Full-waveform inversion-using phase encoded all order multiples

Full waveform inversion (FWI) inherently can handle all wave kinds of waves, such as turning wave, primary, and multiples. However, when an initial model is far from the true model, data containing multiples can increase nonlinearity and FWI tends to converge to the local minima of the objective function. Building up an objective function by decomposing multiples into different controlled orders and performing FWI on a pair of multiples of consecutive orders can accelerate the convergence, but we need to perform many FWIs if we want to use all the orders of the multiples. We propose to build virtual source and receiver supergathers for FWI by assembling all phase-encoded controlled-order multiples. Consequently, we can speed up convergence hence increase the computational efficiency by doing just one FWI and mitigatie cycle skipping issues. Crosstalk artifacts because of interference between the different orders of multiples between the source and the receiver supergather can also be reduced by the phase encoding scheme with a random phase shift. Numerical examples demonstrate that FWI using all-order multiples with phase encoding can increase the efficiency of FWI and significantly increase the convergences.