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Numerically Solving Fractional Laplacian Constant-Q Visco-Acoustic Wave Equation by a Matrix-Transform Method
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 81st EAGE Conference and Exhibition 2019, Jun 2019, Volume 2019, p.1 - 5
Abstract
We introduce a matrix-transform method (MTM) to numerically solve the fractional Laplacian constant-Q visco-acoustic wave equation. The new method is based on a matrix representation of the fractional Laplacians and is different from the traditional Fourier-spectrum representation. With the MTM approach, the visco-acoustic wave equation is discretized in the space-domain, thus the periodic boundary caused by the Fourier-transform method can be avoided. The spatial discretization of MTM offers great convenience to handle various boundary conditions. In the MTM scheme, the fractional power of a huge matrix needs to be computed. We adopt the Lanczos approximation to compute the matrix-vector product directly, thus avoiding forming the huge matrix. Numerical examples verify the feasibility of MTM in simulating visco-acoustic wave propagation.