Long-wavelength FWI updates in the presence of cycle skipping

Abstract

Full-waveform inversion (FWI) has become the tool of choice for building high-resolution velocity models. Its success depends on producing seamless updates of the short- and long-wavelength model features while avoiding cycle skipping. Classic FWI implementations use the L2 norm to measure the data misfit in combination with a gradient computed by a crosscorrelation imaging condition of the source and residual wavefields. The algorithm risks converging to an inaccurate result if the data lack low frequencies and/or the initial model is far from the true one. Additionally, the model updates may display a reflectivity imprint before the long-wavelength features of the model are fully recovered. We propose a new solution to this fundamental challenge by combining the quadratic form of the Wasserstein distance (W2 norm) for measuring the data misfit with a robust implementation of a velocity gradient. The W2 norm reduces the risk of cycle skipping, whereas the velocity gradient effectively eliminates the reflectivity imprint and emphasizes the long-wavelength model updates. We illustrate the performance of the new solution on a field survey acquired offshore Brazil. We demonstrate how FWI successfully updates the earth model and resolves a high-velocity carbonate section missing from the initial velocity model.

Algorithms in Tomography and Related Inverse Problems—A Review

“…Inversion aims to minimize this misfit using the adjoint-state method, calculating gradients of model parameters [149][150][151]. Yet, challenges like cycle skipping and data volume remain [152][153][154]. FWI algorithms use optimization techniques like L-BFGS but face issues such as local minima and data quality mismatches.…”

Seismic wavefield imaging of Earth’s interior across scales

“…The latter is equivalent to performing an inversion of a wavefield damped in time, partially suppressing dispersive surface waves that are difficult to fit. The cycle-skipping problem 106,117,118 , in which observed and simulated waveforms are misaligned by one cycle or more, renders incorrect misfit measurements and hinders convergence. This issue has motivated reformulations of the inverse problem that are less sensitive to cycle skipping, including adaptive waveform inversion 117 , source-receiver extension 119 , extension through time lag 120 , the use of optimal transport distance 106,121-123 and wavefield-reconstruction inversion 124,125 .…”

Cycle-skipping mitigation using misfit measurements based on differentiable dynamic time warping

“…Other misfit functions, e.g., those based on the optimal transport distance (Engquist et al, 2016;Métivier et al, 2016;Yang et al, 2018;Chen and Peter, 2018a,b;Ramos-Martínez et al, 2019) have also been proposed to mitigate the local minima issue for FWI. The transport plan from Monge or Kantorovich formulation (Chen and Peter, 2018b) can be used as an indicator of traveltime difference.…”