Time-lapse nullspace shuttles: VSP vs surface acquisition, shuttling to zero, and sparse monitoring prospects

Kimberly Pike, Kristopher A. Innanen, Scott Keating

Time-lapse nullspace shuttling is a post-inversion optimization method which solves forthe minimum difference between baseline and monitor surveys while preserving the data misfit achieved during full waveform inversion. Time-lapse shuttling provides a consistent time-lapse difference, irrespective of acquisition source effort and time-lapse strategy, for VSP and surface acquisition geometries. However, in a single-source case, VSP acquisition is more robust and less affected by noise in the data than surface acquisition. The size of the baseline and monitor nullspaces, which are measured by the data misfit or objective function value, must be sufficiently reduced prior to time-lapse nullspace shuttling, such that no nullspace overlap exists. In a multi-scale FWI scheme an additional set of refining iterations over the full bandwidth is performed to further reduce data misfit, separating the baseline and monitor nullspaces. The robustness of time-lapse nullspace shuttling is demonstrated using synthetic VSP and surface acquisition scenarios over a plausible CO₂ plume.