We place constraints on the amounts and length scales of seismic velocity variations throughout the mantle that are beyond the resolving capabilities of seismic tomography. We model global stacks of various seismic phases that are thought to have a scattering origin, using a Monte Carlo phonon method.
In Chapter 2, we forward model stacks of over 10,000 high-frequency (~1 Hz) PKP precursor waveforms with velocity perturbations of ~0.1% distributed throughout the lowermost mantle, resolving a debate between older studies. We confirm that models where scattering is distributed uniformly throughout the lowermost mantle better match the observations than those where scattering is restricted to a thin region just above the core--mantle boundary.
In Chapter 3, we characterize the frequency dependence of PKP precursors at central frequencies ranging from 0.5 to 4 Hz. At greater frequencies, we observe more scattered energy, particularly at shorter ranges. We model this observation by invoking heterogeneity at length scales from 2 to 30 km. Amplitudes at 0.5 Hz, in particular, suggest the presence of more heterogeneity at scales >8 km than present in previously published models.
In Chapter 4, we constrain the heterogeneity spectrum of Earth's upper mantle at scales from a few kilometers to tens-of-thousands of kilometers using observations from high-frequency scattering, long-period scattering, and tomography. We explore geodynamically plausible scenarios that might be responsible for the rms and fall-off rate of the proposed spectrum, including a self-similar mixture of basalt and harzburgite.
In Chapter 5, we stack a large global dataset of 1-Hz PKKP waveforms to constrain globally-averaged properties of PKKP precursors. We propose a new 1-D reference model that fits both our PKKP precursor amplitudes and constraints on absolute PKPbc travel times. Our globally averaged PKKP precursor observations are consistent with random CMB topography with rms variations of ~440 m and a horizontal correlation length of ~7 km.
Finally, in Chapter 6, we discuss outstanding challenges and future prospects for deep Earth scattering research.