Research On Full Waveform Inversion Algorithms Based On Sparse Constraints

Full waveform inversion,as an important problem to be solved urgently in seismic exploration,has been puzzling the vast number of scholars.Therefore,it is very important to find a suitable full waveform inversion algorithm to improve the inversion accuracy and efficiency.Firstly,this paper introduces the origin and background significance of the subject,and summarizes the research status of full waveform inversion algorithms by scholars at home and abroad.In order to solve the problem of large amount of computation in full waveform inversion,a strategy of applying Alternating Direction Multiplier Method with parallel strategy to this problem is proposed.Then,by introducing the basic theories of Alternating Direction Multiplier Method 's basic dual ascent method and augmented Lagrange multiplier method,the ADMM to be adopted in this paper is introduced.The definition and common properties of proximity operator are given,and the proximity operator form of the method is deduced.Then,the applicability of the method in seismic full waveform inversion is guaranteed by choosing the target function appropriately,and the specific algorithm flow for the problems studied in this paper is deduced.Then,the velocity inversion of acoustic wave equation in frequency domain is selected as the research object,and the application of ADMM in full waveform inversion is studied.As the basis of inversion,the forward problem is studied in this paper.For the frequency domain wave equation model with absorbing boundary conditions,the difference scheme of the equation is derived.The numerical simulation part verifies the accuracy of the scheme.Finally,in order to detect the feasibility of ADMM in full waveform inversion,an objective function is established to transform it into an optimization problem.Through iterative optimization in two directions,a specific inversion algorithm is given.In the part of numerical simulation,the models of one anomaly body and two anomaly bodies are calculated respectively.By introducing multi-frequency inversion strategy,the inversion of the model is realized.The numerical simulation results show that the proposed algorithm is feasible for the problems studied.