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One-way propagators based on matrix multiplication in arbitrarily lateral varying media with GPU implementation

You, Jiachun, Liu, Zhege, Liu, Jianli, Li, Canping
Computers & geosciences 2019
algorithms, computers, equations, geophysics, image analysis, models
Conventional one-way migration methods have some shortcomings, such as their limitations in imaging large angles. A novel strategy is presented here to solve these issues. The Helmholtz operator of the two-way wave equation is a power of the square root operator of the one-way wave equation. Based on this connectivity, the computation of the square root of the Helmholtz operator based on matrix multiplication and the calculation of a one-way propagator with a Taylor series expansion, is studied. The one-way propagators used in this paper involve complete matrix multiplication, which is a distinct feature of this method and is suitable for parallel implementation. Analysing the values of matrix square roots generated by the classical eigenvalues decomposition method and an algorithm of computing matrix square roots with matrix multiplication, we prove that our algorithm can calculate a stable result, which lays a solid foundation for further study. The impulse response test proves the advantage of our proposed method over conventional one-way migration in describing the wavefield propagation of large angles in a medium with a strong lateral velocity variation. Moreover, we implement GPU and CPU versions of the algorithm and compared their efficiencies. The post-stack migration result of the Salt model and the pre-stack migration result of the Marmousi model further illustrate the superiority of our proposed migration method in imaging the complex and fine-scale structures compared to the conventional one-way migration method. This provides a promising practical application in seismic exploration.