Joint inversion of direct waves, primaries, and multiples for vertical cable seismic data

source/receiver locations. The primary and multiple wavefields are accurately reconstructed based on the reconstructed direct wavefield, and the corresponding reflectivity updates are obtained. The model-domain Hessian matrices consisting of different data are approximated by their diagonal elements to mitigate the nonuniform coverage issue, and the related covariance matrices and data-domain Hessian matrices are defined and approximated, respectively, to alleviate the calculation problem. In addition, the zero-lag correlated wavefields in the gradient are consistent with the actual wavefield propagation process, e.g., a primary wave is generated when the direct wavefield encounters reflectivity, avoiding the crosstalk. Numerical examples for synthetic models and field data illustrate that our method can accurately recover the source/receiver locations and provide high-resolution balanced-amplitude imaging results without evident crosstalk.