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Offshore sensor networks like DONET and S‐NET, providing real‐time estimates of wave height through measurements of pressure changes along the seafloor, are revolutionizing local tsunami early warning. Data assimilation techniques, in particular, optimal interpolation (OI), provide real‐time wavefield reconstructions and forecasts. Here we explore an alternative assimilation method, the ensemble Kalman filter (EnKF), and compare it to OI. The methods are tested on a scenario tsunami in the Cascadia subduction zone, obtained from a 2‐D coupled dynamic earthquake and tsunami simulation. Data assimilation uses a 1‐D linear long‐wave model. We find that EnKF achieves more accurate and stable forecasts than OI, both at the coast and across the entire domain, especially for large station spacing. Although EnKF is more computationally expensive than OI, with development in high‐performance computing, it is a promising candidate for real‐time local tsunami early warning.

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 hyper-parameters, thereby making our solution simple to use. We devise a model-space multi-scale optimization scheme by re-parametrizing the velocity model on spline grids to control the resolution of the model updates. We generate three cycle-skipped 2D synthetic datasets, each containing only one type of wave (transmitted, reflected, 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.

No abstract

Elastic full-waveform inversion (FWI) when successfully applied can provide accurate and high-resolution subsurface parameters. However, its high computational cost prevents the application of this method to large-scale field-data scenarios. To mitigate this limitation, we