System and method for least-squares migration of time-lapse seismic data

A computing device for generating a 4D image of a subsurface based on a least-square migration, LSM, based method, the computing device comprising:

• an interface for receiving seismic data d related to the subsurface, wherein the seismic data d includes a baseline dataset dB and a monitor dataset dM, with the monitor dataset dMbeing taken later in time then the baseline dataset dB, for the same subsurface;
• and
• a processor connected to the interface and configured to,
• calculate 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;
• apply 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
• generate the 4D image of the subsurface based on the LSM baseline data mB and the LSM monitor data mM.

A least-square migration, LSM, based method for generating an image of a subsurface, the method comprising:

• receiving seismic data d related to the subsurface, wherein the seismic data d includes a baseline dataset dB and a monitor dataset dM, with the monitor dataset dMbeing taken later in time then the baseline dataset dB, for the same subsurface;
• iteratively updating a least square migration baseline data mB and a least square migration monitor data mM based on descent directions of (1) a first baseline residual between baseline migrated seismic data LTBdB of the baseline dataset dB and baseline remigrated seismic data LTBLBmB of the least square migration baseline data mB, and (2) a second monitor residual between monitor migrated seismic data LTMdM of the monitor dataset dMand monitor remigrated seismic data LTMLMmM of the least square migration monitor data mM;
• migrating the seismic data d with the updated least square migration baseline data mB and the updated least square migration monitor data mM;
• and
• generating the 4D image of the subsurface based on the migrated seismic data d with the updated least square migration baseline data mB and the updated least square migration monitor data mM,
• wherein the least square migration baseline data mg and the least square migration monitor data mM are preconditioned with a baseline filter B and a monitor filter M, respectively, which are calculated based on a same common reflectivity r of the subsurface and corresponding remigrated baseline data and remigrated monitor data.