Bayesian inversion for finite fault earthquake source models I—theory and algorithm

The estimation of finite fault earthquake source models is an inherently underdetermined problem: there is no unique solution to the inverse problem of determining the rupture history at depth as a function of time and space when our data are limited to observations at the Earth’s surface. Bayesian methods allow us to determine the set of all plausible source model parameters that are consistent with the observations, our a priori assumptions about the physics of the earthquake source and wave propagation, and models for the observation errors and the errors due to the limitations in our forward model. Because our inversion approach does not require inverting any matrices other than covariance matrices, we can restrict our ensemble of solutions to only those models that are physically defensible while avoiding the need to restrict our class of models based on considerations of numerical invertibility. We only use prior information that is consistent with the physics of the problem rather than some artefice (such as smoothing) needed to produce a unique optimal model estimate. Bayesian inference can also be used to estimate model-dependent and internally consistent effective errors due to shortcomings in the forward model or data interpretation, such as poor Green’s functions or extraneous signals recorded by our instruments. Until recently, Bayesian techniques have been of limited utility for earthquake source inversions because they are computationally intractable for problems with as many free parameters as typically used in kinematic finite fault models. Our algorithm, called cascading adaptive transitional metropolis in parallel (CATMIP), allows sampling of high-dimensional problems in a parallel computing framework. CATMIP combines the Metropolis algorithm with elements of simulated annealing and genetic algorithms to dynamically optimize the algorithm’s efficiency as it runs. The algorithm is a generic Bayesian Markov Chain Monte Carlo sampler; it works independently of the model design, a priori constraints and data under consideration, and so can be used for a wide variety of scientific problems. We compare CATMIP’s efficiency relative to several existing sampling algorithms and then present synthetic performance tests of finite fault earthquake rupture models computed using CATMIP

A Probabilistic Approach to Remote Compositional Analysis of Planetary Surfaces

Reflected light from planetary surfaces provides information, including mineral/ice compositions and grain sizes, by study of albedo and absorption features as a function of wavelength. However, deconvolving the compositional signal in spectra is complicated by the nonuniqueness of the inverse problem. Trade-offs between mineral abundances and grain sizes in setting reflectance, instrument noise, and systematic errors in the forward model are potential sources of uncertainty, which are often unquantified. Here we adopt a Bayesian implementation of the Hapke model to determine sets of acceptable-fit mineral assemblages, as opposed to single best fit solutions. We quantify errors and uncertainties in mineral abundances and grain sizes that arise from instrument noise, compositional end members, optical constants, and systematic forward model errors for two suites of ternary mixtures (olivine-enstatite-anorthite and olivine-nontronite-basaltic glass) in a series of six experiments in the visible-shortwave infrared (VSWIR) wavelength range. We show that grain sizes are generally poorly constrained from VSWIR spectroscopy. Abundance and grain size trade-offs lead to typical abundance errors of ≤1 wt % (occasionally up to ~5 wt %), while ~3% noise in the data increases errors by up to ~2 wt %. Systematic errors further increase inaccuracies by a factor of 4. Finally, phases with low spectral contrast or inaccurate optical constants can further increase errors. Overall, typical errors in abundance are <10%, but sometimes significantly increase for specific mixtures, prone to abundance/grain-size trade-offs that lead to high unmixing uncertainties. These results highlight the need for probabilistic approaches to remote determination of planetary surface composition

Development of climate profiles for reclamation

April 1981.Includes bibliographical references (page 58)

Climate profile for the McCallum Emria study area

March 1981.Includes bibliographical references (page 64)

Bayesian inversion for finite fault earthquake source models – II: the 2011 great Tohoku-oki, Japan earthquake

We present a fully Bayesian inversion of kinematic rupture parameters for the 2011 M_w 9 Tohoku-oki, Japan earthquake. Albeit computationally expensive, this approach to kinematic source modelling has the advantage of producing an ensemble of slip models that are consistent with physical a priori constraints, realistic data uncertainties, and realistic but simplistic uncertainties in the physics of the kinematic forward model, all without being biased by non-physical regularization constraints. Combining 1 Hz kinematic GPS, static GPS offsets, seafloor geodesy and near-field and far-field tsunami data into a massively parallel Monte Carlo simulation, we construct an ensemble of samples of the posterior probability density function describing the evolution of fault rupture. We find that most of the slip is concentrated in a depth range of 10–20 km from the trench, and that slip decreases towards the trench with significant displacements at the toe of wedge occurring in just a small region. Estimates of static stress drop and rupture velocity are ambiguous. Due to the spatial compactness of the fault rupture, the duration of the entire rupture was less than approximately 150 s

