地震层析成像中模型参数化研究进展

Parameterization in seismic tomography

模型参数化是对地震波传播介质的定量化描述,是地震层析成像研究的重要部分.模型参数化的选择会影响层析成像正演计算和反演过程,如射线追踪的速度和精度、正则化过程以及重建模型的几何形态.本文回顾了上世纪70年代以来地震层析成像研究中采用的模型参数化方法,并依据其分辨率模式将参数化方法分为单一尺度参数化方法和多尺度参数化方法两大类.单一尺度参数化方法是指在每一个节点上只有一个尺度的分辨率,一般在空间域构建,包括常速度块方法、速度节点方法和基于常速度梯度的三角网格方法等.多尺度参数化方法是指在每一个节点上具有多个尺度的分辨率,一般在谱域构建,包括傅里叶阶数方法和小波域方法.本文讨论了不同参数化方法的应用条件及优缺点,探讨了不同模型参数化方法对地震层析成像结果的影响(包括结果的分辨率、可靠性及多解性),并展望模型参数化方法的未来发展方向.

Model parameterization is a mathematical representation of the medium in which the seismic waves propagate.It is an important part in seismic tomography,which can largely affect the solution of the forward and inverse problem such as the efficiency and accuracy of ray tracing,the utilization of the information in data and the geometry of the reconstructed model.The aim of this paper is to review the advancement of the model parameterization techniques in seismic tomography since 1970 s,and classify all the model parameterization methods into two big classes（single-scale and multi-scale parameterization）according to their resolution style.The single-scale parameterization method constructs velocity mode in spatial domain,and only has one resolution at each node,which includes constant velocity blocks model,velocity grids model and constant velocity gradient triangular grids model. The multi-scale parameterization method constructs velocity model in spectrum domain,and has multiresolution at each node based on coefficients of different wavelength,which includes Fourier series method and wavelet method.The paper analyzes the advantages and disadvantages of different parameterization methods.Finally,this paper also discusses the influences upon the imaging results（including the resolution,reliability and non-uniqueness of inversion）by choosing different model parameterization methods and the prospects in the future development.