Attenuation tomography of the upper inner core

Abstract

The Earth's inner core is one of the very few regions of our planet that is still a puzzle. In order to understand planetary formation and the geomagnetic eld we need to understand the structure and dynamics of the inner core. Seismology provides us with some tools to probe into the core and understand it better, for example, body waves traveling through the deep Earth and interacting with the propagating medium. In this study we use body waves, speci fically the PKIKP phase propagating through the inner core and the PKPbc phase propagating through the outer core to study the attenuation of seismic waves within the inner core. Because these two phases have similar paths through the lowermost mantle and differ only within the core, the attenuation of the PKIKP phase relative to PKPbc can tell us about the regions of the inner core and the extent thereof of the attenuation. This in turn sheds light on possible geodynamical scenarios of the inner core, all of which are still subjects of heated debates. Currently the widely accepted attenuation structure of the inner core is of hemispherical nature with quasi-eastern hemisphere more attenuating than the quasi-western hemisphere, with two competing theories explaining this observation. Using a full-waveform fi tting simulated annealing algorithm we collect a dataset of t* parameter from 50 globally distributed earthquakes from past two decades with magnitude larger than 5.8. t* parameter is directly related to quality factor Q { measure of attenuation in the medium. We

first perform a linearised inversion in which we assume that the logarithm of inverse quality factor Q is normally distributed. We connect the least-squares method with probabilistic framework, and use optimisation techniques, in order to get the maximum posterior probability solution and its uncertainties. The inversion is performed on a fi xed, coarse grid (explicit parameterisation). Regularisation, in form of damping, and separately, smoothing, is used. The results of the inversion and their robust estimate of uncertainty point to an attenuation heterogeneity more complex than the hemispherical structure. While the solution obtained through linearised inversion is robust, imposing a regular global grid and a fixed number of parameters in tomographic studies will often result in introducing artefacts in regions of low ray coverage. Furthermore, explicit regularisation methods are global in character, making small-scale features hard to see or masking them completely. This is why we also perform a transdimensional Bayesian inversion for quality factor Q, in which the complexity of the model is determined by the data and the data noise, estimated in the inversion. Hence there is no need for a fixed parameterisation or explicit regularisation. A more realistic estimate of the uncertainties of the solution is an added bonus of Bayesian inversion. The results of this inversion are in agreement with the linearised one and point to an attenuation structure more complex than the hemispherical one. As such these results give more weight to the models that connect the dynamics of the inner core with the heat flow in the lowermost mantle.