Constraining 3-D variations in mantle attenuation using normal modes: forward modelling and sensitivity tests

Robust estimates of the Earth's temperature, composition and partial melt are difficult to obtain from seismic tomography models based only on wave velocities. Seismic attenuation is able to add crucial additional information and allows us to constrain 3-D variations in temperature as well as answer fundamental questions regarding the presence of water and partial melt within the mantle. A major problem with measuring attenuation is that scattering and focusing effects need to be included in order to distinguish between intrinsic attenuation (transformation of energy to heat) and scattering (redistribution of energy). Here, we will use whole Earth oscillations or normal modes, exploiting the fact that small scale scattering becomes less important at longer periods. In addition, focussing is implicitly included by simultaneously measuring the elastic and anelastic splitting function of a given normal mode. Normal mode data has rarely been used before to constrain 3-D variations in attenuation, hence we first need to assess the feasibility of using whole Earth oscillations to image 3-D variations in attenuation in Earth's upper and lower mantle. Here, we use simple models in forward calculations to evaluate the sensitivity of normal modes to 3-D attenuation variations, and find observable differences in normal mode spectra when 3-D variations in mantle attenuation are included. We also test if 3-D attenuation variations can be recovered using splitting function measurements for synthetic normal mode spectra and investigate potential problems with unaccounted earthquake magnitude variations, noise and wide-band cross-coupling between modes. We find that we are able to recover input synthetic anelastic splitting functions, even when they are an order of magnitude smaller than the elastic splitting functions. Biases in the earthquake seismic moment solutions may lead to 'ghost' anelastic splitting functions being recovered, especially for high degree structure. However, this 'ghost' signal is only relevant if the size of the input anelastic splitting function is 50 per cent smaller than the scaled amplitude signal of expected upper mantle attenuation. Random noise and normal mode coupling also lead to spurious effects in the anelastic splitting functions. However, they manly affect high degree anelastic structure in a non-branch consistent manner. Thus, we are able to robustly recover low anelastic degree structure (s(max) <= 4) in all tested cases.