Seismic Waveform Tomography And Source Parameters Inversion Based On Energy Focusing

Seismic tomography is an essential approach to get an image of the interior of the Earth.By taking advantage of the information carried by the entire seismic wavefield,Full Waveform Inversion(FWI)is able to yield subsurface velocity models with higher resolution compared to seismic traveltime tomography.The traditional FWI evaluates the waveform fitting between the observed and simulated seismograms using the L2norm misfit and inverts for the optimal subsurface velocity models by minimizing it.However,FWI heavily relies on the knowledge of accurate initial models and source information,and could be easily trapped into local minima caused by cycle skipping issue because of its high nonlinearity.These practical issues and challenges make it difficult to be widely used for actual seismic waveforms.To mitigate these issues in FWI,the following efforts have been devoted to modifying the objective functions and obtaining more accurate source information.(1)Based on the energy-focusing principle of back-propagated wavefields,Waveform Energy Focusing Tomography(WEFT)for active seismic sources has been carried out using the acoustic wave equation for isotropic media.Unlike conventional FWI,WEFT utilizes energy focusing around the source instead of waveform fitting at the receivers as the criterion for an accurate model.As it does not aim to fit waveforms and the source location is known for active sources,WEFT does not require other source attributes in advance for the inversion.The estimation of the source wavelet is avoided,as well as errors introduced by it.Moreover,the objective function of WEFT exhibits lower nonlinearity compared to FWI,resulting in less dependence on the initial model and reduced susceptibility to local minima.However,the resolution of the inverted model from WEFT is inevitably lower than that of FWI.This study applied the WEFT method to a 2D seismic profile in the Suqian area and obtained a velocity model with higher resolution along the profile,verifying the applicability of the method through comparison with previous results.(2)A joint inversion method combining energy focusing with waveform fitting criteria has been proposed.To improve the resolution of the inverted model and retain the lower dependence on the initial model of WEFT,the joint inversion objective function is composed of weighted energy and wavewform residuals.By adjusting the weighting,the energy-focusing criterion dominates the inversion when the initial model is poor,which helps FWI to escape from the local minima.When the accuracy of the inverted model reaches a certain level,FWI dominates the inversion and contributes to improving model resolution.This allows for obtaining high-resolution models even with poor initial models.A normalization strategy is then proposed to balance the contributions between energy focusing and waveform fitting more reasonably and further optimize the results.Additionally,the source wavelet is inverted during the joint inversion,avoiding source estimation and making the method more practical.Using the actual field data,the subsurface velocity model of the region is obtained with the joint inversion method,and its advantage is illustrated by comparison with the result from the WEFT.(3)The WEFT method is extended to be applicable to seismic data excited by passive sources.To eliminate the influence of distinct source radiation patterns,the stacking energy of all moment tensor components from back-propagated wavefields around the sources is maximized instead of the back-propagated wavefield to update the velocity models.Thus,the advantages of the method are retained except the rough source locations need to be provided in advance.For the proof of concept,we have validated WEFT using several 2D synthetic tests to show it is less affected by inaccurate source locations and data noise.These advantages render WEFT more applicable for tomography using passive seismic sources when the source information is generally not accurately known.Although the inverted model from WEFT is inevitably influenced by the source distribution as well as its radiation patterns,and has lower resolution than that of FWI,it can act as an intermediate step between seismic traveltime tomography and FWI by providing a more reliable and accurate velocity model for the latter.(4)To obtain a more accurate focal mechanism for passive sources,a new technique called Least-Squares weighted Moment Tensor Inversion based on the timereversal method(LSMTI)has been proposed in this study.The moment tensor can be approximately estimated by time-reversal imaging based on the identity Hessian approximation,which is often not accurate.To better recover the signature of a passive source with a distinct radiation pattern,we recondition the directly recovered seismic source with a Hessian matrix,where Green’s function is approximated with the ray Green’s function.The source location is not required in advance and can be obtained by time-reversal imaging during the inversion.The method has been validated by a series of synthetic tests using the acoustic wave equation,and the influence of rough velocity models,as well as elastic media,has also been discussed.