| 地震偏移分裂算法的稳定性 |
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| 引用本文： | 马在田.地震偏移分裂算法的稳定性[J].地球物理学报,1985,28(1):101-109. |
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| 作者姓名： | 马在田 |
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| 摘 要： | 本文讨论用分裂算法解高阶偏移方程时所用的有限差分方程与原偏微分方程的相容性和算法的稳定性。根据Lax等价原理,这种相容性和稳定性可以保证数值方程收敛于原偏微分方程。我们证明了该分裂算法满足相容性和稳定性要求。这就不但以文献1]中的实例说明了这种算法的实用性,而且从原理上论证了算法的正确性。
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| 关 键 词： | 分裂算法 地震偏移 偏移方程 稳定性 波场 差分式 二阶差分方程 傅氏系数 地球物理学报 二阶偏微分方程 |
| 收稿时间： | 1983-07-02 |
ON STABILITY OF SPLITTING-UP ALGORITHM FOR SOLUTION OF HIGHER ORDER MIGRATION EQUATION |
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| MA ZAI-TIAN.ON STABILITY OF SPLITTING-UP ALGORITHM FOR SOLUTION OF HIGHER ORDER MIGRATION EQUATION[J].Chinese Journal of Geophysics,1985,28(1):101-109. |
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| Authors: | MA ZAI-TIAN |
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| Abstract: | The compatibility of the difference equation with the partial differential equation and stability of splitting-up algorithm for solution of higher order migration equation are discussed. Lax's equivalence theorem shows that a linear finite-difference equation is compatible with a properly posed linear initial-value problem; then stability guarantees convergence. We have proved that difference equation is compatible with partial differential equation and the algorithm is countably stable in our case.Successful practical examples with application of splitting-up algorithm are shown in （1）; but theoretical proof of the validity of this algorithm is given in the present paper. |
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