# US 12,181,622 B2 · Simultaneous common-offset migration > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 12,181,622 B2 - Document ID: US12181622B2 - Status: Granted - Kind: B2 - Application number: 17/652,849 - Filed: 2022-02-28 - Published: 2023-08-31 - Granted: 2024-12-31 - Earliest claimed: 2022-02-28 - Assignees: Saudi Arabian Oil Company - Applicants: Saudi Arabian Oil Company - Inventors: Hussain I. Hammad; Ramzy M. Al-Zayer - Web page: https://patentgrep.com/patent/US12181622B2 ## CPC - G01V 1/305: {Travel times} - E21B 41/00: Equipment or details not covered by groups E21B15/00 - E21B40/00 - E21B 43/16: Enhanced recovery methods for obtaining hydrocarbons - G01V 1/282: {Application of seismic models, synthetic seismograms} - G01V 1/301: {for determining seismic cross-sections or geostructures} - G01V 1/303: {for determining velocity profiles or travel times} - G01V 1/362: {Effecting static or dynamic corrections; Stacking} - E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits - G01V 2210/51: Migration - G01V 2210/512: Pre-stack - G01V 2210/614: Synthetically generated data - G01V 2210/6161: Seismic or acoustic, e.g. land or sea measurements - G01V 2210/6222: Velocity; travel time - G01V 2210/66: Subsurface modeling - G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02) - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS ## Abstract A system and method for forming a seismic image of a subterranean region of interest are provided. The method includes obtaining an observed seismic dataset for the subterranean region of interest and determining a plurality of common-offset sections from the observed seismic dataset. The method further includes determining stochastically migrated common-offset sections for each of the common-offset sections and forming a stochastic image gathers from the plurality of stochastically migrated common-offset sections. The method still further includes forming the seismic image by stacking each of the plurality of stochastically migrated common-offset sections. ## Claims ### Claim 1 A method of forming a seismic image of a subterranean region of interest, comprising: obtaining an observed seismic dataset for the subterranean region of interest; determining, using a computer processor, a plurality of common-offset sections from the observed seismic dataset; determining, using the computer processor, from each common-offset section, a stochastically migrated common-offset section; forming a plurality of stochastic image gathers based, at least in part, on the plurality of stochastically migrated common-offset sections; and forming the seismic image based at least in part, on stacking each of the plurality of stochastically migrated common-offset sections. ### Claim 2 (depends on 1) The method of claim 1, wherein determining the stochastically migrated common-offset section from each common-offset section comprises: for each of a plurality of realizations: selecting a subset of traces from the common-offset section; for each member of the subset of traces: determining a stochastic operator; determining a stochastic receiver wavefield based on the stochastic operator and the trace; determining a back-propagated stochastic receiver wavefield; determining a forward-propagated source wavefield based, at least in part, on the stochastic operator; and forming an incremental image based, at least in part, on the back-propagated stochastic receiver wavefield, the forward-propagated source wavefield, and an imaging condition; and determining the stochastically migrated common-offset section based, at least in part, on an accumulation of the incremental images from each realization. ### Claim 3 (depends on 2) The method of claim 2, wherein the stochastic operator applies a random phase shift to each sample of a trace. ### Claim 4 (depends on 2) The method of claim 2, wherein the stochastic operator applies a random phase shift in a frequency domain. ### Claim 5 (depends on 1) The method of claim 1, further comprising: identifying a target within the subterranean region of interest with a likelihood of containing hydrocarbons based, at least in part, on the seismic image. ### Claim 6 (depends on 5) The method of claim 5, further comprising: planning a wellbore path using a wellbore path planning system based, at least in part, on the target; and drilling a wellbore guided by the wellbore path using a drilling system. ### Claim 7 (depends on 1) The method of claim 1, wherein determining each of the plurality of common-offset sections comprises selecting a plurality of common-offset traces each recorded by a source-receiver pair having a source-receiver separation distance within a predetermined range. ### Claim 8 (depends on 1) The method of claim 1, further comprising determining a seismic velocity model based, at least in part, on the plurality of stochastic image gathers. ### Claim 9 A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for: determining a plurality of common-offset sections from an observed seismic dataset; determining, from each common-offset