Seismic signal can be expressed by nonstationary convolution model (NCM) which integrates acoustic impedance (AI), attenuation factor (AF) and source wavelet (SW) into a single formula. Although it provides attractive potential to invert AI, AF and SW, simultaneously, effective joint inversion algorithm has not been developed because of the extreme instability of this nonlinear inverse problem. In this paper, we propose an alternating optimization scheme to achieve this nonlinear joint inversion. Our algorithm repeatedly alternates among three subproblems corresponding to AI, AF and SW recovery until changes in inverted models become smaller than the user-defined tolerances. Also, when we optimize one parameter, other two parameters are fixed. NCM is an explicit linear formula for AI; therefore, AI recovery is accomplished by linear inversion which is regularized by low-frequency model and isotropy total variation domain sparse constraints. However, NCM is a complicated nonlinear formula for AF. To facilitate the AF inversion, we propose a centroid frequency-based attenuation tomography method whose forward operator and observations are acquired from the time-varying wavelet amplitude spectra which is estimated according to Gabor domain factorization of NCM. SW is decoupled from NCM based on Toeplitz structure constraint, and we obtain an orthogonal wavelet transform domain sparse regularized SW inverse subproblem. Split Bregman technique is adopted to optimize AI and SW inverse subproblems. Numerical test and field data application confirm that the proposed nonstationary seismic inversion algorithm can stably generate accurate estimates of AI, AF and SW, simultaneously.

地震信号可以通过非平稳卷积模型（NCM）表示，该模型将声阻抗（AI），衰减因子（AF）和源小波（SW）集成到一个公式中。尽管它提供了同时反转AI，AF和SW的诱人潜力，但由于此非线性反问题的极度不稳定，因此尚未开发出有效的联合反演算法。在本文中，我们提出了一种交替优化方案来实现这种非线性联合反演。我们的算法在与AI，AF和SW恢复相对应的三个子问题之间反复交替，直到反向模型中的更改变得小于用户定义的公差为止。同样，当我们优化一个参数时，其他两个参数是固定的。NCM是AI的显式线性公式；所以，AI恢复是通过线性反演完成的，线性反演由低频模型和各向同性总变化域稀疏约束进行了正则化。但是，NCM是AF的复杂非线性公式。为了促进AF反演，我们提出了一种基于质心频率的衰减层析成像方法，该方法的前向算子和观测值是根据随时间变化的小波振幅谱获取的，该谱是根据NCM的Gabor域分解估计的。基于Toeplitz结构约束，将SW与NCM解耦，得到正交小波变换域稀疏正则化SW逆子问题。采用Split Bregman技术来优化AI和SW逆子问题。