Applying the Spectral Element Method to Model 3D Attenuation in the Upper Mantle

Mapping 3D variations of intrinsic seismic attenuation within the mantle is crucial for determining the physical cause of observed mantle heterogeneity. While long-wavelength models of upper mantle 3D anelastic structure do exist, obtaining higher-resolution models requires correcting for purely elastic effects of scattering and (de)focusing which can obscure the signal of attenuation at lengthscales shorter than 5000 km. Therefore, it is necessary to both determine the high-resolution elastic structure within the mantle, as well as accurately calculate its effects on propagation of seismic waves. Recent high resolution global models of shear wave velocity and radial anisotropy (e.g. Panning and Romanowicz, 2006) indicate that elastic structure is well-resolved at length scales of < 1000 km. However, even when elastic structure is known precisely, conventional methods of modeling seismic waveforms that rely on the great circle approximation (PAVA: Woodhouse and Dziewonski, 1984) and first-order perturbation theory (e.g. Woodhouse, 1980) are inadequate at modeling wave propagation near the source or receiver, near nodes of the radiation pattern, in locations of strong heterogeneity, and at times long after the source time. We propose a hybrid approach to tomography, in which we calculate accurately the propagation of seismic waves in an arbitrary 3D medium, using the coupled Spectral Element Method (cSEM: Capdeville et al., 2003), and compute the sensitivity kernels approximately, using perturbation theory. This approach allows us to iteratively converge on the correct model as long as the sign of the sensitivity kernels is correct. We have modified cSEM to make it capable of modeling the effects of ellipticity, surface topography / bathymetry, oceans, and 3D crustal structure on wave propagation. In particular, we show that the use of cSEM is crucial for accurately predicting the effect of crustal structure on waveforms. We explore consequences arising from this advantage for retrieved mantle structure below continents. We apply our approach to 3-component long period fundamental and overtone waveforms recorded at more than 100 stations of the IRIS/GSN, GEOSCOPE, GEOFON, and various regional broadband networks.