablain
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Acoustic Wave Propagation ◽  
Central Difference ◽  
Central Difference Scheme ◽  
One Dimensional ◽  
The Finite Difference Method

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

Multipole acoustic waveforms in fluid‐filled boreholes in biaxially stressed formations: A finite‐difference method

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 190-201 ◽  
Author(s):  
Qing‐Huo Liu ◽  
Bikash K. Sinha
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Flexural Waves ◽  
Acoustic Wave Propagation ◽  
Linear Elastic ◽  
Spatial Coordinates

A finite‐difference method is developed to simulate elastic wave propagation in a borehole surrounded by a biaxially stressed solid formation. The linear elastic formation is altered by such tectonic stresses that cause significant changes in the characteristics of wave propagation in a borehole. The 2.5-dimensional problem addressed in this work concerns the three‐dimensional wave propagation in a medium inhomogeneous in two spatial coordinates transverse to the borehole axis. A second‐order finite‐difference method is developed to solve the partial differential equations arising from a published acoustoelastic model for borehole acoustic wave propagation in prestressed formations. The algorithm is validated and applied to model both the borehole flexural and axisymmetric Stoneley waves. The computed waveforms are processed by a variation of Prony’s algorithm that yields dispersion curves for flexural waves polarized both parallel and perpendicular to the stress direction. The flexural dispersion crossover in a uniaxially stressed formation is quantitatively confirmed. The Stoneley dispersion in the presence of such stresses exhibits approximately a uniform shift toward lower slownesses over the entire bandwidth of interest. This implies that azimuthal averaging of formation stiffnesses approximately yields the same effective Stoneley stiffness at different radial positions.

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