Acoustic Multi-source Waveform Inversion with Deblurring

The theory of preconditioned multi-source waveform inversion is presented where many shot gathers are simultaneously back-propagated to form the multi-source gradient of the misfit function. Synthetic tests on 2D Marmousi model data show that multi-source 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 waveform inversion.