The Study On Scalar Wave Full Waveform Inversion Algorithm In Frequency Domain

Full waveform inversion based on the full wave field numerical simulation of wave equation is a typical local optimization problem of nonlinear iterative inversion.Full waveform inversion attempted to find an earth model that minimized the difference between the synthetic data computed by performing modeling using this earth model and the observed wave field,including the seismic traveltime information,amplitude and phase information,with the higher resolution features.In this paper,starting from the basic theory of the full waveform inversion,we describe the several optimization methods of full waveform inversion,and analyze the advantages and disadvantages of the algorithm,to facilitate our different models according to the different inversion method.Wave equation forward modeling is the basis of the full waveform inversion,and we deduce the finite difference equation of modeling in time domain and frequency domain.Traditional finite difference scheme based on rotating coordinate system can only be applied to the same vertical spatial sample interval and horizontal spatial sample interval.In order to break the limitation,this paper develops a 15-point finite difference scheme based on an average-derivative methods,the numerical modeling test proves that ADM 15-point scheme can obviously suppress numerical dispersion and improve computational efficiency without adding too much calculation.Full waveform inversion(FWI)test also assess that rectangular grid is adjust for large offset FWI,and is generally applied to geologic model.Finally,this paper establishes a framework for the full waveform inversion,and we discuss some problems: such as gradient,optimization of calculated step,and the choice of frequencyand so on.we applied the scalar wave full waveform inversion algorithm to some model testing.We tested the effect of full waveform inversion with sunk model,classic Marmousi model,highlighting the abilities of the full waveform inversion to describe configuration details.The low frequency information has a very important position in the frequency domain waveform inversion,which is mainly macro velocity field to ensure the correctness of the iterative direction.But in the actual data,the low frequency components are generally absent,so this paper uses the complex frequency + frequency inversion method for characterization of long wavelength information.After the model test,this method is effective in the problem of low frequency loss,and ensures the correctness of the inversion results.