Abstract
The theory of preconditioned multi-source full waveform inversion (FWI) is presented where many shot gathers are simultaneously back-propagated to form the multi-source gradient of the misfit function. Synthetic tests on the 2D Marmousi data set show that multi-source full waveform inversion using an encoded multi-source deblurring filter as a preconditioner can provide an accurate velocity model at 1/100 the computational cost of conventional FWI.