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Abstract

The design of geophysical surveys or experiments (henceforth, the experimental design) significantly influences the uncertainty in scientific results that can be inferred from recorded data. Typical aspects of experimental designs that can be varied are locations of sensors, sensor types, and the modelling or data processing methods to be applied to recorded data. To tighten constraints on the solution to any inverse or inference problem, and thus to rule out as many false possibilities as possible, the design should be optimised such that it is practically achievable within cost and logistical constraints, and such that it maximises expected post-experimental information about the solution. Bayesian experimental design refers to a class of methods that use uncertainty estimation methods to quantify the expected gain in information about target parameters provided by an experiment, and to optimise the design of the experiment to maximise that gain. Information gain quantifies the decrease in uncertainty caused by observing data. Expected information gain is an estimate of the gain in information that will be offered by any particular design post-experiment. Bayesian experimental design methods vary the design so as to maximise the expected information gain, subject to practical constraints. We introduce variational experimental design methods that are novel to geophysics, and discuss their benefits and limitations in the context of geophysical applications. The family of variational methods relies on functional approximations of probability distributions, and in some cases, of the model-data relationships. They can be used to design experiments that best resolve either all model parameters, or the answer to a specific question about the system studied. Their potential advantage over some other design methods is that finding the functional approximations used by variational methods tends to rely more on optimisation theory than the more common stochastic uncertainty analysis used to approximate Bayesian uncertainties. This allows the wealth of understanding of optimisation methods to be applied to the full Bayesian design problem. Variational design methods are demonstrated by optimising the design of an experiment consisting of seismometer locations on the Earth's surface, so as to best estimate seismic source parameters given arrival time data obtained at seismometers. By designing separate experiments to constrain the hypocentres and epicentres of events, we show that optimal designs may change substantially depending on which questions about the subsurface we wish the experiment to help us to answer. By accounting for differing expected uncertainties in travel time picks depending on the picking method used, we demonstrate that the data processing method can be optimised as part of the design process, provided that expected uncertainties are available from each method.

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This talk gives a brief introduction to Bayesian optimal experimental design for the other members of the SPIN project.

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This talk delivered by my MSc supervisor Bernhard Schuberth is based on the work done for my MSc thesis and subsequent further work by Anna Schneider.

Abstract

Geodynamic inverse models that aim at retrodicting past mantle evolution require accurate estimates of its thermodynamic present-day state. Tomographic models are in principle well suited to provide this information. However, a fundamental problem that impacts the quality of the retrodiction arises from their inherently limited resolving power and the fact that the magnitudes of seismic heterogeneity are difficult to constrain owing to the necessity to regularize the inversions (e.g. by norm damping). To get a better understanding of the magnitudes of heterogeneity in the mantle, one option is to predict seismic velocity variations from the temperature field of forward mantle circulation models (MCMs) in combination with thermodynamic models of mantle mineralogy. Temperature is not a free parameter in these models, but rather constrained by the underlying conservation equations and relevant input parameters. If the geodynamic models are run at earth-like Rayleigh number, temperature variations are expected to feature realistic magnitudes, which, together with the mineralogical mapping, should lead to realistic magnitudes of seismic heterogeneity. This has been investigated in previous studies by computing secondary predictions for the MCMs, such as seismic body wave traveltimes and geoid undulations. A complicating factor, however, is the trade-off between thermal and compositional variations that both may affect the seismic velocities. A further complexity arises from the fact that the elastic velocities of the mineralogical model need to be corrected for the effects of anelasticity, the parameters of which are poorly known. Thus, a range of seismic velocity values may still be possible for a given temperature.

Here, we explore the possibility to use Earth’s normal mode spectrum to narrow the range of plausible magnitudes of seismic heterogeneity in the mantle. To this end, we compute free-oscillation spectra with full coupling of modes below 3.5 mHz in our geodynamic models. In our analysis, we consider different measures to investigate whether the normal mode data may provide complementary information to earlier assessments of MCMs based on body waves. In addition to the direct misfit between spectra of real and synthetic data, the variance of a large number of stacked multiplets can be used to constrain the even degree covariance of lateral heterogeneity under certain assumptions. Using different realizations of seismic MCM structure that differ in terms of the anelastic temperature to velocity mapping, we will analyse the potential of normal mode data to put tighter constraints on the magnitudes of heterogeneity.

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