The 2013 M_w 7.7 Balochistan Earthquake: Seismic Potential of an Accretionary Wedge

Great earthquakes rarely occur within active accretionary prisms, despite the intense long‐term deformation associated with the formation of these geologic structures. This paucity of earthquakes is often attributed to partitioning of deformation across multiple structures as well as aseismic deformation within and at the base of the prism (Davis et al., 1983). We use teleseismic data and satellite optical and radar imaging of the 2013 M_w 7.7 earthquake that occurred on the southeastern edge of the Makran plate boundary zone to study this unexpected earthquake. We first compute a multiple point‐source solution from W‐phase waveforms to estimate fault geometry and rupture duration and timing. We then derive the distribution of subsurface fault slip from geodetic coseismic offsets. We sample for the slip posterior probability density function using a Bayesian approach, including a full description of the data covariance and accounting for errors in the elastic structure of the crust. The rupture nucleated on a subvertical segment, branching out of the Chaman fault system, and grew into a major earthquake along a 50° north‐dipping thrust fault with significant along‐strike curvature. Fault slip propagated at an average speed of 3.0  km/s for about 180 km and is concentrated in the top 10 km with no displacement on the underlying décollement. This earthquake does not exhibit significant slip deficit near the surface, nor is there significant segmentation of the rupture. We propose that complex interaction between the subduction accommodating the Arabia–Eurasia convergence to the south and the Ornach Nal fault plate boundary between India and Eurasia resulted in the significant strain gradient observed prior to this earthquake. Convergence in this region is accommodated both along the subduction megathrust and as internal deformation of the accretionary wedge

Compositional Variations in Sands of the Bagnold Dunes, Gale Crater, Mars, from Visible-Shortwave Infrared Spectroscopy and Comparison to Ground-Truth from the Curiosity Rover

During its ascent up Mount Sharp, the Mars Science Laboratory Curiosity rover traversed the Bagnold Dune Field. We model sand modal mineralogy and grain size at four locations near the rover traverse, using orbital shortwave infrared single-scattering albedo spectra and a Markov chain Monte Carlo implementation of Hapke's radiative transfer theory to fully constrain uncertainties and permitted solutions. These predictions, evaluated against in situ measurements at one site from the Curiosity rover, show that X-ray diffraction-measured mineralogy of the basaltic sands is within the 95% confidence interval of model predictions. However, predictions are relatively insensitive to grain size and are nonunique, especially when modeling the composition of minerals with solid solutions. We find an overall basaltic mineralogy and show subtle spatial variations in composition in and around the Bagnold Dunes, consistent with a mafic enrichment of sands with cumulative aeolian-transport distance by sorting of olivine, pyroxene, and plagioclase grains. Furthermore, the large variations in Fe and Mg abundances (~20 wt %) at the Bagnold Dunes suggest that compositional variability may be enhanced by local mixing of well-sorted sand with proximal sand sources. Our estimates demonstrate a method for orbital quantification of composition with rigorous uncertainty determination and provide key constraints for interpreting in situ measurements of compositional variability within Martian aeolian sandstones

Can a leader be seen as too ethical? The curvilinear effects of ethical leadership

Ethical leadership predicts important organizational outcomes such as decreased deviant and increased organizational citizenship behavior (OCB). We argued that due to the distinct nature of these two types of employee behaviors, ethical leadership decreases deviance in a linear manner (i.e., more ethical leadership leading to less deviance), but we expected ethical leadership to reveal a curvilinear relationship with respect to OCB. Specifically, we expected that, at lower levels, ethical leadership promotes OCB. However, at high levels, ethical leadership should lead to a decrease in these behaviors. We also examined a mechanism that explains this curvilinear pattern, that is, followers’ perceptions of moral reproach. Our predictions were supported in three organizational field studies and an experiment. These findings offer a better understanding of the processes that underlie the workings of ethical leadership. They also imply a dilemma for organizations in which they face the choice between limiting deviant employee behavior and promoting OCB