Study Of Full Waveform Inversion Based On Huber Function And L-BFGS Algorithm

Oil and gas resource is currently one of the world’s most important primaryenergy. With the development of the society, Oil and gas exploration has graduallytransferred from shallow to deep. Traditional exploration technology cannot meet withthe demand of resolution in deep underground inversion. Different from the traveltime tomography and migration velocity analysis, full waveform inversion can makefull use of all information in seismic records. Full waveform inversion is a highresolution inversion method, which can reveal detail information of the structure andlithology under complex geological background.The aim of FWI is the reconstruction of physical property parameter usingamplitude and phase obtained by field acquisition.the realization of FWI depends onminimization of residual between observation and resulting field by using nonlinearoptimization algorithm. By updating velocity model, we can achieve the accuratedistribution of velocity.This paper based on the two-dimensional acoustic medium, for the full waveforminversion of large amount of calculation, high memory requirements, and the actualapplication affected by noise and other issues to do the research, and puts forwardsome solutions to solve.The computational time cost and memory requirement of FWI are huge becauseof that the model updating needs numerous iterations and for each iteration, we needto do the wave-equation forward modeling for numerous sources in order to match theobserved seismic data. Random phase encoding technique was used in forwardmodeling combined several different sources into a super-shot in order to reduce thetime required of forward modeling. And this method is effective to suppressthe crosstalk noise.The local optimization algorithm of full waveform inversion is L-BFGS method. L-BFGS algorithm of fast convergence and high accuracy, does not need to storeHessian matrix, only stores few updated vector Hessian matrix.It is limited by many kinds of noises when the method applied to the real seismicdata. Based on Huber function criterion, the objective function combined with theanti-noise of L1norm and the stability of L2norm in theory. We can also get goodresults in the case of the seismic record have noise contained.