Imaging of structure at and near the core‐mantle boundary using a generalized radon transform: 2. Statistical inference of singularities

Abstract

We present the second part of our approach to high‐resolution imaging of deep Earth's interfaces with large volumes of broadband, three‐component seismograms. We focus on the lowermost mantle, also referred to as D″ region, but the methodology can be applied more generally. The first part describes the generalized radon transform (GRT) of broadband ScS data (comprising main arrival, precursors, and coda). The GRT produces “image gathers,” which represent multiple images of medium contrasts at the same image point near the base of the mantle. With a method for statistical inference we use this redundancy (1) to enhance the GRT images through improved recovery of weak contrasts and through suppression of spurious oscillations in the GRT image gathers and (2) to provide uncertainty estimates that can be used to identify the robust features in the images. Using the image gathers from paper 1 as input, we use mixed effects statistical modeling to produce the best estimates of reflectivity along with their uncertainty. In this framework, random noise in the signal is separated into white and coherent components using the geometry of the (GRT) imaging operators and a generalized cross‐validation method. With synthetic data we show that conventional GRT images deteriorate substantially, in some cases to the point at which weak reflectors can no longer be detected, due to effects of uneven sampling, wave phenomena that are not accounted for in the underlying single scattering approximation, or errors in the assumed background wave speed model. We demonstrate that even in these circumstances, statistical analysis can yield adequate estimates of the true model. GRT imaging produces robust images of the core‐mantle boundary (CMB) beneath Central America and suggests the presence of several structures in the D″ region, in particular between 100 and 200 and between 270 and 320 km above the CMB proper. Most of these structures are significant at the 1σ (that is, 68%) level, but at 2σ (95%) confidence the images show, at various depths above the CMB, intermittent instead of laterally contiguous features.