A computer-implemented method for inversion of measured geophysical data to determine a physical properties model for a subsurface region, comprising: (a) obtaining a group of two or more encoded gathers of the measured geophysical data, wherein each gather is associated with a single generalized source or, using source-receiver reciprocity, with a single receiver, and wherein each gather is encoded with a different encoding signature selected from a set of non-equivalent encoding signatures; (b) summing the encoded gathers in the group by summing all data records in each gather that correspond to a single receiver (or source if reciprocity is used), and repeating for each different receiver, resulting in a simultaneous encoded gather; (c) assuming a physical properties model of the subsurface region, said model providing values of at least one physical property at locations throughout the subsurface region; (d) calculating an update to the assumed physical properties model that is more consistent with the simultaneous encoded gather from step (b), said calculation involving one or more encoded simultaneous source forward (or reverse) simulation operations that use the assumed physical properties model and encoded source signatures using the same encoding functions used to encode corresponding gathers of measured data, wherein an entire simultaneous encoded gather is simulated in a single simulation operation; (e) repeating step (d) at least one more iteration, using the updated physical properties model from the previous iteration of step (d) as the assumed model to produce a further updated physical properties model of the subsurface region that is more consistent with a corresponding simultaneous encoded gather of measured data, using the same encoding signatures for source signatures in the simulation as were used in forming the corresponding simultaneous encoded gather of measured data; and (f) downloading the further updated physical properties model or saving it to computer storage. (a) obtaining a group of two or more encoded gathers of the measured geophysical data, wherein each gather is associated with a single generalized source or, using source-receiver reciprocity, with a single receiver, and wherein each gather is encoded with a different encoding signature selected from a set of non-equivalent encoding signatures; (b) summing the encoded gathers in the group by summing all data records in each gather that correspond to a single receiver (or source if reciprocity is used), and repeating for each different receiver, resulting in a simultaneous encoded gather; (c) assuming a physical properties model of the subsurface region, said model providing values of at least one physical property at locations throughout the subsurface region; (d) calculating an update to the assumed physical properties model that is more consistent with the simultaneous encoded gather from step (b), said calculation involving one or more encoded simultaneous source forward (or reverse) simulation operations that use the assumed physical properties model and encoded source signatures using the same encoding functions used to encode corresponding gathers of measured data, wherein an entire simultaneous encoded gather is simulated in a single simulation operation; (e) repeating step (d) at least one more iteration, using the updated physical properties model from the previous iteration of step (d) as the assumed model to produce a further updated physical properties model of the subsurface region that is more consistent with a corresponding simultaneous encoded gather of measured data, using the same encoding signatures for source signatures in the simulation as were used in forming the corresponding simultaneous encoded gather of measured data; and (f) downloading the further updated physical properties model or saving it to computer storage.