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Abstract

Mass movements are a significant natural hazard and are expected to increase in frequency as global temperatures rise and extreme weather events become more common. The close observation of mass movements can be essential to minimise their adverse effects on society. The efficient use of the available surveying equipment and resources is important when monitoring mass movements. This is because they are often located in inaccessible terrain, and observing them over months or years can be expensive. A deployment pattern and number of sensors (henceforth, the experimental design) can often be optimised to substantially decrease the uncertainty of scientific results that can be inferred from the observed data. We have developed a novel method to optimise the design of seismic node layouts and fibre-optic based Distributed Acoustic Sensor (DAS) cable pathways for monitoring seismic events. We use it to design surveys to focus on slope instability-induced seismicity. Our general Bayesian experimental design framework can take into account prior information on event locations, subsurface seismic velocity models, the nonlinearity of the physics governing seismic traveltimes, different models of attenuation, and the directional sensitivity of different sensor types (e.g. the inline sensitivity of fibre-optic cables). The introduction of a likelihood that a travel-time measurement will be made at a given station for a given seismic event allows us to account for the effect of attenuation on the observed data, and the angular dependence of one-component measurements such as DAS. We show that we can efficiently design seismic node installations, give quantitative recommendations for DAS cable layouts, and show the feasibility of optimising hybrid designs combining both measurement types. We benchmark the experimental design algorithms using an effectively exhaustive data set collected at the Cuolm da Vi slope instability (Swiss Alps, near Sedrun, in Central Switzerland). The data set includes recordings from over 1000 seismic nodes, in a hexagonal grid with roughly 28m receiver spacing over the slope’s surface, of which each recorded data from over 100 dynamite shots spread across the slope. This extremely dense deployment provides the unique opportunity to choose nearly arbitrary designs (i.e. subsets of the nodes) and then test those designs by using them to locate the explosions for which we know the location. By averaging the performance of the probabilistic source location inversions over all dynamite shots, the performance of optimised, heuristic and random experimental designs can be compared. The same design methods can be applied to seismic source localisation in many different contexts, such as locating microseismic events, and other scenarios, such as infrasound source location.

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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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