A Comparative Study Of Three Optimization Methods In Full Waveform Inversion

With the continuous improvement of exploration requirements,the imaging accuracy of ordinary seismic exploration has been difficult to meet the needs of exploration.Full waveform inversion has been sought after by geophysicists for its potential to depict fine structures.Although full waveform inversion is almost perfect in theory,it is difficult to implement in practice.In this paper,a full waveform inversion method based on acoustic equation is realized.The following parts are discussed in detail in the research process.Firstly,the forward part of full waveform inversion is studied.The staggered grid difference scheme of acoustic equation is deducedd in detail.The advantages and disadvantages of PML absorbing boundary condition and CPML absorbing boundary condition are discussed,as well as the stability and dispersion conditions of staggered grid finite difference.The forward simulation of the simple model and Marmousi model is realized by programming.The simulation results show that the staggered mesh finite difference forward with the 16 order of time in second place space under the condition of stability condition and dispersion has high accuracy.By comparing the absorption effect of CPML absorption boundary condition and PML absorption boundary condition,it can be concluded that the absorption effect of CPML absorption boundary condition is better than that of PML absorption boundary condition.Secondly,the gradient calculation formula based on adjoint state method is deduced in detail,and the selection of iteration step,multi-scale inversion strategy and initial model are discussed.The gradient of the full waveform inversion is obtained by programming,and the effectiveness of the adjoint state method is verified.The inversion results of anomalous volume model and Marmousi model show that the methods and techniques adopted in this paper are feasible.The multi-scale inversion strategy can improve the inversion accuracy.The selection of initial model has a strong influence on the inversion results.In addition,for gradient optimization,the paper deduces the formula of L-BFGS algorithm in detail.Compares the full-waveform inversion results of the steepest descent method,conjugate gradient method and L-BFGS algorithm,it can be clearly concluded that the fullwaveform inversion results based on L-BFGS algorithm have the best effect,the inversion results based on conjugate gradient method take second place,and t The fastest descent method has the worst performance relative to the first two.In view of the difficulty of full waveform inversion programming and the huge computation cost,this paper discusses the application effect of the new generation Fortran language and OpenMP parallel technology in full waveform inversion.The results show that the new generation Fortran language has the advantages of easy programming and easy maintenance,and it is very advantageous to write full waveform inversion codes.OpenMP is used to write full waveform inversion codes.It can reduce computing cost to a great extent.