Computational and practical developments in single- and multi-component inverse scattering series internal multiple prediction

Jian Sun

Prediction and removal of internal multiples, especially those caused by unknown generators and with insufficient subsurface information, remains a very high priority research problem in seismic data processing. Inverse scattering series internal multiple predictions are data-driven approaches to prediction in which lower-order reflected events are combined nonlinearly according to well-defined ordering relationships in vertical travel time or pseudo-depth. Implementations of instances of this algorithm in any one of the applicable transform domains encounter computational challenges and challenges caused by the practicalities of field data. In this thesis I systematically examine, develop and refine inverse scattering series internal multiple prediction algorithms and their computer implementations, introducing new ideas concerning calculation domain, search parameter optimization, artifact suppression, and computational cost reduction. A key step in my strategy is to formulate the computation in the horizontal slowness, plane-wave, domains, which is possible because of the clear relationship between horizontal slowness and wavenumber. Numerical and analytic arguments indicate that these domains, which tend to involve sparse representations input events (e.g., primary reflections), is able to proceed with a relatively stationary search parameter value, producing predictions with little numerical noise, suppression of some common high-angle prediction artifacts, and, importantly, at significantly lower computational cost. I next formulate multidimensional internal multiple prediction in 2D in the coupled plane wave domain, and examine its numerical behaviour using a benchmark synthetic dataset. In particular I show a detailed input data preparation workflow. The application of the algorithm to common-midpoint (CMP) gathers requires a modified version of the algorithm, and this is also examined. This is important for efficient prediction of internal multiples caused by dipping strata, because the so-called 1.5D formulation, nominally appropriate only for layered media, can be applied with surprising accuracy to CMP gathers over dipping interfaces. I demonstrate and provide a rationale for this observation. The most significant contribution of this thesis is to analyze and numerically implement the fully elastic form of the inverse scattering series internal multiple algorithm. Theory for this has been in existence since the 1990s, but to date neither implementation nor numerical analyses of any kind have been published. Here the ordering of input data events in pseudo-depth/vertical- traveltime and the relationships between these and the actual depths at which reflections took place is key to obtaining accurate multicomponent predictions. After a full analysis, a plane-wave formulation of the elastic multicomponent inverse scattering series internal multiple prediction algorithm is also introduced. Three candidate approaches are considered for input data preparation: pre-stack Stolt migration, vertical traveltime stretching, and incorporation of best-fit reference velocities. With numerical simulations and analysis, I conclude that: (1) best-fit reference velocities produce the best approximate solution obeying the ordering (travel-time monotonicity) requirement, but it requires a relative large search parameter to be chosen in practice; (2) a combination of vertical traveltime stretching and best-fit reference velocities allows the search parameter to be the chosen with a size comparable to those used in acoustic prediction, while correctly predicting all orders of internal multiples. The first numerical examples of multicomponent elastic internal multiple prediction are then presented.