In this paper, the order reduced velocity-displacement SH-wave equations in VTI media are ﬁrst proposed. During SH-wave simulation, the spatial derivatives of the new SHwave equations are transformed into wavenumber domain and a staggered-grid Fourier pseudospectral time-domain (PSTD) method is used to obtain discretized forms of these wavenumber operators, which in turn, effectively eliminates the Gibbs phenomenon that arises when Fourier transforming a discontinuous function in heterogeneous media. The order reduced velocity-displacement SH-wave equations also make it possible to set hybrid perfectly matched layers around computational boundaries to mitigate artiﬁcial reﬂections. Finally, this new scheme is applied for waveﬁeld modeling in two-layer heterogeneous media. Comparisons of simulation results with PSTD using second-order SH-wave equation further verify its accuracy.
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