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The results of mantle convection simulations are fully determined by the input parameters and boundary conditions used. These input parameters can be for initialisation, such as initial mantle temperature, or can be constant values, such as viscosity exponents. However, knowledge of Earth-like values for many input parameters are very poorly constrained, introducing large uncertainties into the simulation of mantle flow. Convection is highly non-linear, therefore linearised inversion methods cannot be used to recover past configurations over more than very short periods of time, which makes finding both initial and constant simulation input parameters very difficult. In this paper, we demonstrate a new method for making inferences about simulation input parameters from observations of the mantle temperature field after billions of years of convection. The method is fully probabilistic. We use prior sampling to construct probability density functions for convection simulation input parameters, which are represented using neural networks. Assuming smoothness, we need relatively few samples to make inferences, making this approach much more computationally tractable than other probabilistic inversion methods. As a proof of concept, we show that our method can invert the amplitude spectra of temperature fields from 2D convection simulations, to constrain yield stress, surface reference viscosity and the initial thickness of primordial material at the CMB, for our synthetic test cases. The best constrained parameter is yield stress. The reference viscosity and initial thickness of primordial material can also be inferred reasonably well after several billion years of convection. [ABSTRACT FROM AUTHOR]

Abstract: The centroid-moment-tensor (CMT) algorithm provides a straightforward, rapid method for the determination of seismic source parameters from waveform data. As such, it has found widespread application, and catalogues of CMT solutions – particularly the catalogue maintained by the Global CMT Project – are routinely used by geoscientists. However, there have been few attempts to quantify the uncertainties associated with any given CMT determination: whilst catalogues typically quote a ‘standard error’ for each source parameter, these are generally accepted to significantly underestimate the true scale of uncertainty, as all systematic effects are ignored. This prevents users of source parameters from properly assessing possible impacts of this uncertainty upon their own analysis. The CMT algorithm determines the best-fitting source parameters within a particular modelling framework, but any deficiencies in this framework may lead to systematic errors. As a result, the minimum-misfit source may not be equivalent to the ‘true’ source. We suggest a pragmatic solution to uncertainty assessment, based on accepting that any ‘low-misfit’ source may be a plausible model for a given event. The definition of ‘low-misfit’ should be based upon an assessment of the scale of potential systematic effects. We set out how this can be used to estimate the range of values that each parameter might take, by considering the curvature of the misfit function as minimised by the CMT algorithm. This approach is computationally efficient, with cost similar to that of performing an additional iteration during CMT inversion for each source parameter to be considered. The source inversion process is sensitive to the various choices that must be made regarding dataset, earth model and inversion strategy, and for best results, uncertainty assessment should be performed using the same choices. Unfortunately, this information is rarely available when sources are obtained from catalogues. As already indicated by Valentine and Woodhouse (2010), researchers conducting comparisons between data and synthetic waveforms must ensure that their approach to forward-modelling is consistent with the source parameters used; in practice, this suggests that they should consider performing their own source inversions. However, it is possible to obtain rough estimates of uncertainty using only forward-modelling. [Copyright &y& Elsevier]