瞬态瑞雷波反演横波的SVD算法及其应用
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摘要
利用奇异值分解算法对瑞雷波频散曲线进行反演,提高横波速度的反演精度,引入权重矩阵提高数据分辨率,采用自适应修改阻尼因子提高迭代效果并协调分辨率与解的关系。某高速公路软土路基实测资料试算结果表明,用该算法对瞬态瑞雷波频散曲线进行反演,不但具有稳定性好、精度高、分辨能力强的特点,而且能自动分层和反演地层参数,在高速公路软土路基探测等领域中具有广阔的应用前景。
SVD algorithm for inversion of instantaneous Rayleigh wave is proposed in this paper, which improves shear wave precision and resolution by weight matrix, enhances iterative effect and adjusts the relation between resolution and solution by self-adaptation iterative damping factor. The inversion results of field data for some highway soft roadbed indicate that SVD algorithm not only brings good stability, high accuracy and strong resolution, but also automatically inverses shear velocity and thickness. It is proved that SVD is obviously effective and hence shows fairly good application prospects in the soft stratum roadbed detection for highway.
SVD algorithm for inversion of instantaneous Rayleigh wave is proposed in this paper, which improves shear wave precision and resolution by weight matrix, enhances iterative effect and adjusts the relation between resolution and solution by self-adaptation iterative damping factor. The inversion results of field data for some highway soft roadbed indicate that SVD algorithm not only brings good stability, high accuracy and strong resolution, but also automatically inverses shear velocity and thickness. It is proved that SVD is obviously effective and hence shows fairly good application prospects in the soft stratum roadbed detection for highway.
引文
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[13] 宋先海,肖柏勋,黄容容,等.用等厚薄层权重自适应迭代阻尼最小二乘法反演瑞雷波频散曲线[J].物探与化探,2003,27(3):212～216.
[14] SchwabF,KnopoffL.Surfacewavedispersioncomputation.Bull.Seism.Soc.Am.[J],1970,60:321～344.
[15] XiaJ,MillerRD,ParkCB.Estimationofnear-surfaceshearwavevelocitybyinversionofRayleighwave[J].Geophysics,1999,64(3):691～700.
[16] 宋先海.瑞雷波频散曲线的正反演研究[D].武汉:中国地质大学应用地球物理系,2001.
[2] 申秋学.瞬态瑞雷波法在强夯挤淤复合地基检测中的应用[J].地质与勘探,2002(增刊),38(1):132～135.
[3] 童立元,陈征宙,刘定恩.瞬态瑞利面波勘探技术在公路工程勘察中的应用[J].地质与勘探,2000,36(5):73～75.
[4] 刘云祯,王振东.瞬态面波法的数据采集处理系统及应用实例[J].物探与化探,1996,20(1):28～33.
[5] 肖柏勋.工程地球物理学进展[M].武汉:武汉水利电力大学出版社,2000.
[6] 宋先海,肖柏勋,顾汉明,等.反演瞬态瑞雷波频散曲线映射二维横波速度剖面[J].物探化探计算技术,2003,25(2):105～109.
[7] 宋先海,肖柏勋,张学强,等.用瞬态瑞雷波反演横波速度映射二维压折度剖面[J].工程物探,2002,(3):5～9.
[8] 段新胜,顾 湘.用标贯试验锤击数据确定粘性土地基承载力方法探讨[J].地质与勘探,1999,35(4):56～61.
[9] 宋先海,肖柏勋.用瞬态瑞雷波反演横波速度映射二维标准贯入击数剖面[J].岩土工程界,2002,5(10):50～52.
[10] GolubGH,ReinschC.Singularvaluedecompositionandleastsquaresolution[J].Numer.Math,1970,14:403～420.
[11] 胡家富,温一波,谢应齐.利用地震面波频散反演岩石圈结构的奇异值分解算法[J].地球物理学报,1998,211～217.
[12] MarquardtDW.Analgorithmforleastsquaresestimationofnonlinearparameters[J].J.Soc.Indus.Appl.Math.,1963,2:431～441.
[13] 宋先海,肖柏勋,黄容容,等.用等厚薄层权重自适应迭代阻尼最小二乘法反演瑞雷波频散曲线[J].物探与化探,2003,27(3):212～216.
[14] SchwabF,KnopoffL.Surfacewavedispersioncomputation.Bull.Seism.Soc.Am.[J],1970,60:321～344.
[15] XiaJ,MillerRD,ParkCB.Estimationofnear-surfaceshearwavevelocitybyinversionofRayleighwave[J].Geophysics,1999,64(3):691～700.
[16] 宋先海.瑞雷波频散曲线的正反演研究[D].武汉:中国地质大学应用地球物理系,2001.
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