Research On Time-domain Waveform Inversion Based On Multi-level Optimization

With further exploration and development of oil and gas,the detailed description of reservoir has become an important target for seismic exploration and put forward higher requirements for seismic acquisition,processing and interpretation.The estimation of subsurface structures and parameters with the seismograms is a key issue for seismic processing.The most classic data-domain inversion method is full waveform inversion(FWI),which aims to reconstruct the full-wavenumber information of subsurface media parameters by minimizing the misfits between simulated and observed data.With the development of high-performance computing,FWI has become a research hotspot in seismic exploration and has been applied to the real data preliminarily,but the requirement for the real data is very high.Due to the lack of low-frequency information,inaccurate initial model,unknown wavelet and so on,it’s very difficult for FWI with strong nonlinearity to converge to a reasonable inversion result in a real case.We start from the theoretical framework of full waveform inversion(Chapter 2).When the low-frequency information is missing,full waveform inversion usually falls into cycle skipping.We can reconstruct the low-frequency information by a nonlinear transformation.The nonlinearity of the objective function with the low-frequency information will be mitigated,and the dependence of the initial model will be reduced.In the third chapter of the thesis,we firstly introduce the envelope inversion.Then,we propose FWI using a nonlinearly smoothed wavefield,whose objective function is defined with the normalized cross-correlation function.Subsequently,we derive the gradient of the objective function.We also precondition the gradient with a smoothing operator to suppress the high-frequency artifacts and improve the stability of inversion.Based on the concept of multi-scale inversion,we gradually reduce the smoothing width of the low-pass filter in the nonlinearly smoothed wavefield to guarantee the convergence of the inversion.Finally,we demonstrate that the proposed FWI generate convergent results without the need for low-frequency information by numerical examples.The successful application of FWI in real cases depends on first arrivals and diving waves.However,when the aperture is limited(small offset),the penetration of FWI using the first arrivals will be limited to the shallow part,and the deep target area can’t be sensed.Reflection waveform inversion(RWI)can update the parameters of the deep media by back-projecting the residuals along the reflection wavepath.Acoustic RWI is introduced in chapter 4.RWI using traveltime information does not depend on the true-amplitude migration.The reflections can be generated by a migration/demigration process.Therefore,the computational efficiency is high relatively.The difficulty of this method is the estimation of the traveltime misfits,especially for the complex wavefield.Besides,the inversion accuracy is relatively low.RWI based on the optimized imaging takes account of the contributions of the transmition and reflection to the updates of the background model.However,the computational efficiency is low due to the optimized imaging.We can reduce the computational cost by using an approximate Hessian matrix.We demonstrate that the accuracy of RWI based on the optimized imaging is good relatively with the numerical examples on complex models.In chapter 5,we propose elastic RWI with variable density,which provides a better description of the subsurface information than those given by the acoustic assumption.Both the background and the perturbation model are described using the velocity parameterization.The inversion for the perturbations of P-and S-wave velocities and density with the near-offset data is similar to elastic least-squares reverse time migration(LSRTM).An incorrect background model will lead to kinematic-information misfits mainly at the far offsets,which can be utilized to update the background P-and S-wave velocities along the reflection wavepath.We optimize the perturbations and background models in an alternate way.The numerical examples indicate that our elastic RWI with variable density is able to build reasonably good background models for elastic FWI with the absence of low frequencies,and it can deal with the variable density,which is required in real cases.Finally,we develop a multi-level optimization inversion strategy based on the decomposition of the model scale in chapter 5.Based on the content of the previous three chapters,we establish a three-step workflow,which is an important method for the real case.