Abstract：We propose in this paper a three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation.First based on the time-domain three-dimensional first-order velocity-stress acoustic wave equation,an adjoint equation of the time-domain three-dimensional first-order velocity-stress acoustic wave equation and a corresponding gradient equation of P-wave velocity are derived with the adjoint-state method based on the perturbation theory.Then the staggered grid finite difference method is adopted to obtain the synthetic forward wavefield and the backward adjoint wavefield in the time domain.After that the gradient of the P-wave velocity is calculated.On this basis,the conjugate gradient method is used to update P-wave velocity model.Finally the 3D full waveform inversion method based on the first-order velocity-stress acoustic wave equation is implemented.Because this method is based on the first-order velocity-stress acoustic wave equation,the staggered grid finite difference method can be easily applied,and the synthetic wavefield and adjoint wavefield are directly and quickly extrapolated based on GPU in the time domain.The feasibility and effectiveness of the proposed method are demonstrated by model tests.
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