We propose a method of volume estimation based on spherical harmonic coefficients of compensated topography. It shows that volume of compensated topography depends merely on sum of coefficients between compensated topography and windowed constant height. The algorithm shows a simplification of computation and improves efficiency of estimation. Moreover, it demonstrates smaller error than general numerical methods. It can be employed in estimating volume of compensated topography windowed with various shapes. This method provides a good reference for estimation of lunar parameters, especially the elastic thickness over mare basins.

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.