Time-high-order Differential Precision Full Waveform Inversion Based On Huber-MRF Regularization

The full waveform inversion theory can make full use of the kinematics and dynamics information of the seismic wave field contained in the prestack data,and has great potential for high precision imaging and accurate seismic inversion.With the increasing requirements for exploration resolution of oil and gas exploration,full waveform inversion has become a new research hotspot in the field of geophysical exploration.In recent years,it has developed rapidly,especially in the aspect of speed modeling.In order to obtain a stable solution of the full waveform inversion objective function,in addition to using the optimization method for the objective function,the function is also regularized.A good forward modeling is a prerequisite for good inversion results.In this paper,based on the time-high-order differential precision finite-difference forward modeling,the simple layered model and the complex model forward numerical simulation are carried out with the PML perfect matching layer.In the process of inversion,this paper focuses on the full-waveform inversion of Tikhonov regularization,total variation regularization and Huber-Markov regularization constraints.Tikhonov regularization is a regularization method based on L₂ norm.The total variation is based on The regularization method of the L₁ norm has its advantages and disadvantages.Tikhonov regularization can smooth the inversion speed parameters,but weakens the boundary effect and reduces the resolution.The total variation regularization can adapt to the sudden change of the parameters of the underground medium,and can well preserve the boundary of the model.Huber-Markov constraints combine the advantages of two regularization methods with thresholds.The L₂ norm constraint is applied at the inter-layer position to suppress inter-layer interference.At the edge of the layer,the L₁ norm is applied to protect the edge information and enhance the resolution of the thin inter-layer.In this paper,three regularization methods are used to perform full waveform inversion for layered model and complex geological model.The effects of three constraints are compared and analyzed,and the feasibility of Huber-Markov constraint is verified.