Daubechies小波有限元求解GPR波动方程
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Release time:2019-11-22 DOI number:10.6038/cjg20160129 Affiliation of Author(s):中南大学地球科学与信息物理学院 Teaching and Research Group:应用地球物理系 Journal:地球物理学报 Place of Publication:中国 Funded by:41574116，41074085，2015CX008，NCET-12-0551，2014JSJJ001 Key Words:探地雷达；Daubechies小波有限元；自由度凝聚技术；联系系数 波动方程；正演模拟 Abstract:基于可分离小波理论，由一维Daubechies尺度函数的张量积构造二维Daubechies小波基，并将它作为GPR波动方程求解的插值函数，导出了二维Daubechies小波有限元GPR方程离散格式；通过引入转换矩阵，实现小波系数空间与雷达场值之间转换．引入自由度凝聚技术，有效解决了小波有限元求解中小波单元内部自由度过多的问题，节约了计算量并方便与传统有限元法耦合．然后，详细阐述了Daubechies小波有限元联系系数计算方法，有效解决了小波有限元求解偏微分方程的难点与核心问题．最后，以两个典型GPR模型为例，对比了Daubechies小波有限元与传统有限元的雷达正演剖面图与单道波形图，结果表明：在相同的剖分方式及节点数目 条件下，Daubechies小波有限元的紧支性与正交性一定程度上提高了求解效率，它与有限元法求解结果能较好地吻合，验证了Daubechies小波有限元算法的正确性． Co-author:杜华坤, 王珣, 杨炳坤 First Author:冯德山 Indexed by:Applied Research Document Code:DOI：10.6038/cjg20160129 Discipline:地质资源与地质工程 Document Type:J Volume:59 Issue:1 Page Number:342-354 ISSN No.:0001-5733 Translation or Not:no Date of Publication:2016-01-05 Included Journals:SCI -
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