Full cross-correlation inversion for quantitative passive imaging with time-harmonic acoustic waves
For geophysical and medical imaging applications, this work provides a passive imaging framework that eliminates the need for controlled sources, but it is an incremental extension of existing correlation-based methods to a full-waveform inversion setting.
This paper develops a full cross-correlation inversion method for quantitative passive imaging using time-harmonic acoustic waves, enabling reconstruction of medium properties from ambient noise without active sources. Numerical experiments in 2D and 3D demonstrate that the method achieves comparable reconstruction quality to active-source inversions.
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.