Wave equation migration offset gathers

A tangible, non-transitory, machine-readable media, comprising instructions configured to cause a processor to:

• migrate input data via a pre-stack depth migration technique to generate migrated input data;
• encode the input data via an encoding function as a migration attribute to generate encoded input data having a migration function that is non-monotonic versus an attribute related to the input data, wherein the encoding function is dependent on time and varies with the offset;
• migrate the encoded input data via the pre-stack depth migration technique to generate migrated encoded input data;
• and
• generate an estimated common image gather based upon the migrated input data and the migrated encoded input data;
• and
• generate a seismic image utilizing the estimated common image gather, wherein the seismic image represents hydrocarbons in a subsurface region of Earth or subsurface drilling hazards.

A device, comprising:

• a memory configured to store instructions;
• a processor coupled to the memory and configured to execute the instructions, which cause the device to:
• migrate input data via a pre-stack depth migration technique to generate migrated input data;
• encode the input data via an encoding function as a migration attribute to generate encoded input data having a migration function that is non-monotonic versus an attribute related to the input data, wherein the encoding function is dependent on time and varies with the offset;
• migrate the encoded input data via the pre-stack depth migration technique to generate migrated encoded input data;
• and
• generate an estimated common image gather based upon the migrated input data and the migrated encoded input data;
• and
• generate a seismic image utilizing the estimated common image gather, wherein the seismic image represents hydrocarbons in a subsurface region of Earth or subsurface drilling hazards.