In this study, we introduce a staggered time integrator to solve the first-order linear wave equation accelerated by using the Jacobi-Anger expansion. The numerical schemes which uses the expansion method are refered as the rapid-expansion method (REM) in the context of the exploration geophysics. It is shown that the time integrator using the Jacobi-Anger expansion converges more quickly to the actual solution when combined to the the Fourier pseudospectral method than the finite difference (FD) scheme which uses the Lax-Wendroff expansion. This is because the Jacobi-Anger expansion can effectively represent the sinusoidal function, which in our case is the sine function. Because of this nature, the proposed method can reduce the computational cost by about half of the FD method under the equivalent modeling condition, such as time step length, grid interval and maximum wave propagation speed. Such property is also verified by numerical examples, which demonstrates the practicality of the proposed time integrator.


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