Based on the principle of self-adaptive Simpson integration method, and by incorporating the‘fifth-order’Filon’s integration algorithm [Bull. Seism. Soc. Am. 73(1983) 913], we have proposed a simple and efficient numerical integration method, i.e., the self-adaptive Filon’s integration method (SAFIM), for computing the synthetic seismograms at large epicentral distances. With numerical examples, we have demonstrated that the SAFIM is not only accurate but also very efficient. This new integration method is expected to be very useful in seismology, as well as in computing similar oscillatory integrals in other branches of physics.
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