Elastic-wave propagation in two evenly-welded quarter-spaces

abstract This paper deals with elastic-wave propagation in two evenly-welded quarter-spaces. A compressional line source can be located at any point within either medium. The numerical solutions to this problem have been obtained by using the finite difference method. A computer program has been written to obtain synthetic seismograms of the horizontal and vertical displacements at all nodes of the superimposed grid, for the following cases: (a) elastic-wave propagation in a quarter-space, and (b) elastic-wave propagation in two quarter-spaces. Reflected, converted, transmitted, and diffracted phases are identified and interpreted. Surface and interface waves, originated at the corner by diffraction of the source pulse, are investigated as a function of the rigidity contrast and the velocity contrast between the two media and of the position of the source. Two-dimensional seismic modeling techniques have been used to provide a qualitative experimental verification of the numerical results.

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Elastic wave propagation in fractured media using the discontinuous Galerkin method

Geophysics ◽

10.1190/geo2015-0602.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. T163-T174 ◽

Cited By ~ 28

Author(s):

Jonás D. De Basabe ◽

Mrinal K. Sen ◽

Mary F. Wheeler

Keyword(s):

Wave Propagation ◽

Elastic Wave ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Additional Term ◽

Elastic Wave Propagation ◽

Weak Formulation ◽

Penalty Term ◽

Interface Waves

We have formulated and implemented a discontinuous Galerkin method (DGM) for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults. The approach is based on the interior-penalty formulation of DGM, and the fractures are simulated using the linear-slip model, which is incorporated into the weak formulation by including an additional term that is similar to the penalty term but uses the fracture compliance instead of an arbitrary penalty parameter. We have calibrated our results against an analytic solution of fracture-induced anisotropy for a set of elongated horizontal fractures, and we have evaluated numerical examples that simulate the reflection and transmission of waves at a fracture and at fracture interface waves. This method can further be used with models containing intersecting fractures and multiple fracture sets in 2D or 3D domains.

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Analytic results for roots of two irrational functions in elastic wave propagation

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000012376 ◽

1998 ◽

Vol 40 (1) ◽

pp. 72-79 ◽

Cited By ~ 18

Author(s):

L. M. Brock

Keyword(s):

Wave Propagation ◽

Elastic Wave ◽

Surface Waves ◽

Elastic Wave Propagation ◽

Interface Waves ◽

Rayleigh Surface Waves ◽

Standard Operations

AbstractThe velocities of Rayleigh surface waves and, when they exist, Stoneley interface waves can be obtained as the roots of two irrational functions. Here previous results are extended by using standard operations related to the Wiener-Hopf technique to provide expressions in quadrature for these roots.

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