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.

Ordinary particle swarm optimization PSO fails frequently in estimation of low sensitivity selenophysics parameters. With an adaptive inertia weight and a mutation factor, an admixed particle swarm optimization ADPSO is proposed. It is found that misfit is not reduced as increasing number of particles and probability of mutation. For four-parameter inversion, the best-fitting parameters can be estimated as considering about 400 particles and a low probability (<0.03) of mutation. With employment of gravity filed model GL0990d and altimeter data from LRO, we apply the method into selenophysical parameter inversion on southern highland of the moon. It shows a best-fit between modeled admittance spectral and observed values. Small residual of gravity anomaly verifies success of parameter inversion and validity of the method. The approach can be used in selenophysics research and could provide a reference for large-scale estimation of parameters.

With application of particle swarm optimization to lunar geophysical parameters inversion, problems resulted from limitation of lunar seismic network and/or unsuitability of conventional inversion methods are avoided. Parameters investigated include load ratio, crustal thickness, crustal density, subsurface load depth and lithospheric elastic thickness. It indicates that the approach is able to calculate model parameters best fitting observed ones automatically and simultaneously. It performs better in computational speed. It is therefore quite useful in lunar multi-parameters inversion and can be employed in lunar interior precision structure research.