Abstract：In this paper,we use the fast marching method (FMM) algorithm to calculate the traveling time field.According to the definition of the function approximation and orthogonal polynomial,we use Chebyshev orthogonal polynomials to approximate the traveltime field so that the error minimizes in the least-square sense.Then the differential function in the Chebyshev interpolation function is directly used to calculate the gradient of the traveling field.And finally the ray path is obtained.Numerical experiments show that the proposed method improves greatly the accuracy and efficiency of ray path calculation.
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