oa A Simple Method to Incorporate Correlation Information into the Inversion Process of Full-wave Tomography

Inversion process in the Full-wave tomography (FWT) is delicate for noise. This is because the process cannot distinguish between signal and noise, and hence it works to fit even noise to model. A partial solution of this problem is to take care of the data uncertainty. While Tarantola's probabilistic theory, which is a basis of the standard waveform inversion, advises a formal methodology for this direction, his formula is not easy to realize in the practical calculation. A simplified expression, however, suggests that incorporation of correlation information of medium can be an approximation of the method. To seek a method to manipulate a noisy dataset, I did a numerical study based on the simplified expression. Since one of the efficacies of FWT is its high resolving power, I set up a discontinuous structure to see if it maintains the resolution at the discontinuity. Then I observed effects of random noise and tested a procedure for incorporation of correlation information. Consequently I found, 1) the effect of random noise appears as velocity fluctuation， 2) the incorporation of correlation information is effective, and 3) if appropriate correlation lines and reasonable candidates for correlation length are established, improvement of tomograms with maintaining the resolution can be achieved via an AIC-based method.