back-propagation

Back-propagation in seismic processing refers to the mathematical reversal of wavefield propagation through the subsurface, reconstructing where a seismic wave was at an earlier time by applying the wave equation in reverse time using the recorded surface wavefield as the starting condition and the subsurface velocity model as the propagation medium, and this seismic back-propagation concept is the theoretical foundation of reverse-time migration (RTM), the most accurate and computationally intensive seismic imaging algorithm used in the Western Canada Sedimentary Basin to produce interpretable subsurface images beneath the complex thrust-fold structures of the Rocky Mountain Foothills and beneath the laterally varying velocity fields of the deep basin Montney and Duvernay plays where simpler migration algorithms produce defocused or geometrically distorted images. The wave equation that governs seismic back-propagation in isotropic acoustic media is the second-order partial differential equation: (1/v^2)(d^2P/dt^2) = nabla^2 P + S(x,t), where P is the pressure wavefield, v is the P-wave velocity at position x, t is time, and S is the source term; forward propagation solves this equation with t increasing from the shot time to the maximum record time, while back-propagation solves it with t running backward from the maximum record time to zero, using the recorded shot gather at the surface as the boundary condition that injects wavefield energy back into the model at each receiver location; the subsurface image is formed at every point where the forward-propagated source wavefield and the back-propagated receiver wavefield are simultaneously non-zero, an imaging condition called the cross-correlation imaging condition (I(x) = integral over t of P_source(x,t) times P_receiver(x,t) dt) that produces a reflectivity image proportional to the impedance contrast at each subsurface point. In the WCSB context, seismic back-propagation in RTM is specifically valued for three imaging challenges that earlier migration methods (Kirchhoff migration, one-way wave equation migration) cannot adequately address: the steeply dipping thrust-fault structures in the Alberta and British Columbia Foothills where dips exceed 60 to 90 degrees (Kirchhoff migration fails at dips approaching vertical because the stationary-phase approximation breaks down); the complex overburden velocity fields above WCSB Duvernay and Montney reservoirs where reefal carbonates, salt dissolution collapse features, and glacial till create strong lateral velocity variations that defocus conventional migration; and the imaging of pre-salt reflectors below Devonian evaporite sequences in the Peace River area where the high-velocity salt creates shadow zones that require accurate wave-equation propagation to illuminate. Understanding seismic back-propagation mechanics (wave equation finite-difference solution, boundary conditions, imaging condition), the RTM versus Kirchhoff versus one-way wave equation migration performance trade-offs for WCSB imaging targets, the velocity model accuracy requirement that makes or breaks RTM image quality, and the massive computational requirements that limit RTM to areas where improved image quality justifies the cost gives WCSB exploration geophysicists, seismic processing contractors, and reservoir characterization teams the algorithmic foundation to select and evaluate the migration approach appropriate to each WCSB subsurface imaging challenge.

