A Comparative Study Of Several Local Optimization Methods In Full Waveform Inversion

In recent years,with the continuous improvement of exploration accuracy and the continuous development of migration technology,the imaging accuracy of common inversion methods has been difficult to satisfy people's actual needs.Full Waveform Inversion(FWI)is a kind of inversion method that its objective function is two norm of difference between actual data and simulated data.FWI imaging results have the characteristics of high precision and high resolution,so it has been widely concerned by geophysicists.At present,however,there are still many unsolved difficulties in full waveform inversion,such as the multi-solution problem of inversion,the strong nonlinear problem of inversion and the problem of huge calculation amount in the inversion process.Therefore,studying the problem of full waveform inversion still has very important theoretical significance and practical value.In this paper,for the full waveform inversion of the acoustic wave equation,the following aspects of research work are carried out:First of all,the thesis has made a detailed study on the forward modeling of seismic wave which is the basis of full waveform inversion.Starting with the concept of difference approximation,the staggered-grid finite difference scheme for first-order acoustic wave equations is derived in detail.Basing on the acoustic wave equation difference scheme,the stability condition of the finite difference method is derived,and then studying the numerical dispersion of the finite difference with different condition.Discussing the different spatial boundary conditions and the most commonly used CPML boundary conditions are derived in detail.Finally,the model test proves that the eighth-order precision staggered grid finite difference method and CPML boundary conditions can satisfy the requirements of forward modeling.Secondly,the paper discusses the theoretical basis of full waveform inversion in detail.Aiming at the key difficulty of full waveform inversion-obtaining gradient and step size,a detailed introduction is given from the theoretical aspect.The method of obtaining gradient is the adjoint-state method,and gives a specific derivation process in paper.Introducing a variety of method of obtaining steps.The effectiveness of the full waveform inversion and the adjoint-state method is verified by actual programming simulation.Then,the paper discusses three optimization methods in detail.The principle of the steepest descent method and the conjugate gradient method are discussed,and the advantages and disadvantages of both are analyzed by the Rosenbrock function,the L-BFGS algorithm is analyzed and derived in detail,and gives the algorithm flow of the above three methods.Through the actual model test,it can be clearly concluded that the full waveform inversion based on the L-BFGS algorithm is the best,while the inversion based on the steepest descent method is the worst and the conjugate gradient method is mediate.Lastly,in order to reduce the computing time of inversion,the paper introduces a parallel technology with CUDA.Introducing characteristics of CUDA parallel computing from aspects of hardware and software.Finally,the effectiveness and high efficiency of CUDA parallel technology are proved by the actual test results.At the same time,it also gives conditions that CUDA parallel technology can't be used.