Reduces FWI Dependence on Long Offsets for Deeper Velocity Model Updates
There has been an increase in activity in recent years to reformulate FWI algorithms to deliver deep velocity model updates in a stable manner without relying on very long offsets. The PGS Full Waveform Inversion (FWI) solution uses diving waves, refractions and reflections together to achieve this without artifacts or cycle skipping problems. This enables better inversions for robust ranking and more reliable derisking of prospects.
Traditional FWI Methods Provide Shallow Velocity Models
Although well established as part of the velocity model building flow, most successful applications of FWI to date have been limited to shallow water environments. This can be attributed to the fact that typical implementations rely heavily on refracted energy or diving waves. Put this together with the offset limitations that exist in seismic data, streamers and nodes alike, it follows naturally that shallow settings lend themselves easiest to being addressed by FWI as they are better sampled by refractions. FWI inverts for the velocity model by solving a nonlinear inverse problem minimizing the difference between modeled data and recorded field data. The matching is quantified by the residuals of a least-squares objective function, and the model update is computed as a scaled representation of its gradient.
Using Reflections to Build High-resolution Velocity Models at Greater Depths
To move beyond the typical limitations outlined above, PGS has reformulated their FWI algorithms to include reflected energy to retrieve long-wavelength updates. The fundamental idea is to compute a gradient in which undesired reflectivity i.e. migration isochrons are eliminated, and the full wavefield can be used in FWI to produce high-resolution velocity models that accurately predict refractions and reflections. This is a key step when using these velocity models for depth migration and imaging.
PGS FWI separates the low from the high wavenumber components in the gradient so that long wavelength velocity updates are delivered at depths greater than the penetration depth of the diving waves. In our implementation of FWI, these improvements to the physics of FWI are complemented by the introduction of new and robust regularizations schemes to stabilize the solution to the inversion step, i.e. improving the mathematics of the implementation.