True Amplitude Migration Based On Wave Equation

Exploration seismology has been applied for scientific research on the geological history of the earth interior by use of the observed geophysical data. The study of subsurface structure and the inversion of rock properties are the primary aim of exploration seismology. The seismic migration as a key technique of reflection prospecting plays an important role in the theoretical research and application of seismic exploration and has been developed from the original structure imaging to a synthetic system including imaging, velocity analysis and seismic properties estimation.The pre-stack depth migration based on wave theory has an extensive application within the imaging of the complex area. With the increasing demands of seismic exploration by energy industry, the use of imaging amplitude of seismic migration to provide reliable rock parameters and reservoir information for AVO-AVA analysis has become an inevitable trend of the development of seismic exploration technique. As one of forward-looking problems, the theory and method of the true amplitude one-way wave equation pre-stack depth migration has gradually become the emphasis and focus of geophysicists and exploration industry.On the basis of the theory of one-way wave equation pre-stack depth migration, the paper presents the efficient methods of true amplitude one-way wave equation migration which is valuable on theory and application from three parts: the study on physical meaning of one way wave equation, the study of theory and methods on true amplitude one-way wave equation migration and the application of the true amplitude one-way wave equation migration.The study on physical meaning of one way wave equation provides the theoretical basis for the study of the theory and methods on true amplitude one-way wave equation migration. In the paper, the approximation of one-way wave equation which describes the kinetic character in complex medium is discussed and derived in detail with the physical meaning and the amplitude fidelity of each term. The equivalence between the splitting method of scalar wave equation based on the theory of pseudo-differential operators and that based on the theory of scattering perturbation is demonstrated by theoretical derivation. The study on true amplitude one-way wave equation migration includes four parts: the annotation of true amplitude migration, true amplitude one-way wave extrapolation methods, true amplitude reflection coefficient imaging conditions and true amplitude one-way wave equation pre-stack depth migration methods.The paper gives the exact definition of true amplitude migration from the point of view of the influence of the medium on amplitude in which seismic wave propagation, and provides true amplitude one-way wave extrapolation methods which adapted for spherical divergence principle and satisfied with one-way wave energy conservation principle. According to the definition of reflection coefficient, the paper provides the spatial domain imaging condition based on Claerbout imaging principle which applied to the case of single shot record true amplitude pre-stack depth migration and the angular domain imaging condition based on local angle transform principle which applied to the case of common shot gathers true amplitude pre-stack depth migration. On the grounds of above achievements, the paper presents the frequency-wavenumber domain true amplitude one-way wave equation pre-stack depth migration for horizontally layered medium or the medium with slowly varying lateral velocity. As for the lateral velocity variation case, the stable Fourier Finite-Difference one-way wave extrapolation method is proposed to solve the numerical instability. By means of discussing two kinds of true amplitude one-way wave extrapolation strategies, the paper presents the frequency-spatial domain true amplitude one-way wave equation pre-stack depth migration for the case of lateral variation of medium velocity.The trial results for the theoretical model data and the real seismic data confirm the correctness of the theory and the practical algorithms of the true amplitude wave equation migration.