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.
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(Received September 21, 2000, revised December 4, 2000, accepted December 13, 2000)
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Carcione, J., Cavallini, F., Mainardi, F. et al. Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives. Pure appl. geophys. 159, 1719–1736 (2002). https://doi.org/10.1007/s00024-002-8705-z
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DOI: https://doi.org/10.1007/s00024-002-8705-z