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.

The San Gabriel Mountains (SGM) of southern California provide the opportunity to study the topographic controls on erosion rate in a mountain range where climate and lithology are relatively constant. I use a combination of digital elevation model data, detailed channel survey data, decadal climate records, and catchment-averaged erosion rates quantified from 10Be concentrations in stream sands to investigate the style and rates of hillslope and channel processes across the transition from soil-mantled to rocky landscapes in the SGM. Specifically, I investigate (1) the interrelations among different topographic metrics and their variation with erosion rate, (2) how hillslopes respond to tectonic forcing in "threshold" landscapes, (3) the role of discharge variability and erosion thresholds in controlling the relationship between relief and erosion rate, and (4) the style and pace of transient adjustment in the western SGM to a recent increase in uplift rate. Millennial erosion rates in the SGM range from 0.03-1.1 mm/a, generally increasing from west to east. For low erosion rates (< 0.3 mm/a), hillslopes tend to be soil-mantled, and catchment-averaged erosion rates are positively correlated with catchment-averaged slope, channel steepness, and local relief. For erosion rates greater than 0.3 mm/a, hillslopes become increasingly rocky, catchment-mean hillslope angle becomes much less sensitive to erosion rate, and channels continue to steepen. I find that a non-linear relationship observed between channel steepness and erosion rate can be explained by a simple bedrock incision model that combines a threshold for erosion with a probability distribution of discharge events where large floods follow an inverse power-law. I also find that the timing of a two-staged increase in uplift rate in the western SGM based on stream profile analysis agrees with independent estimates. Field observations in the same region suggest that the relict topography that allows for this calculation has persisted for more than 7 Ma due to the stalling of migrating knickpoints by locally stronger bedrock and a lack of coarse sediment cover.