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Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.
Through the Fourier-Bessel series expansion of wave functions, the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced. order to ensure that the analytical solution is valid for higher frequency incident waves, the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves, avoiding the solution of linear equations systems and corresponding numerical issues, which in turn expand the frequency band in which the analytical solution is valid. Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct. Stillrther, the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.