Full Waveform Inversion Technique Based On Envelope Data

Full waveform inversion based on envelope data is a inversion method using the envelope of seismic observation data as input data,One point of full waveform inversion based on envelope data different from conventional full waveform inversion(full waveform inversion directly using seismic observation records)is that the low-frequency information contained in the seismic data can be extracted,and then the large-scale information can be recovered in the inversion model.Since the envelope is derived from the amplitude of the complex seismic trace,the high-frequency signal is amplitude-modulated with the low-frequency signal,so the high frequency information is missing.Therefore,the model retrieved from the envelope data is usually used as the initial model of conventional full waveform inversion.In addition,due to the slow change of the envelope data,the periodic wave skipping problem in full waveform inversion is effectively avoided.In other words,the full waveform inversion based on the envelope avoids the problem that the objective function easily falls into the local minimum,and the final inversion result converges to the correct position.However,the current full waveform inversion research based on envelope data mainly focuses on the extraction of the envelope and the calculation of the gradient of the objective function of the envelope data,but does not discuss the specific implementation techniques in depth.Therefore,starting from the theory of full waveform inversion based on envelope data,this paper firstly reviews the issues of the envelope’s definition,its source,and the calculation of the envelope,and analyzes the information of the extracted envelope data including;Secondly,it discusses in detail the issues such as the calculation of the gradient function and the step size in the objective function and model update based on the envelope data,and finally realized the full waveform inversion based on the envelope data.The numerical test results show that the results based on the ·inversion of envelope data provide a general macroscopic initial model that is close to the real model for the conventional full waveform inversion,effectively overcoming the error functionals encountered in the conventional full waveform inversion.Strong nonlinearity,the objective function easily falls into local minimums and other issues..