Full waveform inversion by model extension: theory, design and optimization

We describe a new method, full waveform inversion by model extension (FWIME) that recovers accurate acoustic subsurface velocity models from seismic data, when conventional methods fail. leverage the advantageous convergence properties of wave-equation migration analysis (WEMVA) with accuracy and high-resolution nature (FWI) combining them into robust mathematically-consistent workflow minimal need for user inputs. The novelty FWIME resides in design cost function novel optimization strategy to combine two techniques, making our approach more efficient powerful than applying sequentially. observe mitigates initial low-frequency long-offset which can be challenging acquire. Our objective contains components. First, we modify forward mapping FWI problem adding data-correcting term computed an extended demigration operator, whose goal is ensure phase matching between predicted observed even inaccurate. second component, modified WEMVA function, allows us progressively remove contributions throughout process. coupling components handled variable projection reduces number adjustable hyper-parameters, thereby solution simple use. devise model-space multi-scale scheme re-parametrizing on spline grids control resolution updates. generate three cycle-skipped 2D synthetic datasets, each containing only one type wave (transmitted, reflected, refracted), analyze how successfully solutions same procedure all cases. In paper, apply realistic examples where simultaneously invert modes.