Robust full-waveform inversion using q-statistics

Imaging of the subsurface is central in seismic exploration and a topic of great economic interest. A promising technique for seismic imaging is a wave-equation-based method called full-waveform inversion (FWI). FWI is a data-fitting technique that minimises the difference between the observed data in the seismic records and the simulated data, which is extracted from the solution of the wave equation. Usually, FWI is formulated as an optimisation problem that minimises the least-squares distance. In the perspective of likelihood theory, the minimisation of the least-squares distance assumes a Gaussian distribution of the residual data. In this work, we deal with the q-Gaussian distribution associated with the Tsallis statistics to construct a robust optimisation problem, which we call q-FWI. We tested our method in a typical geophysics velocity model with noisy data. Our results show that q-FWI, based on the q-statistics, is a powerful methodology in noisy environments, especially in the presence of outliers. The long tail of the q-distribution exploits the outliers’ information, which helps in the image reconstruction. Furthermore, q-FWI provides better image reconstruction without additional computational cost compared to the traditional approach of using the Gaussian distribution for the residuals.