多尺度全波形反演的正则化思想及速度模型的多尺度分解

Regularization Idea of Multi-scale Full Waveform Inversion and Multi-scale Decomposition of Velocity Model

多尺度全波形反演方法是一种重要的全波形反演方法,通过多尺度分解首先求出宏观的速度模型,然后逐渐更新速度模型,使其逼近真实速度模型。文章首先分析了多尺度反演的正则化思想,指出其属于一种正则化方法,然后分析了多尺度全波形反演的实现过程。通过对盐丘速度模型的Curvelet分解,表明Curvelet变换分解的大尺度模型对应于宏观的速度结构,小尺度模型对应于速度的精细构造,因此是一种适合速度模型分解的多尺度变换;通过对大尺度盐丘模型和原始盐丘速度模型的正演,分析炮集的频谱特点,发现在近偏移距大尺度模型正演数据的频谱和原始模型正演数据的频谱类似,在远偏移距原始模型正演数据的低频成分缺失严重,因此可以从近偏移距数据开始反演大尺度模型。

Multi-scale inversion is a branch of full waveform inversion,a macro velocity will be found at first,and then updating it gradually to make it approximate the true velocity model.This paper analyzed the regularization theory of multi-scale inversion at first,and denotes that it is actually a regularization method,and then the realization of multi-scale full waveform inversion was discussed.After the decomposition of SEG-EAGE salt model by using Curvelet transform,the obtained large scale model corresponds to macro structure of velocity model,and the small scale model corresponds to fine structure of the velocity model.Thus,Curvelet transform is a good candidate for velocity decomposition.Comparison of different traces of the modeling results of large scale and the original model indicate that their frequency spectrums are similar at near-offset traces,thus large scale model may be inversed from near-offset data.