Seismic Imaing Based On Inversion In Complex Media

With the development of seismic exploration,our exploring target gradually shifts from simple structural reservoirs to complex lithological reservoirs,subtle reservoirs,composite reservoirs or unconventional reservoirs with features of smaller geological scale,increased complexity,high heterogeneity and serious lateral velocity variation.In these complex geological settings,ray-based propagation operator is prone to problems of caustics and shadow zone and its corresponding inverse operator can only extracts travel-time information from seismic reflection waveform data,which limits the precision of seismic imaging and makes the inverse problems unstable.Under the assumption of acoustic constant-density medium,we develop seismic imaging based on inversion(SII)with wave-equation propagation operator using seismic reflection waveform data.The most classic imaging method based on inversion is waveform inversion(WI),which provides the subsurface model with high precision by minimizing the misfit between synthetic and observed data.WI is not applicable in real data processing due to the problem of high dependence on initial model,wavelet estimation,noise and so on.More practical scheme in oil-and-gas industry is decompose subsurface model into two components,that is,high wavenumber(reflectivity)and low wavenumber(background velocity),and then apply migration and velocity analysis to image the reflectivity and background velocity respectively.As the limited precision of conventional migration and velocity analysis methods,the imaging result is insufficient in geological interpretation of lithological reservoirs,so it's urgent to develop high-precision seismic imaging method based on inversion.In order to connect reflectivity imaging and background velocity building under the unified framework of seismic imaging based on inversion,the first chapter defined different types of extended model space and corresponding modeling equations.Based on extended modeling,we proposed the objective function of extended waveform inversion(EWI),which relates with conventional WI and non-linear migration velocity analysis.To decrease the computational cost of EWI,we derive the objective function and gradient formula of linearized extended waveform inversion(LEWI),which also related with reflectivity imaging and migration velocity analysis.The last section of the first chapter provides numerical tests to show the convex property of the LEWI objective function and pseudo-local property of Hessian operator,which is the theoretical basis of the following chapters.Seismic migration is the standard method to image the reflectivity model in the exploration seismology.Compared with one-way wave-equation migration,reverse-time migration(RTM)is more accurate because there is no limitation on propagation angle in two-way wave-equation.However,conventional cross-correlation imaging condition is only the adjoint,not the inverse,of the linearized Born modeling operator,which limites the imaging precision.Least-squares migration(LSM)casts the reflectivity imaging as a least-squares inverse problem,that is,minimizing the linearzed Born modeling data and observed data to retrieve the optimal reflectivity model.After solving the inverse problem using iterative algorithms,LSM provides a more accurate image with higher resolution and more balanced amplitude information,which is more suitable for AVO/AVA analysis and lithological interpretation.Similarly to WI,LSM is also prone to local minimum when the difference between synthetic and observed data is larger than half wavelength due to the inaccuracy of background velocity.In order to solve this problem,we introduce extended reflectivity model and match the linearized extended Born modeling data and observed data.With iterative inversion,the amplitude of extended reflectivity is gradually corrected.As another dimension adds more degree of freedom in the model space,the original over-determined problem changes to under-determined and the solution of the inverse problem becomes ambiguous.To solve this problem,we review different kinds of model regularization and point out that proper regularization operator makes the inversion problem stable and improve the inversion solution.As the computational cost is increased after applying extended imaging condition in RTM,it's very computational demanding in least-squares extended reverse-time migration(LSERTM).In order to improve the efficiency of LSERTM,we proposed several strategies.The first strategy is compressing seismic data by shot encoding technology.With optimized encoding function and regularization operator,the crosstalk will be suppressed dramatically.The second strategy is constructing image-domain objective function to implement target-oriented imaging with much smaller model size.The third strategy is approximating the diagonal Hessian and using it as preconditioner to accelerate the convergent rate.The last strategy is improving the iterative algorithm to make the solution process faster.Even though reflectivity extension helps to match the travel-time difference between synthetic and observed data,the imaging position of physical reflectivity depends on background velocity.When the background velocity is incorrect,LSM will image the reflector at the wrong position.So,the fourth chapter discusses the velocity building problem under the framework of linearized extended waveform inversion.According to different optimal image criterions,we review three types of migration velocity analysis(MVA)objective functions.Compared with other two criterions,differential semblance optimization(DSO)is fully automatic and less dependent on the initial velocity model,so this chapter focuses on this method.We also derive the formula of wave-equation tomography operator,image residual and regularization operator.After then,we propose the idea of image warping to compute the image residual for MVA,which can suppress the gradient artifacts well known in DSO.As the computational cost of wave-equation tomography operator is high,we also review several strategies to improve the efficiency in the fourth chapter.Similar to LSM,shot encoding technology can compress the data size so as to decrease the computational cost of WEMVA.Moreover,we can apply target-oriented velocity building strategy with image-domain encoding technology,which can optimize the acquisition configuration and decrease the data size.Then,we approximate the diagonal Hessian of WEMVA and use it as preconditioner to accelerate the convergent rate of WEMVA.The final chapter draws conclusions about two kinds of seismic imaging based on inversion method,that is,least-sqaures migration and migration velocity analysis.We also give future plan on SII in this chapter.