section, a stochastically migrated common-offset section; forming a plurality of stochastic image gathers based, at least in part, on the plurality of stochastically migrated common-offset sections; forming a seismic image based at least in part, on stacking each of the plurality of stochastically migrated common-offset sections; and identifying a target within a subterranean region of interest with a likelihood of containing hydrocarbons based, at least in part, on the seismic image. ### Claim 10 (depends on 9) The non-transitory computer readable medium of claim 9, wherein determining the stochastically migrated common-offset section from each common-offset section comprises: for each of a plurality of realizations: selecting a subset of traces from the common-offset section; for each member of the subset of traces: determining a stochastic operator; determining a stochastic receiver wavefield based on the stochastic operator and the trace; determining a back-propagated stochastic receiver wavefield; determining a forward-propagated source wavefield based, at least in part, on the stochastic operator; and forming an incremental image based, at least in part, on the back-propagated stochastic receiver wavefield, the forward propagated source wavefield, and an imaging condition; and determining the stochastically migrated common-offset section based, at least in part, on an accumulation of the incremental images from each realization. ### Claim 11 (depends on 10) The non-transitory computer readable medium of claim 10, wherein the stochastic operator applies a random phase shift to each sample of a trace. ### Claim 12 (depends on 10) The non-transitory computer readable medium of claim 10, wherein the stochastic operator applies a random phase shift in a frequency domain. ### Claim 13 (depends on 9) The non-transitory computer readable medium of claim 9, wherein determining each of the plurality of common-offset sections comprises selecting a plurality of common-offset traces each recorded by a source-receiver pair having a source-receiver separation distance within a predetermined range. ### Claim 14 (depends on 9) The non-transitory computer readable medium of claim 9, the instructions further comprising functionality for determining a seismic velocity model based, at least in part, on the stochastic common-offset gathers. ### Claim 15 A system, comprising: a seismic acquisition system configured to acquire an observed seismic dataset; and a seismic processor configured to: receive the observed seismic dataset for a subterranean region of interest from the seismic acquisition system; determine a plurality of common-offset sections from the observed seismic dataset; determine, from each common-offset section, a stochastically migrated common-offset section; form a plurality of stochastic image gathers based, at least in part, on the plurality of stochastically migrated common-offset sections; form the seismic image based at least in part, on stacking each of the plurality of stochastically migrated common-offset sections; and identify a target within the subterranean region of interest with a likelihood of containing hydrocarbons based, at least in part, on the seismic image. ### Claim 16 (depends on 15) The system of claim 15, wherein determining the stochastically migrated common-offset section from each common-offset section comprises: for each of a plurality of realizations: selecting a subset of traces from the common-offset section, for each member of the subset of traces: determining a stochastic operator; determining a stochastic receiver wavefield based on the stochastic operator and the trace; determining a back-propagated stochastic receiver wavefield; determining a forward-propagated source wavefield based, at least in part, on the stochastic operator; and forming an incremental image based, at least in part, on the back-propagated stochastic receiver wavefield, the forward propagated source wavefield, and an imaging condition; and determining the stochastically migrated common-offset section based, at least in part, on an accumulation of the incremental images from each realization. ### Claim 17 (depends on 16) The system of claim 16, wherein the stochastic operator applies a random phase shift to each sample of a trace in a frequency domain. ### Claim 18 (depends on 15) The system of claim 15, further comprising: a wellbore path planning system configured to plan a planned wellbore path based, at least in part, on the target; and a drilling system to drill a wellbore guided by the wellbore path. ### Claim 19 (depends on 15) The system of claim 15, wherein determining each of the plurality of common-offset sections comprises selecting a plurality of common-offset traces each recorded by a source-receiver pair having a source-receiver separation distance within a predetermined range. ### Claim 20 (depends on 15) The system of claim 15, wherein the seismic processor is further configured to determine a seismic velocity model based, at least in part, on the at least one stochastic common-offset gathers.