A numerical investigation of Matched Source Waveform Inversion applied to acoustic transmission data

TL;DR

This paper explores a numerical approach called Matched Source Waveform Inversion (MSWI) that improves seismic model estimation by reducing cycle skipping issues, especially in single-arrival acoustic transmission data, and can enhance full waveform inversion results.

Contribution

The paper introduces a numerical investigation of MSWI, demonstrating its ability to produce reliable models from single-arrival data and its potential to initialize FWI, especially under noisy conditions.

Findings

MSWI provides reasonable model estimates where FWI fails.

MSWI's effectiveness persists with moderate noise levels.

MSWI is not theoretically equivalent to travel-time tomography for multiple arrivals.

Abstract

Iterative inversion of seismic, ultrasonic, and other wave data by local gradient-based optimization of mean-square data prediction error (Full Waveform Inversion or FWI) can fail to converge to useful model estimates if started from an initial model predicting wave arrival times in error by more than half a wavelength (a phenomenon known as cycle skipping). Matched Source Waveform Inversion (MSWI) extends the wave propagation model by a filter that shifts predicted waves to fit observed data. The MSWI objective adds a penalty for deviation of this filter from the identity to the mean-square data misfit . The extension allows the inversion to make large model adjustments while maintaining data fit and so reduces the chances of local optimization iterates stagnating at non-informative model estimates. Theory suggests that MSWI applied to acoustic transmission data with single-arrival wavefronts may produce an estimate of refractive index similar to the result of travel time inversion, but without requiring explicit identification of travel times. Numerical experiments conform to this expectation, in that MSWI applied to single arrival transmission data gives reasonable model estimates in cases where FWI fails. This MSWI model can then be used to jumpstart FWI for further refinement of the model. The addition of moderate amounts of noise (30\%) does not negatively impact MSWI's ability to converge. However, MSWI applied to data with multiple arrivals is no longer theoretically equivalent to travel-time tomography and exhibits the same tendency to cycle-skip as does FWI.