Physics-based preconditioned multidimensional deconvolution in the time domain

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Multi-Dimensional Deconvolution is a data-driven method that is at the center of key seismic processing applications - from suppressing multiples to inversion-based imaging. When posed in an interferometric context, it can grant access to overburden-free seismic virtual surveys at a given datum in the subsurface. As such, it constitutes an essential processing operation that achieves multiple imaging objectives simultaneously in redatuming or target-oriented imaging: e.g., suppressing multiples, removing complex overburden effects, and retrieving amplitude consistent image gathers for impedance inversion. Despite its potential, the deconvolution process relies on the solution of an ill-conditioned linear inverse problem sensitive to noise artifacts due to incomplete acquisition, limited sources, and band-limited data. Typically, this inversion is performed in the Fourier domain where the estimation of optimal regularization parameters hinders accurate waveform reconstruction. We reformulate the problem in the time domain - long believed to be computationally intractable - and introduce several physical constraints that naturally drive the inversion towards a reduced set of reliable, stable solutions. This allows to successfully reconstruct the overburden-free reflection response beneath a complex salt body from noise-contaminated data.