Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives
Abstract
Kjartansson's constant-Q model is solved in the time-domain using a new modeling algorithm based on fractional derivatives. Instead of time derivatives of order 2, Kjartansson's model requires derivatives of order 2γ, with 0 <γ< 1/2, in the dilatation-stress formulation. The derivatives are computed with the Grünwald-Letnikov and central-difference approximations, which are finite-difference extensions of the standard finite-difference operators for derivatives of integer order. The modeling uses the Fourier method to compute the spatial derivatives, and therefore can handle complex geometries. A synthetic cross-well seismic experiment illustrates the capabilities of this novel modeling algorithm.
- Publication:
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Pure and Applied Geophysics
- Pub Date:
- 2002
- DOI:
- 10.1007/s00024-002-8705-z
- Bibcode:
- 2002PApGe.159.1719C
- Keywords:
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- Key words: Viscoelastic waves;
- fractional calculus;
- numerical modeling;
- seismology.