Study Of The Efficiency Of Different Objective Functions In Waveform Inversion

Imaging subsurface structure is one of the most important problem in geophysics.Using seismic waves is one of the main ways to obtain information of the interior of the Earth.In seismological studies,only using arrival times or a certain phase will inevitably lose some information.Therefore,we use the whole seismic waveform(including surface wave and body wave)as the object of the inversion,and constantly synthesize the theoretical seismograms to fit the real data.However,how to judge the goodness of the fitting between the real data and theoretical seismograms is a key problem in inversion.In this thesis,we present two different types of objective functions,cross correlation based in the time domain,and wavelet transform based in time-frequency domain to obtain the waveform envelope and phase difference.When we use the cross-correlation based objective function in the time domain,we add the normalized cross-correlation information,the difference of the absolute amplitude and the difference in the objective function.In the process of theoretical testing of waveform inversion,we find that cross correlation based ovjective function between waveforms can effectively find the optimal model during the inversion.However,the depth information of the velocity interfaces are not sensitive to the object functions and the model can be easily trapped in the local minimum.We use the grid search to further investigate the sensitivity of the objective function on model parameters.In the time-frequency domain,we use wavelet transforms to obtain envelope and phase from signal and divide the objective function into the time-frequency envelope fit-goodness(TFPG)and the time-frequency phase fit-goodness(TFEG).We use these two objective functions for theoretical testing of waveform inversion.The results show that the two time-frequency domain-based objective functions can quickly invert the velocities and quality factors(Q)in the model.Then we use these two objective functions for the inversion of the structure of Midwestern United States crust,and compare it with the velocity structure defined from the the waveform modeling method.Using TFEG as the objective function can provide better waveforms fitting than the TFPG,which may be due to the much large amplitude of the surface wave than that of body wave,so the amplitude information in the waveform occupies more weight than the phase information.The TFEG containing the amplitude difference information between the waveforms is more effective than the TFPG which only considers the phase difference information.For the latter studies,velocity model initially fitted to the surface wave,we should increase the weight of TFPG to better use of the body wave information.