Nearly Analytic Discrete Methods For 3D Frequency-Domain Full Waveform Inversion

With the development of computer performance,high-precision and high-efficiency algorithms,full waveform inversion(FWI)has become a hotspot in the field of computational geophysics.The full waveform inversion in the frequency domain is one of the most important in the field.FWI in the frequency domain refers to solving the wave equation in the frequency domain to obtain the frequency domain wave field,and performing FWI on the basis of the frequency domain wave field.Most researchers studied frequency-domain FWI in two-dimensional cases,including acoustic wave equations and elastic wave equations.The forward modeling method includes the nearly analytic discrete method and typical finite difference method.The inversion optimization method uses the conjugate gradient method or the quasi-Newton method.It is necessary to carry out research of the nearly analytic discrete methods for 3D frequency-domain full waveform inversion.The nearly analytic discrete(NAD)method is a kind of nite dierence method that have many advantages.In this paper,first we discrete 3D frequency-domain acoustic wave equation with the NAD method and obtain linear system equations.Before discrediting,PML absorbing boundary condition has been introduced into the acoustic wave equation to absorbing wave in boundary and eliminating the influence of reflected wave.In addition,we perform 3D wave-field simulation to show the superiority of the NAD method comparing with typical finite difference methods.On the base of the NAD forward method,we suggest the 3D frequency-domain FWI algorithm and present some inversion experiments like two-layer medium model and complex model–SEG/EAGE 3D Overthrust model.In the experiment of two-layer medium model,we found there had some wrong results of FWI in the place where we putting sources and receivers,so smoothing kernel of 3D gaussian function is introduced to smoothing the gradient.Inversion results of numerical experiments indicate that FWI in frequency domain based on the NAD method works effectively.