Establishment method of initial model for elastic full waveform inversion based on single-frequency energy spectrum in time-frequency domain
Elastic full waveform inversion(EFWI)is a highly ill-conditioned nonlinear process,and its inversion accuracy heavily depends on the accuracy of the initial model of compression wave velocity and shear wave velocity as well as the available low-frequency components in multi-component shot gathers.When the accuracy of the initial model is too low,and the input three-component shot gathers lack effective low-frequency information,the inversion often cannot converge to the global minimum,which leads to inversion failure.The paper studies a method for constructing initial models of EFWI based on single-frequency energy spectrum inversion in time-frequency domain.Firstly,S-transform is used to extract single-frequency energy spectra of different frequencies from shot gathers which lack low-frequency information.The objective function,gradient expression,and accompanying seismic source formula for energy spectrum inversion in time-frequency domain are also derived,and then an elastic single-frequency energy spectrum inversion of multi-component data is achieved.By using the single-frequency energy spectrum inversion results as the initial models for multi-scale EFWI in the mixed domain,a high-precision EFWI of multi-component data is achieved in the absence of low-frequency information.The model testing results show that the method can establish a good initial model of compression wave velocity and shear wave velocity when multi-component seismic data lack low-frequency information,effectively improving the inversion accuracy of EFWI.
elastic full waveform inversionS-transformsingle-frequency energy spectrum inversionlow frequency modelobjective function
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