The Wave Equation Adaptive Waveform Inversion Method Research In Time Domain

The full waveform inversion method has become a hotspot in the field of geophysics with the advantages of multi-parameter modeling and high precision.In this method, the simulated wave field obtained by forward modeling is matched with the real wave field. The minimum mean square error of the two is used as the target function, and the global or local optimization method is used to solve the extremum of the objective function.The full-wave method has a high degree of non-linearity in mathematics, and it is more dependent on the initial velocity model when performing inversion.When the difference between the initial velocity model and the real speed model is large, the periodic jump is likely to occur, so that the objective function converges to the local minimum value, resulting in the inversion effect is not ideal or the error occurs.Inversion in this paper, the double objective function can effectively suppress the periodic jump, and the inversion effect is obviously improved.The paper mainly studies the following points:(1) In the forward modeling numerical simulation, the finite difference method is used to discretize the two-dimensional acoustic equation in the time domain, and the high - order finite difference formula of the wave equation is deduced.The optimal matching layer (PML) is introduced to deal with the boundary, and the problems such as numerical dispersion, stability and source are analyzed.(2) Based on the forward modeling principle, adaptive waveform inversion is developed on the basis of full waveform inversion, and a new solution is given for the cycle jump.The proposed filter changes the objective function from a single objective function to a two-objective function. The phase difference between the real data and the analog data is reduced by iteration. By introducing the accompanying source and gradient of the adaptive waveform inversion, the conjugate gradient method is used to invert.After verifying the correctness of the forward modeling, the optimal matching layer is used to deal with the boundary pseudo-reflection problem.In the inversion verification, when the initial model containing some of the underground media information is adopted, the full waveform inversion and the adaptive waveform inversion can achieve better inversion effect.When the initial model is different from the real model , The full waveform inversion effect is not ideal, adaptive waveform inversion can be more accurate inversion of the underground media model.