XWI: FWI beyond conventional limits

AWI-RWI-FWI Multi-Cost Function Inversion Sequence

Key Questions

• How far away from the true answer can we start?
• How do we update the deep macro model directly from raw data?
• How do we robustly account for unmodeled physics whilst fitting kinematics?

Data Fitting Feedback Loop

FWI Outputs:

• Velocity
• Reflectivity
• AVA

Inherent Challenges with Conventional FWI:

• Local minima from distant starting models AWI
• Weak macro model updates below diving waves RWI
• Amplitude mismatch from strong contrasts, multiples separation

Advantages:

• Search for best-fit model
• Combine distance measures
• Start far away
• No ultra-low frequencies
• No windowing/masking of traces
• Treat primaries and multiples separately in cost function

Stage 1 - AWI (Adaptive Waveform Inversion) + TV Constraints

• Convexification - cycle skip mitigation without local time/phase differences
• Matching filter cost function which minimizes distance from ideal filter
• Corrects errors in heterogeneous overburden
• Spatial derivative TV constraints to homogenize salt

Stage 2 - RWI (Reflective Waveform Inversion)

• Kernel separation - long wavelength updates along reflection wavepaths from raw data
• DTW cost function minimizing residual moveout
• Corrects errors in deeper background model trend

Stage 3 - True Amplitude Least-Squares FWI

• Spatial resolution to half wavelength
• MSE cost function
• Recovers de-ghosted and multiple-free reflectivity

RWI Schematic

• Perturb full wavefield twice to obtain RWI gradient
• 4 wavefields - correlate along reflection wavepaths
• Update from reflector up

Models: F vs A-R-F

• Synthetic streamer configuration
• RWI gives smooth, macro model updates below the diving waves