Abstract: We propose a theoretical model of lunar crater to suppress Gibbs phenomenon by introducing a smooth-factor. The model makes crater close to its real morphology of a bowl. Considering revolving symmetry, we model merely its section topography and expand it in Legendre polynomials for simplification. It shows that the smooth-factor smoothes crater's boundary and avoids generation of oscillations in Gibbs phenomenon. For estimation of expansion coefficients, ASY shows advantage of stability than REC, particularly at super-high degrees. It provides a reference for selenophysical parameters estimation, especially for effective elastic thickness over craters.

Key words: crater topography, Legendre polynomial expansion, Gauss-Legendre quadrature, asymptotic expansion