Wave-equation Reflection Traveltime Inversion

Estimation of an accurate macro velocity model plays animportant role in seismic imaging and model parameter inversion.Full waveform inversion(FWI)is the classical data-domain inversion method.However,FWI needs a good initial model or reliable low frequency component and long offset data.Due to the narrow range of reflection angle aperture,the reflections typically be used to recover short wavelength components.In this paper,the velocity model is decomposed into a lowwavenumber part and a high-wavenumber part.Based on the traveltime inversion and full-waveform inversion,we achieve the low wavenumber components inversion of velocity model using wave-equation reflection traveltime inversion.Traveltime inversion and full-waveform inversion(FWI)are two different methods that geophysicists use to estimate subsurface velocity models from reflection seismic data.Because the traveltime shift,compared to the data difference,is more sensitive and more linearly related to the long-wavelength model perturbation,traveltime inversion better resolves the low-wavenumber background model.Then,conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high wavenumber details.The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.In WERTI,we used dynamic image warping(DIW)to estimate the time shifts between recorded data and synthetic data.When compared with correlation-based techniques often used in traveltime estimation,DIW can avoid cycle skipping and estimate the time shifts accurately,even when shifts vary rapidly.Hence,by minimizing traveltime shifts estimated by dynamic warping,WERTI reduces errors in reflection traveltime inversion.Then we construct the reflected wave paths,the wave paths can accurately describe the propagation of seismic waves in the Earth media.Compared with the traditional ray paths,‘wave paths’ can avoid the phenomena that ray paths will focus on high velocity region and diverge on slow areas.Based on the travel time residual of the reflected wave,the target functional is constructed,and the gradient formula of WERTI is established.Thus,the conjugate gradient waveform inversion process based on MPI is established,and the wave equation travel time inversion is realized.Finally,the numerical examples are used to verify the rationality and effectiveness of the method.Wave equation travel time retrieval method based on reflected wave travel time has successfully updated the lowwavenumber part of velocity model,and improve the FWI results.