2009/08/24 by Mohammad Motamed, Motamed, Mohammad, Olof Runborg +1
Earth and Planetary Sciences · #65N99 #FOS: Mathematics #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.0908.3416
openalex publication_date 2009/08/24 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The Gaussian beam superposition method is an asymptotic method for computing\nhigh frequency wave fields in smoothly varying inhomogeneous media. In this\npaper we study the accuracy of the Gaussian beam superposition method and\nderive error estimates related to the discretization of the superposition\nintegral and the Taylor expansion of the phase and amplitude off the center of\nthe beam. We show that in the case of odd order beams, the error is smaller\nthan a simple analysis would indicate because of error cancellation effects\nbetween the beams. Since the cancellation happens only when odd order beams are\nused, there is no remarkable gain in using even order beams. Moreover, applying\nthe error estimate to the problem with constant speed of propagation, we show\nthat in this case the local beam width is not a good indicator of accuracy, and\nthere is no direct relation between the error and the beam width. We present\nnumerical examples to verify the error estimates.\n