3-D acoustic modeling by a Hartley method |
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| Authors: | Yang Qi-qiang Lin Chan Zhong Cheng Zhang Shulu Wang Changlong |
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| Institution: | 1. Qiongzhou University, Sanya-572000, China;2. Dalian University of Technology, Dalian-116029, China;3. BGP, CNPC, Beijing-100080, China;1. GIPSA-lab, Image and Signal Department, BP 46, 38402 Saint Martin d''Hères, France;2. Lebanese International University (LIU), Beirut, Lebanon;3. IEMN lab, TELICE group, 59655 Villeneuve d''Ascq, University of Lille, France;1. Computational NeuroEngineering Laboratory, University of Florida, United States;2. Lab. for Biological Information Processing, São Luís, MA, Brazil;1. Beijing Key Laboratory of Work Safety Intelligent Monitoring, Beijing University of Posts and Telecommunications, Beijing 100876, China;2. Beijing Key Laboratory of Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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| Abstract: | Numerical methods using the Hartley transform are described for the simulation of 3-D wave phenomena with application to the modeling of seismic data. Four topics are covered. The first deals with the solution of the 3-D acoustic wave equation. The second handles the solution of the 3-D two way nonreflecting wave equation. The third involves modeling with an areal source. The fourth treats wave phenomena whose direction of propagation is restricted within ± 90° from a given axis.The numerical methods developed here are similar to the Fourier methods. Time stepping is performed with a second-order differencing operator. The difference is that expressions including space derivative terms are computed by the Hartley transforms rather than the Fourier transforms. Being a real-valued function and equivalent to the Fourier transform, the Hartley transform avoids computational redundancies in terms of the number of operations and memory requirements and thus is more efficient and economical than the Fourier transform. These features are crucial when dealing with 3-D seismic data. The numerical results agree with the analytical results. The use of areal source in modeling can efficiently provide data for testing some schemes that deal with the areal shot-records. Using the transform methods, we can impose constraints on the direction of the wave propagation most precisely in the wavenumber domain when attempting to restrict propagation to upward moving waves. The implementation of the methods is demonstrated on numerical examples. |
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