We propose a finite difference algorithm for predicting elastic wave fields in tasks of reverse-time migration, full-waveform inversion, borehole seismology, seismic modelling, and others. The method is based on Summation By Parts (SBP) and Simultaneous Approximation Term (SAT) approaches for generating stable finite-difference schemes and uses forward and backward SBP operators of first derivatives on curvilinear grids. Main distinctions of the method are as follows: up to 12th order of accuracy in interior points and up to 4th order of accuracy on boundaries, second and fourth order of time integration. The algorithm is stable for general type of coordinate transformation. Free surface and far-field boundary conditions for heterogeneous anisotropic media are derived and implemented in form of SAT source terms. All expected properties of the algorithm are validated by numerical tests using corresponding parallel MPI code.


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