• Reverse-time migration implementation and computational requirements for WCSB 3D seismic: RTM in 3D requires solving the acoustic wave equation on a 3D finite-difference grid at every time step (typically 0.5 to 2 milliseconds) from time zero to the maximum record time (4 to 8 seconds for WCSB Montney and Duvernay targets at 3,000 to 5,000 m depth), then storing the full 4D source wavefield (3D space plus time) for later cross-correlation with the back-propagated receiver wavefield. The storage requirement for the forward wavefield in a typical WCSB 3D RTM program (500 km2 survey area, 6.25 m x 6.25 m receiver grid, 4-second record length, 1 ms time step) is approximately 40 to 80 terabytes per shot gather, requiring either full wavefield storage on high-speed disk (cost-prohibitive for large surveys) or wavefield reconstruction using checkpointing (saving only periodic snapshots and recomputing intermediate times as needed). WCSB RTM processing is performed on GPU computing clusters where the parallel architecture of modern GPUs reduces RTM compute time by 20 to 50 times versus equivalent CPU implementations, making 3D RTM economically feasible for WCSB Foothills and complex Montney surveys that would have been impractical before 2015.
• RTM imaging of thrust-belt structures in the WCSB Alberta Foothills: The Alberta Foothills west of Calgary and Red Deer contains Mesozoic and Paleozoic reservoir targets (Cardium, Nikanassin, Rundle, Banff) beneath complexly deformed thrust-fold structures with dips of 50 to 90 degrees and overturned limbs where reflectors are actually dipping more steeply than vertical. Kirchhoff migration, which approximates the wave equation using a ray-tracing stationary-phase approach, produces artifacts and defocused images when reflector dips exceed 60 degrees because the ray-based approximation fails at steep dip angles. RTM back-propagates the full wave equation without dip limitation and correctly images the steep Foothills thrust surfaces, enabling interpretation of subsurface geometry that guides well placement in Foothills targets where conventional migration produces false or ambiguous structural closures. WCSB Foothills RTM programs typically use pre-stack depth migration (PSDM) with RTM and an iteratively updated tomographic velocity model, with processing costs of $500,000 to $2,000,000 per 3D survey versus $150,000 to $500,000 for Kirchhoff PSDM on the same data.
• Velocity model accuracy as the controlling factor in WCSB RTM image quality: RTM image quality is limited by the accuracy of the velocity model used to propagate the source and receiver wavefields: a velocity model error of 5% at a depth of 4,000 m produces a position error of approximately 200 m in the RTM image, which at WCSB Duvernay tight oil trap scales of 500 to 2,000 m closure dimensions represents a significant fraction of the target size. WCSB RTM velocity model building uses full-waveform inversion (FWI) or reflection tomography to iteratively update the velocity model by minimizing the difference between the observed surface wavefield and the wavefield predicted by the current model, converging on a velocity model accurate enough for RTM to produce a focused image. FWI-derived velocity models for WCSB Montney programs in northeast BC achieve velocity accuracy of 1 to 2% RMS error in the 2,000 to 4,000 m depth range, sufficient for sub-25 m positioning accuracy of structural features at reservoir scale.
• One-way wave equation migration versus RTM for WCSB basin imaging: One-way wave equation migration (also called downward continuation migration or phase-shift migration) propagates the wavefield using a one-way wave equation that allows only downward-traveling waves, missing the backscattered and turning-wave energy that RTM correctly images. For structurally simple WCSB basin targets (flat-lying to gently dipping Cardium, Viking, Mannville at less than 20 degrees dip) where the one-way approximation is valid, one-way wave equation migration produces images of equivalent quality to RTM at 5 to 10 times lower computational cost and is the preferred algorithm for routine WCSB basin seismic processing. RTM is reserved for the subset of WCSB imaging problems where the one-way approximation fails: steep Foothills dips, overturned reflectors, sub-salt imaging, and complex overburden with strong lateral velocity gradients above deep Montney and Duvernay targets where backscattered and refracted energy contributes significantly to the subsurface image.
• Least-squares RTM for amplitude-preserved imaging in WCSB reservoir characterization: Standard RTM produces a reflectivity image whose amplitudes are affected by the irregular illumination of the subsurface from the seismic acquisition geometry (source and receiver spacing, azimuth coverage, acquisition footprint), making amplitude-versus-offset (AVO) analysis and seismic inversion for reservoir properties less reliable. Least-squares RTM (LSRTM) iteratively minimizes the difference between the observed data and the data predicted from the current image, producing a reflectivity image with more uniform illumination compensation and more accurate relative amplitudes than standard RTM. WCSB Duvernay tight oil programs use LSRTM on wide-azimuth 3D seismic data to improve the reliability of AVO gradient analysis for fluid discrimination between oil-saturated and brine-saturated Duvernay reservoir intervals at 3,500 to 4,500 m depth, where the AVO signature difference between oil and brine is 5 to 15% in amplitude, comparable to the illumination artifacts in standard RTM that LSRTM removes.

RTM Imaging Resolving Foothills Thrust Structure for WCSB Nikanassin Gas Exploration

A west-central Alberta Foothills 3D seismic program over a prospective Nikanassin tight gas structure at 4,200 m depth was initially processed with Kirchhoff pre-stack depth migration, which produced a structurally ambiguous image with two competing structural interpretations: a simple anticline with 800 m of closure and a doubly faulted pop-up structure with 400 m of closure. The Kirchhoff PSDM image showed reflector dips up to 72 degrees on the western limb that were at the limits of Kirchhoff imaging fidelity. Reprocessing with RTM using a FWI-updated velocity model reduced the ambiguity significantly: the RTM image resolved the western limb as a thrust-faulted reverse flank with 68 degree dip, confirming the pop-up interpretation with 420 m of closure in the Nikanassin. The operator drilled an appraisal well to the RTM-defined crest, encountered the Nikanassin at the predicted depth within 18 m, and tested 75 MMscf/day on a multi-stage stimulation program, validating the RTM structural interpretation and justifying the $1.4 million additional processing cost over the Kirchhoff baseline.

Related Terms

Back-propagation is the primary entry covering the neural network training algorithm that uses back-propagation of error gradients to update weights; this companion entry covers the entirely separate seismic processing application of back-propagation, where the wave equation is solved in reverse time to reconstruct subsurface wavefields for seismic migration and imaging of WCSB reservoirs. Seismic migration is the processing step in which seismic back-propagation is applied to move recorded reflections from their apparent surface position to their true subsurface position; RTM is the most accurate WCSB migration algorithm because it applies the full two-way wave equation without the dip and velocity-contrast limitations of Kirchhoff or one-way wave equation methods. Velocity model is the 3D distribution of P-wave velocity that controls the accuracy of seismic back-propagation in RTM; WCSB FWI-derived velocity models with 1 to 2% accuracy are the enabling technology that makes RTM images reliable enough for Foothills structural interpretation and Duvernay reservoir characterization. Full-waveform inversion (FWI) is the velocity model building technique that itself uses back-propagation of the data residual to compute velocity gradient updates, linking the seismic and machine-learning senses of back-propagation in a single algorithm that iteratively minimizes the mismatch between observed and modeled WCSB seismic data. Common depth point (CDP) gather sorting is the prerequisite seismic data organization step before RTM, grouping traces by subsurface midpoint location so that the back-propagated receiver wavefields from multiple offset traces illuminate each subsurface point from multiple angles, improving the signal-to-noise ratio of the RTM image and enabling AVO analysis for WCSB reservoir fluid discrimination.