Frequency-domain Full Waveform Inversion Based On Nearly Analytic Discrete Methods

Full waveform inversion in the frequency domain is one of the hot and difficult spots in geophysical researches.Many computational mathematicians and geophysicists have made a lot of outstanding work.This dissertation proposes to use nearly-analytic discrete(NAD)methods for forwarding modelling in frequency-domain full waveform inversion processes.At first,the frequency-domain wave equations are discretized by forth-order NAD method.The NAD discrete processes and the achievements of Perfectly Matched Layer(PML)absorbing boundary condition are introduced in detail to obtain a large sparse linear algebraic system.The structure properties of this linear system are analysed in detail and solved by a class of inexact rotated block triangular preconditioned Krylov subspace methods.The eigen-properties of the corresponding preconditioned matrices are further developed and numerical experiments are implemented to compare the efficiencies of such preconditioned iteration methods and other two conventional iteration methods.The numerical results show the advantages of the methods introduced in this dissertation,to be more specific,speeding up for at most dozens of times.Then,the wavefield simulations and dispersion analyses are performed in various media to compare the efficiencies of forth-order NAD method and other two classical numerical schemes.Numerical results indicate that frequency domain NAD methods have stronger ability to suppress numerical dispersion.Based on the forth-order NAD method,this dissertation develops numerical schemes to accelerate frequency-domain forward modelling according to two approaches,respectively.One idea is to use more accurate sixth-order NAD method.At first,the construction of numerical stencils is introduced in detail for discretizing frequency-domain wave equations to obtain a linear system and the block structure and expressions of elements of its coefficient matrix are introduced in detail.Then,wave-field simulations and numerical dispersion analysis are performed to compare the efficiency of sixth-order and forth-order NAD methods.Numerical results indicate that sixth-order NAD method is more able to suppress numerical dispersion and can save approximately 25% computing time in forward modelling.The other idea is to develop forth-order NAD method according to optimize the coefficients of numerical stencils to make the condition numbers of the linear system after discretion decrease.Thus,it is easier to solve such linear system and save computing time.According to wave-field simulation,developed NAD methods can save approximately 10% computing time under the premise of keeping the ability to suppress numerical dispersion.Finally,this dissertation presents frequency-domain full waveform inversion algorithm based on NAD methods.The fundamental theory and methods of frequencydomain inversion are introduced and some details of inversion process are described.Then,the inversion processes are performed in two-layer media of different scales and more complicated Marmousi medium.The accurate inversion results are obtained to illustrate the effectiveness of proposed methods.