Determination of Tidal Response of the Moon with Fully Three-dimensional Elastic and Density Structures Using a Perturbation Method

The Moon displays a number of hemispherically asymmetric (i.e., harmonic degree-1) features, including those in its topography, crustal thickness, mare volcanism, surface chemical compositions and deep seismicity distribution. These features suggest a long-wavelength (i.e., 3-D) structure in the Moon’s interiors, which may have resulted from long-term lunar dynamic evolution. In recent years, high precision measurements of the Moon’s gravity field and topography have been made possible by the advancement of space geodetic techniques. New theoretical tools that can use those measurements to constrain the Moon’s 3-D interior structure are needed. In this thesis, I present a new semi-analytical method based on a perturbation theory that calculates the elastic response of a terrestrial planet with 3-D interior structures to time-varying body tides. The 3-D structure is represented by small lateral heterogeneities in the elastic properties and density of the planet. The presence of the 3-D structure excites response modes to tidal force that are added to those from the 1-D reference state. In a spherical harmonic representation, that every eigenstructure in the lateral heterogeneities is characterized by its induced modes and their relative responses holds the theoretical basis for inversion studies. The perturbation method is applied to solving the tidal response of the Moon, in which harmonic degree-1 lateral heterogeneities are assumed predominant. The perturbation solutions have been interpreted and compared with those from a finite element method, thus verifying the correct implementation of the perturbation method. My perturbation method is optimizable for inversions and promises to provide constraints on the Moon’s long-wavelength interior structures, with improved tidal response measurements from the GRAIL mission and future lunar missions