Multi-offset VSP Velocity Analysis And Reverse-time Migration

Vertical seismic profiling (VSP) has been playing a significant role in both the exploring and developing of energy and mineral resources for its advantages. Though widely discussed, it's still a challenge to build a suitable velocity model and use the model to image underground structures in a satisfied way from multi-shot VSP data alone in the presence of anisotropy. Therefore, this thesis tries to study the velocity analysis and reverse-time migration of multi-offset VSP data under the hypothesis of tilted transversely isotropic (TTI) media approximation of the rock velocity, in which some aspects of seismic knowledge, such as the finite difference (FD) solution of quasi-P wave equation, ray tracing for first arrivals and reflections, treveltime inversion for velocity parameters, and reverse-time migration, are included.First briefly reviews some basic theories relevant to propagation of elastic waves in TTI media. Based on FD coefficients for any order derivatives with any even order accuracy computed from a linear system solver, the FD approximation of the quasi-P wave equation with accuracy of two-order in temporal and any even order in spatial domain is built to model synthetic VSP data. Subsequently, by making use of the equivalence of plane waves between TTI and isotropic media, the stability condition and dispersion relation of the FD approximation are presented. And a VSP reverse-time migration scheme based on the FD approximation of quasi-P wave equation and with zero-lag correlation imaging condition is given.An existing interpolation algorithm for first arrival traveltime computation in VTI media is extended to the case of TTI media. According to the first arrival traveltime calculation algorithm and the Fermat principle, the traveltime computing and ray tracing algorithms for reflections in TTI media by a search for minimum traveltime along reflection interfaces are presented.From the group velocity expression for TTI media, this thesis sets up the traveltime expressions for first arrivals and reflections, as well as the partial-derivative formulas of treveltime with respect to velocity parameters (velocity of quasi-P wave in symmetry direction, dip of symmetric axis and two Thomsen parameters) for multi-offset VSP, and uses Gauss-Newton method to implement velocity parameters inversion for TTI media.In combination with traveltime inversion and reflection data migration, the thesis presents an iterative velocity analysis approach. From the initial model, the approach fixes positions of velocity interfaces and uses VSP traveltimes to invert velocity parameters, then implements reverse-time migration by using the inverted results. From the migration results, new interfaces are estimated and a new traveltime inversion is conducted to form an iterative algorithm. At last, the effect of the algorithm is demonstrated by both a set of synthetic and a set of field multi-offset VSP data.