A generalization of the Fourier pseudospectral method

Geophysics - Tập 75 Số 6 - Trang A53-A56 - 2010
José M. Carcione1
1Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Trieste, Italy. E-mail: .

Tóm tắt

The Fourier pseudospectral (PS) method is generalized to the case of derivatives of nonnatural order (fractional derivatives) and irrational powers of the differential operators. The generalization is straightforward because the calculation of the spatial derivatives with the fast Fourier transform is performed in the wavenumber domain, where the operator is an irrational power of the wavenumber. Modeling constant-[Formula: see text] propagation with this approach is highly efficient because it does not require memory variables or additional spatial derivatives. The classical acoustic wave equation is modified by including those with a space fractional Laplacian, which describes wave propagation with attenuation and velocity dispersion. In particular, the example considers three versions of the uniform-density wave equation, based on fractional powers of the Laplacian and fractional spatial derivatives.

Từ khóa


Tài liệu tham khảo

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Geophysics

Tập 75 Số 6

A53-A56

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