Robust fullwaveform inversion using qstatistics
Abstract
Imaging of the subsurface is central in seismic exploration and a topic of great economic interest. A promising technique for seismic imaging is a waveequationbased method called fullwaveform inversion (FWI). FWI is a datafitting 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 leastsquares distance. In the perspective of likelihood theory, the minimisation of the leastsquares distance assumes a Gaussian distribution of the residual data. In this work, we deal with the qGaussian distribution associated with the Tsallis statistics to construct a robust optimisation problem, which we call qFWI. We tested our method in a typical geophysics velocity model with noisy data. Our results show that qFWI, based on the qstatistics, is a powerful methodology in noisy environments, especially in the presence of outliers. The long tail of the qdistribution exploits the outliers' information, which helps in the image reconstruction. Furthermore, qFWI provides better image reconstruction without additional computational cost compared to the traditional approach of using the Gaussian distribution for the residuals.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 June 2020
 DOI:
 10.1016/j.physa.2020.124473
 Bibcode:
 2020PhyA..54824473D
 Keywords:

 Seismic imaging;
 qGaussian;
 Inverse theory;
 FWI;
 Tsallis entropy