Study On Seismic Forward Modeling And Least-squares Migration In Complex Media

With the development of oil and gas exploration,the geological structure is becoming more and more complex,which brings great challenges to the seismic exploration.In view of the complexity of geological structure in China,it is necessary to systematically carry out the study on seismic wave propagation and high precision imaging theory for complex media,which can provide more important geophysical basis for oil reservoir identification,description and development.In order to accurately simulate the wave field characteristics in presence of topography,we present a novel finite-difference method.The method is based upon the fully staggered grid combined with body-fitted grid to honor the topography and a mimetic solution for the free-surface condition.This algorithm have three main advantages: First,the using of body-fitted grid to discrete topography,not only eliminates the ladder of discrete problems,but also can adapt to very complex topography.Second,by introducing the fully-staggered grid to curvilinear coordinates,our method can avoid not only the interpolation error when standard staggered grid used but also the high-frequency oscillations with the collocated-grid.Therefore,our method improved the simulation accuracy,and reduced the complexity of the algorithm degrees.Third,we use the mimetic finite-difference which have the same differential accuracy in boundary and internal to implement free boundary conditions in curvilinear coordinates.Thereby our method further improves the simulation accuracy and has a more reliable theoretical basis compared with traction image method.In this thesis,the pseudo-depth idea is introduced into the forward modeling.By using the gradient and divergence formula in curvilinear coordinates,we derived the first-order velocity-stress equation in pesudo-depth domain and implemed the pseudo-depth domain seismic modeling algorithm.Meanwhile,take into account the horizontal sampling is uneven;we introduced the adaptive variable-length spatial operators to calculate the horizontal spatial derivatives and proposed seismic forward modeling method with adaptive variable-length spatial operators in pseudo-depth domain.Compared with the conventional migration method,least-squares reverse time migration(LSRTM)has a lot of advantages,such as higher imaging resolution,amplitude preservation and amplitude balance and so on.Therefore,LSRTM is the focus of current research.However,current LSRTM algorithms are mostly established based on the second-order scalar constant density acoustic wave equation.They ignore the effect of density on the amplitude,so conventional LSRTM which based on the amplitude matching strategy become difficult to obtain a fidelity imaging result in variable density medium.In this thesis,we propose a new LSRTM algorithm based on first order velocity-stress wave equation.First,we derive a first-order linear wave equation,and then the misfit function of first-order equation LSRTM is given based on a L2 norm.Using the adjoint-state method we obtain the adjoint equation.Finally,a theoretical framework of our first-order velocity-stress wave equation LSRTM method is established.In this thesis,several optimization and improvement strategies are studied.First,by introducing the stochastic optimization in phase encoding multi-source LSRTM,it is greatly reduced the amount of computation and improved computational efficiency.And then,by modifying the objective function we propose a mean-residual normalized cross-correlation LSRTM algorithm.Studies have shown that the normalization strategy can weakens the demanding of source wavelet estimation.Thirdly,in order to eliminate the influence of wavelet on LSRTM,we have developed the source-independent LSRTM using convolved wavefields.In addition,the field data often contain a lot of noise.The L2 norm based LSRTM algorithm is very sensitive to noise,especially when the data contains outliers.In this case,the conventional LSRTM result is serious contaminated by noise.Compared to L2 norm,Student's t distribution has better robustness.Therefore,an LSRTM algorithm based on Student's t distribution is proposed to improve the robustness of the algorithm.Finally,in view of the current least-squares reverse time migration mainly for the horizontal surface of the acoustic medium,does not meet the actual underground conditions,we developed the least-squares reverse time migration algorithm under the complex medium.First,based on body-fitted mesh,the undulating surface least-squares reverse time migration algorithm is developed,which can deal with complex topography better.Secondly,the pseudo-depth domain least-squares reverse time migration algorithm is implemented,which solves the problem of imaging under complex structure and reduces the dependence on velocity accuracy.Thirdly,the least-squares reverse time migration is extended to the elastic medium,and the elastic wave least-squares reverse time migration algorithm based on the first order velocity-stress equation is realized,which is more suitable for the underground media.