Depth Migration

Key Takeaways

• Kirchhoff depth migration is the most computationally efficient depth migration algorithm and the most widely used for 3D seismic datasets, operating by summing (stacking) the seismic amplitudes along diffraction traveltime curves calculated for each subsurface image point using the input velocity model — the same principle as Kirchhoff time migration but extended to handle lateral velocity variation by computing traveltimes through the full 3D velocity model rather than using the simplifying assumptions of a vertically varying medium; Kirchhoff depth migration can handle complex acquisition geometries (irregular shot and receiver patterns, marine streamer feathering, ocean bottom cable layouts) and is computationally practical for the multi-billion-trace 3D datasets typical of modern offshore exploration; its limitation is that it does not properly handle multi-pathing (the situation where seismic energy travels from a source to a reflector and back to the receiver via multiple paths of different traveltimes, which occurs beneath complex velocity structures including salt flanks and overturned reflectors), which can leave migration artifacts in the depth image in structurally complex areas.
• Reverse time migration (RTM) is the most accurate depth migration algorithm for complex geology because it propagates the seismic wavefield forward in time from the shot source and backward in time from the receiver, using the full wave equation at each time step to account for all wave propagation effects including multi-pathing, turning waves, and wide-angle reflections that carry information about steep geological structures; the correlation of the forward-propagated source wavefield with the backward-propagated receiver wavefield at each image point produces the reflectivity image, and the accuracy of RTM is limited only by the accuracy of the velocity model rather than by geometric approximations; RTM became the industry standard for sub-salt imaging in the Gulf of Mexico deep water in the 2000s because Kirchhoff migration failed to properly image sub-salt targets where the wavefield propagated through complex salt geometries, and the dramatic improvement in sub-salt image quality from RTM directly enabled the discovery of multiple billion-barrel oil fields (Jack/St. Malo, Tiber, Kaskida) in previously poorly imaged deepwater plays; the computational cost of RTM is 10-100 times greater than Kirchhoff migration, requiring GPU computing clusters or high-performance cloud computing to process 3D datasets of practical size.
• Velocity model building is the critical and iterative step that precedes depth migration because the quality of the depth image is determined entirely by the accuracy of the velocity model used: the standard workflow begins with semblance analysis of common mid-point (CMP) gathers to estimate root-mean-square (RMS) velocity and convert to interval velocity by Dix inversion, provides an initial model that is refined through iterative migration velocity analysis (MVA) or full waveform inversion (FWI); MVA updates the velocity model by examining how well the migrated gathers flatten across offset (well-focused reflections in the correct velocity should produce flat events in the migrated angle or offset domain), and any residual moveout indicates that the velocity model needs adjustment in the corresponding depth interval; FWI is the most data-driven velocity model building method, iteratively minimizing the difference between the recorded seismic data and the synthetic data produced by a wave equation forward model of the current velocity estimate, updating the velocity model to drive convergence to the observed wavefield; FWI requires very long-offset, low-frequency data (below 5 Hz) to resolve the long-wavelength velocity structure without cycle-skipping, and broadband acquisition programs specifically record this low-frequency content to enable FWI-based velocity model building.
• Anisotropic depth migration is required when the seismic velocity of the subsurface rocks varies with the direction of wave propagation, as it does in shale-rich sediments (which have vertical transverse isotropy or VTI symmetry, with slower velocity in the vertical direction than horizontal due to the preferred horizontal orientation of clay minerals), in fractured reservoirs (with horizontal transverse isotropy or HTI symmetry, with faster velocity in the fracture direction), and in tilted sediment layers (with tilted transverse isotropy or TTI); ignoring anisotropy in depth migration causes velocity model errors and reflector mispositioning even when the isotropic velocity model has been carefully calibrated to well data, because the measured P-wave stacking velocity is a function of both the true vertical velocity and the Thomsen anisotropy parameters epsilon and delta that describe the velocity variation with propagation angle; anisotropic depth migration using the Thomsen anisotropy parameters estimated from borehole sonic logs, VSPs, or seismic waveform modeling produces significantly improved image quality and depth accuracy in shale-dominated sections such as the Gulf of Mexico Cenozoic section above deep water salt bodies, where VTI anisotropy of 10-20% is common.
• Well tie validation of depth migration confirms that the depth image is accurately positioned in space by comparing the depths of reflectors in the migrated seismic section to the depths of corresponding geological boundaries (formation tops) picked from well logs at nearby wells: an accurate depth migration should tie the seismic reflectors to the formation tops within the vertical resolution of the seismic data (approximately half the dominant seismic wavelength, typically 10-30 meters in exploration seismic), with any systematic mismatch (the reflectors being consistently deeper or shallower than the well tops) indicating a velocity bias in the migration model; well tie error is quantified as the depth error normalized by the true vertical depth (typically expressed as a percentage), and subsurface exploration and development decisions (drilling target depths, reservoir thickness estimates, volumetric calculations for reserve assessments) require depth tie errors of less than 0.5-1.0% to be fit for purpose; wells drilled to depth-migrated targets are the ultimate validation of depth migration accuracy, and the well-by-well depth error history of a project area is used to calibrate velocity uncertainties and probabilistic depth uncertainty volumes that quantify the risk of missing the geological target in depth.