Phase Cross-Correlation Seismic Velocity Modeling for Cycle-Skipping

The patent introduces phase cross-correlation as an intermediary mechanism between observed and simulated seismic traces. Instead of directly inverting waveforms (which causes cycle-skipping), the method uses phase correlation to establish reliable phase relationships first, then uses this information to guide the velocity model updating process. This intermediary approach bridges the gap between noisy direct comparison and accurate velocity estimation.

The patent transforms the inversion problem by changing the parameter space from direct waveform amplitude comparison to phase correlation-based metrics. By reformulating the objective function to use phase cross-correlation coefficients and penalty functions that reward phase consistency, the method changes the optimization landscape to avoid cycle-skipping local minima while maintaining convergence to accurate velocity models.

The patent segments the seismic trace comparison process into distinct components: phase extraction, phase cross-correlation calculation, penalty function evaluation, and velocity model updating. By dividing the complex inversion process into these manageable segments, each can be optimized independently. The phase cross-correlation is computed only for relevant trace pairs, and the penalty function selectively penalizes only the most problematic cycle-skipping cases, reducing overall computational burden.

The patent applies partial action by using phase cross-correlation selectively for trace pairs that are most likely to exhibit cycle-skipping behavior, rather than computing full waveform inversion for all traces. The penalty function is applied with varying weights depending on the specific trace pair characteristics, applying stronger corrections only where needed. This partial application of the complex methodology reduces computational complexity while maintaining alignment accuracy.