When the internal density of a celestial body changes,the surface gravity potential also changes accordingly,resulting in corresponding gravity anomalies around the celestial body.Gravity anomalies reflect the nonuniform distribution of internal density of celestial bodies and are commonly used for the inversion of internal structure.Given that the internal density of most celestial bodies is non-uniformly distributed,it is crucial to design a fast method for calculating the gravity anomaly of such bodies in practical work.Traditional methods estimate the gravity potential of a celestial body directly through numerical integration,which is time-consuming,inefficient,and costly,making it unsuitable for fast and large-scale inversion estimation of gravity potential.Based on the spherical harmonics of the generalized Fourier transform,which possess orthogonality among different orders,they are commonly used to expand physical quantities related to celestial body surfaces in spherical harmonics.The non-uniform density of different structural layers inside celestial bodies can also be expanded into spherical harmonics using the generalized Fourier transform.The estimated gravity potential can then be efficiently calculated using the sampling theory of the Fourier transform,thereby improving computational efficiency.With these considerations in mind,this thesis mainly carries out research in the following two areas:(1)Based on the variable density body,the spherical harmonic function was used to study the gravity potential formula generated by variable density.It was found that the gravity potential generated by the variable density body between two interface layers can be expanded by the density spherical harmonic expansion coefficients,and is related to the radius between the two interface layers.To verify the rationality of the algorithm,a variable density body with a certain density distribution was designed.Two methods were used to derive the surface gravity potential distribution of the model: one directly from the variable density body and the other based on the spherical harmonic algorithm derived from the study.The results showed that the residual values of both methods gradually increased from the equator to the poles,but the residual values did not exceed 0.001,which was within the allowable error range and verified the rationality of the proposed method.The spherical harmonic algorithm proposed in this study was applied to estimate the gravity potential of the lunar variable density shell,and it was found that the gravity potential of the shell was consistent with the density distribution characteristics,which further validated the rationality and reliability of the algorithm.(2)In order to further verify the reliability of the algorithm,this thesis estimated the physical parameters of a specific region on Mars.Different load models of variable density shells were constructed to estimate the corresponding gravity anomalies on the surface of Mars.Combined with the Martian topographic model,using the chi-square estimation function,the elastic thickness of the specific region was estimated.It was found that the elastic thickness values of Olympus and Elysium on Mars were similar to those of other studies,which verified the rationality of the variable density shell gravity potential spherical harmonic algorithm proposed in this thesis.Furthermore,the method was applied to the Isidis Basin on Mars,where for the first time,the optimal elastic thickness value of the basin was successfully estimated in the academic community,providing a reference for related research on the formation mechanism of Martian massif basins. |