# The anisotropic seismic structure of the Earth's mantle : investigations using full waveform inversion

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I have developed a waveform inversion procedure to invert 3 component broadband seismic data for models of the anisotropic seismic structure of the Earth and applied the technique to an investigation of wave propagation through anisotropic media and earthquake data sampling the upper mantle beneath the East European platform. The procedure combines the conjugate-gradient and very fast simulated annealing methods and attempts to minimize a cross-correlation misfit function comparing data to synthetic seismograms. A series of inversion passes are performed over a range of frequency and time windows to progressively focus in on structural details. The intent is to obtain P and S velocity models that simultaneously match all components of the data (radial, vertical and tangential). The variables in the problem are the seismic velocities ([alpha] and [beta]) as a function of depth. When radial anisotropy is required this set is expanded to include the five variables that determine the seismic velocities in a radially anisotropic medium ([alpha subscript h, alpha subscript v, beta subscript h, beta subscript v, eta]). I investigate the propagation of seismic waves through radially anisotropic media, evaluate which elements of radial anisotropy are best resolved by seismic data and discuss strategies for identifying radial anisotropy in the Earth. S anisotropy, [beta]%, and the horizontal component of P velocity, [alpha subscript h], are typically well resolved by multicomponent seismic data. P anisotropy, [alpha]%, and [eta] are often poorly resolved and trade off with one another in terms of their effect on S[subscript V] arrivals. Erroneous structure will be mapped into models if anisotropy is neglected. The size of the erroneous structure will be proportional to the magnitude of anisotropy present and extend well below the anisotropic zone. The effects of anisotropy on P models produced with an isotropic assumption are most similar to the effects on isotropic S[subscript H] models. When comparing isotropic models, [alpha/beta subscript sh] is therefore often a better measure than [alpha/beta subscript sv] for characterizing mantle petrology. Isotropic S[subscript H], S[subscript V] and P models developed separately using the same data set can provide a good initial estimate of the presence, location and magnitude of anisotropy and those results can be used to create an initial model for an anisotropic inversion solving simultaneously for all 3 components of the data. Finally, I present models for the P and S velocity structure of the upper mantle beneath the East European platform including an analysis of radial anisotropy. The data are 3-component broadband seismograms from strike-slip earthquakes located near the edge of the platform and recorded in Russia and Europe. The timing, amplitude and interference characteristics of direct arrivals (S, P), multiply reflected arrivals (SS, PP), converted phases and surface waves provide very good radial resolution throughout the upper 400 km of the mantle. The platform is underlain by a radially anisotropic seismic mantle lid extending to a depth of 200 km with a largely isotropic mantle below. The model has a positive velocity gradient from 41 km to 100 km depth, and a relatively uniform velocity structure from 100 km to 200 km depth with high S[subscript H] and P[subscript H] velocities (4.77 km /s, 8.45 km/s). Shear anisotropy is uniform at 5% ([beta subscript H] > [beta subscript V]) from 41 to 200 km depth, drops to 2% from 200 to 250 km and is isotropic below that. The average shear velocity from 100 to 250 km is also uniform at 4.65 km/s and the drop in anisotropy is matched by a drop in [beta subscript H] to 4.70 km/s combined with an increase in [beta subscript V] to 4.60 km/s. Below 250 km there is a positive velocity gradient in both P and S velocity down to 410 km. P anisotropy is not well resolved, but P structure mimics the S[subscript H] velocity structure, suggesting that P is also anisotropic within the lid.