Abstract: A joint timelapse full waveform inversion (FWI) method for estimating physical properties of a subsurface includes receiving seismic data related to the subsurface, wherein the seismic data includes a baseline dataset dB and a monitor dataset dM, defining an objective function of the FWI method, calculating a baseline gradient gB of the objective function for the baseline dataset dB, and a monitor gradient gM of the objective function for the monitor dataset dM, computing a baseline preconditioner P?B for the baseline dataset dB and a monitor preconditioner P?M for the monitor dataset dM so that each of the baseline preconditioner P?B and the monitor preconditioner P?M reflects similarities and/or differences of geometrical features of the baseline and monitor acquisition surveys, and determining physical properties of the subsurface based on a baseline physical properties update and a monitor physical properties update.

Abstract: A least-square migration, LSM, based method for generating a 4D image of a subsurface, the method including receiving seismic data d related to the subsurface, the seismic data d including a baseline dataset dB and a monitor dataset dM, calculating a baseline filter B and a monitor filter M based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data mB1 and remigrated monitor data mM1 so that the base filter B applied to the remigrated baseline data mB1 equals the monitor filter M applied to the remigrated monitor data mM1, applying the baseline filter B to raw migrated baseline data mB0 and applying the monitor filter M to raw migrated monitor data mM0 to generate LSM baseline data mB and LSM monitor data mM, and generating the 4D image of the subsurface based on the LSM baseline data mB and the LSM monitor data mM.