The interior structure of the Moon is constrained by its mass, moment of inertia, and k(2) and h(2) tidal Love numbers. We infer the likely radius, density, and (elastic limit) rigidity of all interior layers by solving the inverse problem using these observational constraints assuming spherical symmetry. Our results do not favor the presence of a low rigidity transition layer between a liquid outer core and mantle. If a transition layer exists, its rigidity is constrained to 43-9+26GPa, with a preference for the high rigidity values. Therefore, if a transition layer exists, it is more likely to have a rigidity similar to that of the mantle (approximate to 70GPa). The total (solid and liquid) core mass fraction relative to the lunar mass is constrained to 0.0098-0.0094+0.0066 and 0.0198-0.0049+0.0026 for interior structures with and without a transition layer, respectively, narrowing the range of possible giant impact formation scenarios.

abstract: Stratification is a dominant feature of all planetary interiors. Fine-scale structure associated with layering, as well as heterogeneities hold important clues on a planet's compositional, thermal, and dynamical state, as well as its evolution. This research centers on using data from seismic arrays, networks of seismic sensors, and array processing methodologies to map the fine scale structure in the Earth's upper mantle and deep layering in the Moon - Earth and Moon are the only two planetary bodies with seismic available data for such analyses. Small-scale structure in the Earth's upper mantle can give rise to seismic wave scattering. I studied high frequency data from the Warramunga Array in Australia using array seismology. I developed and employed back-projection schemes to map the possible upper mantle scattering or reflection locations. Mapped scatterers show good correlation to strong lateral P-wave velocity gradients in tomography models and may be associated with the complex tectonic history beneath north of Australia. The minimum scale of scatterers relates to the seismic wavelength, which is roughly between 5 and 10 km in the upper mantle for the frequencies we study. The Apollo Passive Seismic Experiment (APSE) consisted of four 3-component seismometers deployed between 1969 and 1972 that continuously recorded lunar ground motion until late 1977. I studied the deep lunar interior with array methods applied to the legacy APSE dataset. The stack results suggest the presence of a solid inner and fluid outer core, overlain by a partially molten boundary layer, but their reflector impedance contrasts and reflector depths are not well constrained. With a rapidly increasing number of available modern broadband data, I developed a package, Discovery Using Ducttape Excessively (DUDE), to quickly generate plots for a comprehensive view of earthquake data. These plots facilitate discovery of unexpected phenomena. This dissertation identifies evidence for small-scale heterogeneities in Earth's upper mantle, and deeper lunar layering structure. Planetary interiors are complex with the heterogeneities on many scales, and discontinuities of variable character. This research demonstrates that seismic array methods are well-suited for interrogating heterogeneous phenomena, especially considering the recent rapid expansion of easily available dense network data. / Dissertation/Thesis / Ph.D. Geological Sciences 2011