一种新的三维速度结构反演模型参数化方法

本文针对三维速度反演问题中的一个重要步骤——模型的参数化作了探讨和研究,提出了一种新的参数化方法.同以往采用的矩形分块或划分网格点的方法不同,将待求扰动场按其空间频率展开,反演各阶频率系数.从三维傅氏级数理论出发,导出了一个简明且便于计算的三维空间频谱展开公式,并从理论上分析了在空间域内离散模型和空间频率域内离散模型的不同之处. 理论分析表明,在空间域内采用过参数化离散模型来反演,会在所得到的解中混入人为的虚假结构,从而使反演解发生畸变.采用在频率域内离散模型的频谱参数化方法反演,可以有效地避免这一点.频谱参数化方法也使得我们可以过参数化（over-parameterization）离散模型,便于最大程度地从资料中提取正确信息,对模型的分辨程度完全取决于观测系统的分辨能力.这种方法在得到稳定的反演解的同时,还可得到观测系统在空间三个方向上的分辨率.数值模拟实验结果证实了以上结论.

A NEW MODEL PARAMETERIZATION METHOD FOR INVERSION OF 3-DIMENSIONAL VELOCITY STRUCTURE

In this paper an important step in the inversion of 3-dimensional velocity structure, the model parameterization, has been discussed and a new parameterization method has been developed. Instead of dividing the model into rectangular blocks, we discretize the model in spatial frequency domain by expanding the perturbation of wave slowness within the area of study into Fourier series and the coefficients of the series can be evaluated by linearized inversion of travel time residuals. A simple form of frequency domain expansion formula, in 3-dimensional space has been derived by using Fourier transformation theory. The difference between discretizing models in the space domain and in the spatial frequency domain is analysed and the advantages of the latter are emphasized.Over-parameterization in space domain will distort the inverted solutions, but this can be effectively avoided by the frequency domain expansion parameterization which discretizes the model in spatial frequency domain. The new parameterization method also makes it possible to over-parameterize the model without limiting the resolving power of the observational system. The final representation includes not only the stable solutions but also the resolving power of the data in earch direction.In order to test the feasibility of the new method, a numerical simulation has been devised. The reulsts confirm the analysis given above.