Global Full-Waveform Tomography Using the Spectral Element Method: New Constraints on the Structure of Earth's Interior
The radially anisotropic shear-velocity structure of the earth's mantle provides a critical window on the interior dynamics of the planet, with isotropic variations interpretable in terms of thermal and compositional heterogeneity and anisotropy in terms of flow. Indeed, more than 30 years after the advent of global seismic tomography, many open questions remain regarding the dual roles of temperature and composition in shaping mantle convection, as well as interactions between different dominant scales of convective phenomena. To this end, we use full-waveform inversion of the long-period teleseismic wavefield to image radially anisotropic shear-wave velocity at the scale of the entire globe. In particular, we use a technique which we have termed the "hybrid" waveform-inversion approach, which combines the accuracy and generality of the spectral finite element method (SEM) for forward modeling of the global wavefield, with non-linear asymptotic coupling theory for efficient inverse modeling. This hybrid technique helps considerably in making SEM-based global waveform inversion tractable, as it allows for the use of a rapidly converging Gauss-Newton scheme for optimization of the underlying seismic model. We take additional steps to reduce the cost of these inversions using novel techniques for treatment of the earth's crust. Namely, naive modeling of thinly layered crustal structure can lead to an overly restrictive time-stability condition in the SEM, which in turn drives up the cost these simulations. Instead, taking advantage of the physics of long-period wave propagation, we introduce alternative parameterizations of crustal structure which appear identical to the wavefield, but relax these constraints on stability.
We approach this imaging problem in an iterative fashion, hoping to learn something about the earth's interior at each step. First, we present our work focused on the upper mantle and transition zone (≤ 800km depth) in the form of the global model SEMum2, discussing both its development and general properties. Second, we take a detailed look at novel structures in SEMum2 - namely, never-before-seen low-velocity structures in the upper mantle beneath the ocean basins, showing intriguing correlations with other geophysical observables (e.g. absolute plate motions and the geoid). Third, we move on to imaging of the whole mantle, examining the relationships between different scales of convective phenomena in the upper and lower mantle, and particularly those previously seen in SEMum2. Finally, we discuss novel computational aspects of our work, focusing specifically on applications of the partitioned global address-space model of parallel computation to the large-scale data-driven calculations underlying our hybrid inversion approach.