Research On Methods For Wave Equation Pre-stack Depth Migration And Velocity Model Construction

Based on the reviews on the history, current status and the problems of the waveequation depth migration and migration velocity analysis, in this thesis, a systematicresearch of the theory on the wave equation pre-stack depth migration and velocitymodel construction is carried out by using of the one-way wave equation of waveequation.Firstly, the stable Born approximation of generalized screen propagator, the stablequasi-linear Born approximation of generalized screen propagator and the stableRytov approximation of generalized screen propagator are presented through thetheoretic study on the generalized screen propagator developed in lately years withmeans of scatter theory of wave-field propagation. Secondly, the general formula ofhigh-order of generalized screen propagator is introduced by the use of theapproximation expansion of the operator. Finally, the comparison and review oncharacteristics of three kinds of wave-field propagator widely used at present aregiven, in the research on the methods for wave equation pre-stack depth migration.These wave-field propagators have been tested by theoretic models. The results showthat these propagators are correct and accurate. Based on the study on the wave-fieldpropagators, we present not only the wave equation pre-stack depth migrationalgorithms for shot-receiver domain gathers data and midpoint-offset domain gathersdata, but also the unified algorithm of wave equation pre-stack depth migration forplane-wave gathers data. We also present a generalized synthesis of seismic data andits wave equation pre-stack depth migration algorithm. The analysis of the characters(such as implementation, efficiency of calculation, the adaptability to the lateralvariation of velocity and the supportability to migration velocity analysis) of thesemigration algorithm is given. All these migration algorithms have been tested onMarmousi model data. The results of the tests are very good, which shows that thesemigration algorithms are reliable and practical.In the research of velocity model construction, based on the dependence upon thewave equation pre-stack depth migration, velocity model and its construction, wepresent a two-step method of velocity construction: initialized velocity modelconstruction and wave equation migration velocity analysis. For the initializedvelocity'model construction, we present a plane wave scan stack method that does notneed NMO velocity analysis and NMO correction. With means of the horizontal timeT₀ on stack section and the pre-stack seismic data layer-stripping by wave equationcontinuation, we present a layer-stripping interval velocity analysis approach toinitialized velocity model construction, from which the depth domain interval velocitymodel is obtained. For the migration velocity model-updating, making use of theresidual move-out of common image point gathers on p_s domain, and thecombination of the horizontal depth Z₀ on the stack section of the p_s domain common image point gathers with the wave equation continuation layer-stripping forp_s plane wave gathers data, we present a migration velocity model vertical updatethat not only breaks down the limitations, such as small offset, velocity homogenousin lateral and small dip, but also directly gives the updated interval velocity model indepth domain. This method has been tested with Daqing non-marine fault-controlleddepression model seismic data. The result is satisfied by using the velocity modelobtained from the test, it shows that the two-step method of velocity modelconstruction is practicable.Besides, we make the discussions on the relationships about time migration anddepth migration, the conventional migration presented by Claerbout and the doublefocusing migration presented by Berkhout, and macro-velocity model for migration.Some deep understanding of wave equation pre-stack depth migration and velocitymodel construction is gained.There are six chapters in the thesis. Chapter one is about the review of theimportance, history and existing problems of wave equation pre-stack depth migrationand velocity model construction. Chapter two is about the research on wave-fieldpropagator, including the introduction to the theoretic derivation of the stablegeneralized screen wave-field propagator based on one-way wave equation, andcomparison and the review on the wave-field propagators widely used in waveequation pre-stack depth migration at present. Chapter three is about the research onthe wave equation pre-stack depth migration algorithms, including the introduction tothe algorithms and their characteristic analysis for different pre-stack data andartificial synthesis data. Chapter four is about the velocity model construction,including the introduction to the two-step method of velocity construction for initialvelocity model construction and wave equation migration velocity analysis based onthe dependence upon the wave equation pre-stack depth migration, velocity modeland its construction. Chapter five is about the discussion on wave equation pre-stackdepth migration, including the introduction to the further understanding of waveequation pre-stack depth migration and velocity model construction. Chapter six is theconclusions.The main innovations in the thesis are as followings1) Posing the wave-field propagators with more precision, adaptability to velocitystrong lateral variations and stability, such as stable Born approximation wave-field propagator, stable Rytov approximation wave-field propagator, stable quasi-linear Born approximation wave-field propagator, as well as the general formula ofhigh order generalized screen wave-field propagator.2) Posing the unified algorithm to pre-stack seismic data plane wave migration.3) Posing the generalized synthesis of seismic data and its migration approach.4) Posing the plane wave scan stack approach to pre-stack seismic data.5) Posing the wave equation continuation layer-stripping interval velocity analysismethod, based on the plane wave scan stack.