Global mantle waveform tomography using the Spectral Element Method

Abstract:

In the past 20 years, we developed several generations of global mantle shear velocity models based entirely on time domain waveform inversion. This implies computations of synthetics in 3D earth models. Initially, the method of choice relied on normal mode perturbation theory, within which we built the framework of our inversion methodology. The latter includes, among others, windowing of waveforms to bring out contribution of weak amplitude phases, (e,g, Sdiff), and a fast converging quasi-Newton inversion with an approximate Hessian calculated using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995).

Recently, the Spectral Element Method (SEM) was introduced in global seismology as a powerful numerical method to compute the seismic wavefield accurately in arbitrary 3D models (Komatitsch and Vilotte, 1998; Komatitsch and Tromp, 2002). Implementing the numerical SEM synthetics was straightforward, albeit with significantly increased cost of computation. In order to advance mantle imaging at the global scale, we introduced computational efficiencies, such as (1) substituting a fine layered crustal model by an equivalent, smooth, "homogeneized" crust designed to fit a global surface wave dispersion dataset, (2) continuing quasi-Newton inversion using NACT rather than adjoints, which involved the development of an efficient matrix assembly method (French et al., 2015), and (3) stepping progressively from long to short periods. The resulting models (Lekic and Romanowicz, 2011; French et al., 2013; French and Romanowicz, 2014), in particular, confirm the presence of deep mantle plumes beneath many major hotspots (French and Romanowicz, 2015). We discuss the choice of inverse approach, and illustrate the stability of our global models, in view of the use of NACT kernels, with respect to the choice of the starting model.

Global inversion remains a challenge as higher resolution implies reaching higher frequencies to capture more of the scattered wavefield produced by dynamically relevant features. Continuing to develop efficiencies while progressively improving images, recently, we have extended our approach to focus on a particular region of the deep mantle, while minimizing the number of global simulations (Masson et al., 2014). We illustrate applications of this approach.