Full-waveform inversion by model extension: Theory, design, and optimization

Abstract

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