In this paper, the acoustic full waveform inversion based on the wavelet method is proposed. It allows to determine density and velocity parameters simultaneously in the time domain. The forward problem is solved based on the wavelet method. The numerical schemes for modelling are constructed in detail. The stability condition is derived for the first time. The inversion is an optimization process for minimizing the mismatch between the synthetic data and the observed data. The computational scheme for the gradient of the objective function is constructed based on the matrix analysis technique. The inversion is implemented from low frequency to high frequency successively. Furthermore, the inversion result of current low frequency is served as the initial guess of next high frequency. This hierarchic strategy includes the smaller wavelengths progressively and improves the inversion robustness. Numerical computations for the benchmark Marmousi model demonstrate that the method has good ability to reconstruct media parameters in complex structures.

本文提出了一种基于小波方法的声学全波形反演方法。它允许在时域中同时确定密度和速度参数。基于小波方法解决了前向问题。详细构造了用于建模的数值方案。稳定性条件是首次得出的。反转是用于使合成数据与观测数据之间的不匹配最小化的优化过程。基于矩阵分析技术，构造了目标函数梯度的计算方案。从低频到高频依次进行反转。此外，将当前低频的反演结果用作下一高频的初始猜测。这种分层策略逐步包括较小的波长，并提高了反演的鲁棒性。基准Marmousi模型的数值计算表明，该方法具有在复杂结构中重建介质参数的良好能力。