Various aspects of survey design have a profound impact on how noise appears on the coherent signal of interest, thus impacting conventional inversion methods in complex environments. We propose a multistage physics-driven prior-based processing technique that is versatile and can be used in a wide range of inversion-based processing applications such as source separation and/or interpolation for any acquisition environments (e.g., land, marine, and ocean-bottom nodes). The inversion-based multistage approach progressively builds the coherent signal model while eliminating the aliasing, blending, and background noise in a signal-safe manner. To stabilize the inversion process, we include physics-driven priors in the multiple stage process, which enhances the sparsity of the coherent signal in the transform domain. Results using real data from land and ocean-bottom node surveys validate the potential of the proposed approach to produce optimal processing results while dealing with the common geophysical challenges related to different seismic acquisitions.