A Synthetic Study on Full Seismic Waveform Inversion for One Dimensional Velocity Structure

CUI Congyue, WANG Yanbin†

Department of Geophysics, School of Earth and Space Sciences, Peking University, Beijing 100871; † Corresponding author, E-mail: ybwang@pku.edu.cn

Abstract A conjugate gradient full waveform inversion program is coded to verify the effectiveness of full seismic waveform inversion and to study its characteristics. Firstly, a one dimensional inhomogeneous model is inverted using one source and one receiver. Then, by modifying different parameters of the inversion, the factors that affect the inversion result are discussed. It is shown that full waveform inversion can produce accurate result when data is abundant. The number of sources and stations is the primary factor that affect the inversion result. Multiscale inversion and better initial model can significantly improve the stability of the inversion. Noise applied to the observed seismogram can cause small scale disturbance on the result, though large scale characteristics of the result remain more or less unaffected. Key words adjoint method; conjugate gradient method; full waveform inversion

确定地球的内部结构是地球物理领域的重要课题之一。反演问题的非线性特点给计算带来较大的难度, 因此发展出各种基于近似理论的反演方法。其中, 基于地震记录中各个震相的走时进行反演的方法被广泛应用[1], 并取得很大的成功。通过走时得到地球内部不同地震波的速度结构图像, 为地球

[2–5]内部的动力学研究提供了基础 。但是, 基于走时的方法有较明显的局限性: 它所依赖的射线理论只对高频地震波成立, 因此减少了可利用的信息量,也会给识别震相带来误差, 导致结果准确性降低。

随着计算机硬件技术及算法理论的发展, 使用数值方法模拟地震波场变得越来越容易, 使得基于精确求解波动方程而非基于近似理论的反演方法成为可能。全波形反演是一种通过对合成地震图与观测地震图的差别(即目标函数)求极小值, 从而得到介质结构的反演方法。伴随状态法可以用较小的计算量求得目标函数的梯度, 然后使用共轭梯度法等非线性优化算法得到反演结果, 由于利用了完整的波形信息, 通常情况下能够得到比线性化算法分辨率更高的反演结果。Tarantola[6–8]首先提出基于最