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Abstract

Summary

A new method of solving the acoustic one-step wave extrapolation matrix is proposed. In our method the analytical wavefield is separated in its real and imaginary parts and the first-order coupled set of equations is solved by the Tal-Ezer’s technique. The Chebyshev expansion is used to approximate the extrapolate operator exp(A Δt), where A is an anti-symmetrical matrix and the pseudodifferential operator Φ is computed using the Fourier method. Thus, the proposed numerical algorithm can handle any velocity variation. Its implementation is straightforward and if an appropriate number of terms of the series expansion is chosen, the method is unconditionally stable and propagates seismic waves free of numerical dispersion. In our method the number of FFTs is explicitly determined and it is function of the maximum eigenvalue of the matrix A. An numerical example is shown to demonstrate that the proposed method has the capability to extrapolate waves in time using a time step up to Nyquist limit.

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/content/papers/10.3997/2214-4609.20141527
2014-06-16
2024-04-27

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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141527
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Chebyshev Expansion Applied to the One-step Wave Extrapolation Matrix
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141527
/content/papers/10.3997/2214-4609.20141527
/content/papers/10.3997/2214-4609.20141527
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