地震波反演的基本问题分析

Bayes 理论框架下的地震波全波形反演是油气勘探中的导引性技术，其基本思想在去噪音、反褶积、 地震数据规则化、一维波阻抗反演、AVA（叠前）弹性参数反演、叠前偏移成像、速度分析及层析成像中占 据核心位置。但由于观测数据与反演模型参数之间的高度非线性性，导致在实际地震数据处理中地震波 全波形反演（FWI）的难度增大。据此，首先从概率论的观点说明了地震波反演的本质，指出在假设观测噪 音为高斯白噪的情况下，Bayes 估计可以在最小二乘意义下实现；接着分析了数据空间向参数空间映射的 数学物理含义，指出映射的非线性性强弱取决于数据和模型之间的非线性关系，更准确地说取决于介质 模型的复杂性和描述地震波物理传播过程的正算子的复杂性；最后在分析陆上和海上地震数据特点的基 础上，指出了地震波反演走向实用化的策略。通过以上分析，提出：①速度场的反演是利用特征波场的反 演（CWI），而不是全波形的反演；②合理地增加波场的相位信息在泛函中所占的比例；③尽量充分考虑初 始模型的先验信息。只有满足以上3 个条件，才能使地震波全波形反演逐步走向实用化。

Analysis of the basic problems of seismic wave inversion

FWI（FullWaveform Inversion） which is based on the framework ofBayes theory is the leading technology of seismic exploration.The basic idea of FWI is widely used for de-noising,deconvolution,seismic data regularization,1D impedance inversion,AVA elastic parameter inversion,pre-stack migration imaging,velocity analyzing and tomography.Due to the nonlinearity between the observed data and inverse model parameters,there are still a lot of difficulties when FWI is used for field data processing.The essence of FWI was presented under the frame of statistic theory firstly.It was pointed out that Bayes estimation can be implemented with least squares by assuming that the noise satisfies Gaussian distribution.Then the mathematics physics meaning of the mapping from data space to model space is explained.And the nonlinearity of this mapping is decided by the nonlinear relationship between data space and model space,or decided by the complexity of the model parameter and forward operator.At last,the strategy which can push the practical use of FWI was presented after the comparison of the characteristics between land data and marine data.It was believed that：①the velocity inversion should be based on CWI（characteristic waveform inversion）,but not FWI;②the proportion of phase error in error function should be increased legitimately;③the prior information about data space and model space should be considered more adequately.Only by these ways,FWI can be pushed to its practical use.