Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2007.Includes bibliographical references (p. [163]-175).In this thesis, concepts from inverse scattering and modem statistics are combined into a powerful tool for imaging interfaces in Earth's deep interior. Specially, a generalized Radon transform (GRT) approach is developed to image heterogeneity at and near interfaces in Earth's lowermost mantle with broadband, three-component seismograms from Global Seismograph Networks (GSN). With this GRT method I transformed ~100,000 transverse-component ScS waveforms into image gathers of a core mantle boundary (CMB) patch beneath Central America and juxtaposition of stacks of these gathers produces a 2-D image profile. To enhance this image profile, I collaborated with statisticians and used mixed-effects statistical modeling to produce the best estimates of reflectivity along with their uncertainty. I demonstrate that the method outlined above works well and - thus - paves the way to large-scale seismic exploration of the lowermost mantle. With the new technology I mapped the structure at and near the CMB beneath Central and North America. Several interfaces are detected, and some of them are consistent with expectations from phase transformations in Magnesiiim perovskite. If we know which interface is associated with a particular phase transformation, and if we know the thermodynamic (P-T) relations of the stability fields of the phases, then we can estimate temperature from the pressure as inferred from the depth at which the transition occurs in the seismic sections. Here we associate a seismically observed wavespeed increase with the perovskite to post-perovskite transition and a wavespeed decrease with the back transformation to perovskite.(cont.) Using P-T data from experimental and theoretical mineral physics we can then estimate the lateral temperature variations and radial (thermal) gradients near the CMB. In addition, the temperature of the CMB and global heat loss are estimated. To improve D" imaging even further, I have constructed a generalized Radon transform approach, compensating for the liquid outer-core, which can be used to transform seismic signals passing trough the outer-core, such as SKKS and its precursors and coda. I apply this method to the same region as used in ScS studies. The image gathers computed from SKKS are in excellent agreement with the results (for the same image points) obtained from ScS. With this development we now have a tool for detailed D" imaging - on sub-global scale - with joint interpretation (by means of the GRT and mixed-method statistics) of the broadband ScS and SKKS wavefields.by Ping Wang.Ph.D.