变密度声波方程多参数全波形反演策略

多参数全波形反演中各参数之间的相互耦合增加了反演的非线性程度.通过分析各参数之间的相互影响，提出合理的多参数反演策略是解决该问题的有效途径.本文从变密度声波方程出发，首先研究了密度在速度反演中的重要作用，然后分析了速度对密度反演的影响程度，进而提出了一种有利于速度、密度分步联合反演的策略.第一步，利用给定的初始模型对速度、密度进行同时反演，得到比较可靠的速度反演结果；第二步，利用第一步反演得到的速度和给定的初始密度作为初始模型，继续进行双参数同时反演，这样可以同时得到比较可靠的速度、密度反演结果.为了进一步提高反演精度，将第二步反演得到的速度、密度作为初始模型，再进行下一轮双参数联合反演.二维理论模型实验结果充分说明了本文提出的这种反演策略的有效性.

A multi-parameter full waveform inversion strategy for acoustic media with variable density

Multi-parameter full waveform inversion (FWI) is an ill-posed inverse problem. Different parameters can be more or less coupled as a function of aperture angle, and thus increases the nonlinearity of the inverse problem. Hierarchical inversions of the data components and hierarchical update of the multiple parameters might be viewed as an appropriate approach to reduce such nonlinearity. In this study, we propose a multi-stage multi-parameter FWI strategy that can simultaneously recover the velocity and density in acoustic media. First, the velocity and density are simultaneously inverted, yielding relatively reliable velocity and less accurate density. During the second stage, the recovered velocity in the first stage is used as the initial velocity model. Then, the velocity and density are reconstructed at the same time. Consequently, both the velocity and density are reconstructed well. To further improve the inversion accuracy, we can implement the third stage to simultaneously update the velocity and density, in which we employ the inversion results of the second stage as the initial models. Numerical tests on synthetic data prove the effectiveness of this strategy.