The investigators propose a quantitative, multi-disciplinary investigation of Earth's core mantle boundary, the remote interface between Earth's solid silicate mantle and its liquid iron-alloy outer core. With innovative techniques for interpreting (very) large amounts of broad-band waveform data - obtained from dense networks of seismograph stations - they aim to map, characterize, and interpret multi-scale variations in acousto-elastic properties at and near interfaces in Earth's deep interior. Initially, the team focuses on the physical shell that encompasses Earth's lowermost mantle, the core mantle boundary (CMB), and the outermost core. They will (1) investigate inverse scattering theory based on microlocal analysis making use of generalized Fourier integral operators (GFIOs), (2) develop statistical models based on such operators, and (3) apply the new techniques to a large number (millions) of seismogram windows containing waves that reflect at the top (ScS) and underside (SKKS) of the CMB. From a mathematical sciences perspective, the anticipated result is a generalized Radon transform (GRT) that can generate common image point gathers (IGs) from large data volumes. The IGs are used to (i) detect and determine the depth to elasticity contrasts (singularities), (ii) determine the regularity of the singularities, and (iii) study characteristic length scales of variations in the inferred parameters. Novel statistical methods will be used to enhance the S/N in the transforms, glean more information from the IGs, and provide uncertainty estimates. The geosciences motivation is to use these gathers to improve the understanding of (i) the contact between high-viscous mantle and liquid core, (ii) the effect of convective flow on the D'' structure and the character of the CMB, and (iii) outer core heterogeneity (if any) and its relationship to outer core magneto-hydrodynamics. The collaboration will not only contribute to our general understanding of the composition and phase chemistry of the deep mantle and outermost core, core-mantle transitions and interactions, and planetary formation. It also offers a unique educational experience for the students, postdocs, and senior staff involved. Indeed, the investigators believe that educating students in geophysics with strong background in mathematics is important for the future development of the field.
