Simultaneous sourcing during both seismic acquisition and seismic inversion

Method for acquiring, at reduced acquisition cost, seismic data using simultaneous, field-encoded sources in the field (702), and then constructing pseudo source-records (703) that better meet the requirements for using additional simultaneous computer-encoded sourcing for computer simulations or forward modeling (706) as part of (707) iterative FWI (Full Wavefield Inversion) or RTM (Reverse Time Migration), with additional reduction in computational costs. By better meeting the requirements of simultaneous sourcing for FWI or RTM (701), artifacts and crosstalk are reduced in the output. The method can be used for marine streamer acquisition and other non-fixed spread geometries to acquire both positive and negative offsets and to mitigate the "missing data" problem for simultaneous-source FWI. It can also be used for land data to overcome issues with moving spreads and long continuous records.