One-step Extrapolation Method And Its Application In Reverse Time Migration

RTM (Reverse Time Migration) is a new imaging algorithm developed in seismicexploration in recent years. RTM is based on the two-way wave equation, which hasadvantages of accurate phase, high imaging precision and avoiding lateral variable speedand high-steep dip limitations. However, wavefield extrapolation in RTM requires highcomputational cost, which constrains the application of RTM.Inordertoaddresstheproblem,thispaperfocusesontheexpressionofthepropagatorin the OSE (One-step Extrapolation). By introducing the randomized algorithm, a moreefficientOSEmethod isproposed, whichreducesthecomputationalcostofexpressingthepropagator. The main contributions of this paper are1. theoretical proving the low-rank property of the propagator.2. proposing an OSE method based on the randomized SVD algorithm. By apply-ing the randomized algorithm of SVD to the OSE method, this paper improve theaccuracy of the expression of the propagator and enhance the method’s general ap-plicability.3. puttingforwardaGaussiandampingfactorbasedonPML(PerfectlyMatchedLayer).Compared with common damping factors, the Gaussian damping factor has advan-tages of less boundary reflections and higher SNR (Signal-to-Noise Ratio).Numerical experiments illustrate this paper’s work. On the one hand, the compu-tational cost of the proposed OSE method making use of the propagator’s low-rank isreduced to O(n(s+1)N2logN+N2log(l)+2l2N), in comparison with the originalO(nN4logN), where n is the total of extrapolation steps, s is the ε-rank of the propa-gator, l is a parameter and the problem is assumed two-dimensional. The proposed OSEmethod also maintains the accuracy of the numerical solution, of which the error is lessthan107with ε=105. On the other hand, the Gaussian damping factor has better per-formancethanthecommondampingfactors. Intheexperimentsofhomogeneousmedium,the maximum amplitude of the boundary reflections is attenuated to less than104. Andin the multi-layer model experiment, the SNR of the single shot record obtained with theGaussian damping factor always be higher than that of others.