【作者】 丁科；

【导师】 宋守根；

【作者基本信息】 中南大学 ， 地球探测与信息技术， 2002， 博士

【摘要】 地震数据处理方法中，地震偏移、地震层析成像和波动方程系数反演构成了二十世纪后期研究的主要方向，其中以地震偏移研究地球内部细结构最为成功，地震层析成像和波动方程系数反演取得了很大进展。然而，这些方法存在的一个根本性问题是在进行反演时需要建立一个速度模型，反演结果的好坏在很大程度上依赖于速度模型建立得恰当与否。而地震波的传播速度是地震勘探中一个至关重要的参数，如果已知了传播速度，那就没必要再进行反演了。因此，解决这一根本性的矛盾是现在和以后研究的重大课题。 地震波反演的另一个障碍，主要是所记录的地震波响应中频率信息及相应的振幅真值的不完整与严重缺失。其中高频信息的缺失，直接影响地震波对地层层位识别的分辨率；低频成分的缺失导致重构波阻抗的失败。采集系统特性和技术指标决定了所记录的地震波振幅值为近似的相对振幅，用这样的相对振幅作为地震波参数反演的振幅真值依据，必然导致反演参数值的严重失真。这样使得即使在满足弱散射的条件，运用Born近似反演技术，也仅可以获得界面位置，而得不到反射系数的真值。实际上，从地球物理的实用观点出发，人们特别关心的往往并不是要求恢复全部的物性参数，而是要知道它的间断性及梯度变化较大的状况和位置(即奇性点)。 考虑到上述问题，本文在Bleistein和Cohen等人对Born近似的深入研究基础上，运用地震逆散射理论进行深度成像，反演地层奇性界面的位置。Born近似反演由于只利用了散射序列中的第一项，它只适应于小扰动量的成像，对于大扰动量的成像，它会产生很大的误差。本文提出的反演理论，考虑到散射序列中高阶项对成像结果的影响，在反演时利用逆散射序列中的高阶项以弥补散射场数据的丢失，使得在大扰动量的情况下同样能够实现界面位置和形态的精确成像，解决了大对比度情况下的成像问题。 本文第二章对Born近似反演算法进行了深入研究和分析，指出了Born近似反演存在的问题。Born近似成像对于小扰动量的情况，能够取得较好的结果，但其反演的奇性界面位置，除第一个界面较准确外，其余均与真实位置有一定偏差，并且这种偏差随着界面的反射系数的增加而迅速增大。 本文第三章和第四章，就散射理论和逆散射理论进行了研究。在第三章，首先对散射理论进行了研究，分析了散射序列中各项的物理意义，并推导了一维情况下多层介质的散射场表达式。然后，就一维情况下的逆散射序列奇性反演算法进行了推导，运用摄动法求解逆散射序列，得到了一套理论公式，并用模型数据验证了算法的有效性。在第四章，主要研究了三维情况下的逆散射奇性反演算法。通过2.5维模型数据的检验，证明了算法的有效性。 本文提出的反演理论，主要是基于声波波动方程展开讨论和研究的，其研究方法对于弹性波方程和粘弹性波方程同样适应。更多还原

【Abstract】 In seismic data processing, the main research directions are seismic migration, seismic tomography and wave equation coefficient inversion in late 20th century. In these methods, seismic migration is the most successful to study the subtle structure in the earth. Seismic tomography and wave equation coefficient inversion have greatly improved. But, these methods have a dead problem, i.e., the velocity model is necessary. The inverse results depend on the velocity model. If the model is correct, then the result is credible. Otherwise, the result is false. But the velocity of seismic wave is an important parameter in seismic prospecting. If we obtain the velocity model, it is not necessary to do inversion. So solving the problem is a great subject at present and in the future.The other problem in seismic inversion is that the frequency information and amplitude real value recorded by seismograph are incomplete and severely absent. The absence of high frequency information influences distinguishing location of layer. And the absence of low frequency information leads to fail to reconstruct the wave impedance. Technical parameters and characters of sampling system determine that seismic wave amplitude recorded by seismograph is approximate relative amplitude. Using these data necessarily leads to serious distortion of inverse parameters. So using Born approximation can only obtain the location of interface even if the earth medium is little disturbance. In fact, our aims are not to obtain all parameters, only know the discontinuity or singularity of interface in most case by applied opinion.Considering problem mentioned in above part and founding on Bleistein’s and Cohen’s researches on Born approximation, the author carries out depth imaging inversion by using inverse scattering series for obtaining the singularity locations of layers. Because of taking only advantage of the first item in scattering series, method of Born approximation inversion is only suitable to little disturbance imaging. And it will produce great error in condition of great perturbation. The inversion theory advanced in this paper can also obtain the real location and shape of interface in great perturbation as a result of using the high items in scattering series. It solves the imaging problem in great contrast.In chapter 2, the author deeply studies and analyzes the arithmetic of the method of Born approximation inversion and points out the limitations and disadvantage of the method. The good inverse results can be obtained in little disturbance by Born approximation. But the singularity location inversed by Born approximation inversionis false except the first interface. With reflect coefficients increasing, the error is rapidly enlarged.In chapter 3, the author studies the scattering theory and analyzes the physical meaning of each item in scattering series. At same time, the author deduces the formula of scattering fields in one dimension. Then, the singularity inversion arithmetic of inverse scattering series is deduced in one dimension. Using perturbation method to solve inverse scattering series, the author obtains a set of inverse formula and verifies its validity through model data. In chapter 4, the author studies the singularity inversion arithmetic of inverse scattering series in three dimensions and proves validity of arithmetic through 2.5D theoretic model data.The study in the paper is based on acoustic wave equation, but its research methods are also suitable to elastic and viscoelastic wave equation.更多还原