Time Migration

Key Takeaways

• The choice between time migration and depth migration depends on the complexity of the velocity field and the structural goals of the interpretation — time migration is appropriate when velocities vary smoothly laterally and the main velocity gradient is vertical (typical of many sedimentary basins away from major structural complexity); under these conditions, time migration produces an accurate image in which structural geometry is correctly positioned, fault planes are sharply imaged, and the migrated travel time is approximately proportional to true depth; depth migration becomes necessary when significant lateral velocity contrasts exist — beneath salt bodies (where the high-velocity salt creates strong ray bending that time migration cannot correctly handle), in areas with steep fault-related folding, in areas with strong lateral velocity changes from facies transitions or fluid effects, or in areas where pre-drill depth prediction accuracy is critical for well planning; the computational cost of depth migration is typically 5-10 times that of time migration, and it requires a carefully constructed 3D velocity model as input (rather than the simpler RMS velocity field used by time migration), making it a more resource-intensive choice that is justified only when the structural complexity requires it.
• Prestack time migration (PSTM) produces better image quality than poststack time migration and preserves the amplitude information needed for AVO analysis — poststack migration (applied after traces are summed in the stacking process) assumes that all events in the stacked trace behave as if recorded at zero offset, which is an approximation that degrades image quality in areas with complex structure and is inadequate for amplitude-preserved processing; PSTM applies the migration operator to individual offset traces before summation, correctly handling the geometry of each offset's reflection path and producing a migrated gather where the moveout of reflections is consistent with the subsurface velocity structure; these migrated gathers are then used for AVO (amplitude versus offset) analysis to extract lithology and fluid information from the reflection amplitude variation with offset — an analysis that requires correctly imaged, amplitude-preserved gathers that only PSTM (or its depth domain equivalent PSDM) can provide; the shift from poststack migration to PSTM as the default processing flow for exploration-grade 3D seismic in the 1990s was one of the most significant improvements in seismic image quality and enabled the routine application of AVO analysis for direct hydrocarbon indicators that characterizes modern exploration workflows.
• Diffraction collapse is the most visually dramatic evidence that time migration has worked correctly — in an unmigrated seismic section, any abrupt lateral termination of a reflector (a fault tip, a channel edge, a reef flank) creates a diffraction hyperbola — a curved, hyperbolic "bowtie" pattern of seismic energy that spreads laterally across many traces and could be misinterpreted as a lens, a structure, or an artifact by an interpreter unfamiliar with wave physics; after migration, these diffraction hyperbolae collapse to their apex points (the actual location of the diffracting feature), converting a confusing spread of curved events into the sharp, focused image of the feature that generated the diffractions; the effectiveness of migration at collapsing diffractions can be assessed by examining fault terminations, channel edges, or reef boundaries in both unmigrated and migrated versions of the data; properly migrated data shows crisp, sharp terminations at geological boundaries while under-migrated data (migration applied with velocities too slow) shows residual "smiles" (partial hyperbola remnants) and over-migrated data (velocities too fast) shows "frowns" (overcollapsed diffractions where the hyperbola has been pulled too far).
• Migration aperture and maximum dip parameters must be correctly specified to avoid truncation artifacts that degrade fault imaging — time migration algorithms sum seismic energy along hyperbolic paths defined by the velocity field, with the summation aperture (the lateral distance over which energy is gathered) determining the maximum dip of reflectors that can be correctly repositioned; if the migration aperture is too narrow, steeply dipping reflectors and fault plane reflections are not fully migrated, appearing in the migrated image as smeared or truncated; if the aperture is too wide, migration noise (energy from distant parts of the seismic dataset that are incorrectly included in the summation for a given output point) degrades the signal-to-noise ratio; optimizing migration aperture requires knowing the maximum dip expected in the survey area (typically estimated from the pre-migration data or from regional geological knowledge) and specifying an aperture sufficient to capture energy from those maximum dips while limiting migration noise; in areas with very steep faults or overturned limbs (dips exceeding 60-70 degrees), standard time migration may not correctly image the fault planes even with a large aperture, and depth migration with ray bending corrections or reverse time migration (RTM) algorithms may be required.
• Migration velocity analysis is an iterative process that simultaneously improves both the velocity model and the migration image quality — time migration uses a root-mean-square (RMS) velocity field derived from normal moveout (NMO) velocity analysis to define the hyperbolic summation paths for the migration operator; if the migration velocity is incorrect, reflections will not fully collapse and the image will be incorrectly positioned; the quality of the migration can be evaluated by checking whether common reflection point (CRP) gathers (the output gathers at each subsurface location from the PSTM) are flat — indicating that all offsets are imaging the same reflection point with no residual moveout; non-flat CRP gathers indicate velocity error, and the velocity model can be updated iteratively by analyzing the residual moveout in the CRP gathers, updating the RMS velocity field, and re-migrating until the gathers are flat; this tomographic velocity updating loop — migrate, analyze gathers, update velocities, re-migrate — is a standard part of the PSTM processing workflow for exploration-grade data and produces a velocity model that is simultaneously a better input for depth conversion and a more accurate migration operator.