AI 中文总结
该研究针对被动成像中物理特性定量重建的反问题，聚焦时谐声波传播，利用随机源假设及波动方程一阶公式建立数值框架，通过迭代最小化和伴随状态法进行定量重建，并对比了不同反演方法的数值实验结果。
AI 中文摘要
我们考虑被动成像中物理特性定量重建的反问题，利用环境波场推断介质。数据建模为随机源产生的波的叠加。本文聚焦时谐声波传播，假设激励介质的随机源零均值且空间不相关。在此假设下，两点记录信号互相关的期望值与确定性格林函数和源项协方差相关。采用波动方程的一阶公式处理不同类型波场间的相关性，为所得非线性反问题开发了数值框架。通过迭代最小化方案进行定量重建，利用伴随状态法计算失配泛函的梯度。使用合成数据进行二维和三维数值实验，比较基于互相关期望值的反演与基于有源采集直接波场测量的反演。
英文摘要
We consider the inverse problem for the quantitative reconstruction of physical properties in the context of passive imaging, where ambient wavefields are used to infer a medium. The data are modeled as a superposition of waves generated by stochastic sources. In this work, we focus on time-harmonic acoustic wave propagation and assume that the stochastic sources exciting the medium are zero-mean and spatially uncorrelated. Under these assumptions, the expected value of the cross-correlation between signals recorded at two locations can be related to the deterministic Green's function and the covariance of the source terms. We follow a first-order formulation of the wave equation, which enables the treatment of correlations between different types of wavefields. A numerical framework is developed for the resulting nonlinear inverse problem. The quantitative reconstruction is carried out using an iterative minimization scheme, in which the gradient of the misfit functional is computed via the adjoint-state method. Numerical experiments in two and three dimensions are performed using synthetic data, and inversions based on the expected value of cross-correlations are compared with those relying on direct wavefield measurements from active-source acquisitions.
Comments26 pages, 9 figures
