New Methods Research On Wave-equation Forward Modeling & Imaging Under Complex Structure Conditions

Based on former wok, In this paper, we combine the τ-p transform with reflect seismic wave field forward modeling and imaging, deduce a set of efficient and exact formula of forward modeling and imaging. This set of formula is exact even under complex structure conditions, but there is a limitation that the velocity is constant transversely. In order to get a set of formula which fit to velocity varying transversely, we first generalize the Fourier-Difference migration's extrapolation formula presented by Dietrich Ristow to a formula suited not only to niigration but also to forward modeling, and get an efficient and accurate hybrid continuation method. Based on the discussion above, hybrid zero-offset forward modeling method and hybrid pre-stack depth migration with common-shot gathers are deduced, which are efficient and accurate under the conditions of complex structure and lateral velocity varying because of absorbing the stability, accuracy and efficiency for dip steep advantages of Phase-shift extrapolation and the stability, efficiency and ability of processing lateral velocity抯 varying advantages of Finite-difference continuation in frequency domain, furthermore, converted P-SV,S-P and VSP migration methods are also deduced. In order to find a way for doing common-shot forward modeling, we combine geometrical seismic theory and wave seismology and get a set of common-shot forward modeling formulae for P-P, P-SV waves, and VSP. Through the work above, we realize the nature of nonzero offset forward modeling and present Positioning Principlel and Positioning Principle2, or Extrapolating Geophone Principle and Locating Geophone Principle, which are demonstrated by the making of converted S桺 wave抯 common- shot gathers. We also expand Phase-shift plus Finite-difference method to 3D, and get 3D zero offset depth migration and depth forward modeling formulae. Finally velocity problem is discussed. After recalling today's research on reflect tomography, based on the varies criteria of tomography, we combine geometrical ray tracing and wave extrapolation method again, and present hybrid reflection tomography formula.