Moment tensor inversions of icequakes on Gornergletscher, Switzerland

We have determined seismic source mechanisms for shallow and intermediate-depth icequake clusters recorded on the glacier Gornergletscher, Switzerland, during the summers of 2004 and 2006. The selected seismic events are part of a large data set of over 80,000 seismic events acquired with a dense seismic network deployed in order to study the yearly rapid drainage of Gornersee lake, a nearby ice-marginal lake. Using simple frequency and distance scaling and Green’s functions for a homogeneous half-space, we calculated moment tensor solutions for icequakes with M_w-1.5 using a full-waveform inversion method usually applied to moderate seismic events (M_w>4) recorded at local to regional distances (≈50–700 km). Inversions from typical shallow events are shown to represent tensile crack openings. This explains well the dominating Rayleigh waves and compressive first motions observed at all recording seismograms. As these characteristics can be observed in most icequake signals, we believe that the vast majority of icequakes recorded in the 2 yr is due to tensile faulting, most likely caused by surface crevasse openings. We also identified a shallow cluster with somewhat atypical waveforms in that they show less dominant Rayleigh waves and quadrantal radiation patterns of first motions. Their moment tensors are dominated by a large double-couple component, which is strong evidence for shear faulting. Although less than a dozen such icequakes have been identified, this is a substantial result as it shows that shear faulting in glacier ice is generally possible even in the absence of extreme flow changes such as during glacier surges. A third source of icequakes was located at 100 m depth. These sources can be represented by tensile crack openings. Because of the high-hydrostatic pressure within the ice at these depths, these events are most likely related to the presence of water lenses that reduce the effective stress to allow for tensile faulting

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

Real-time inversions for finite fault slip models and rupture geometry based on high-rate GPS data

We present an inversion strategy capable of using real-time high-rate GPS data to simultaneously solve for a distributed slip model and fault geometry in real time as a rupture unfolds. We employ Bayesian inference to find the optimal fault geometry and the distribution of possible slip models for that geometry using a simple analytical solution. By adopting an analytical Bayesian approach, we can solve this complex inversion problem (including calculating the uncertainties on our results) in real time. Furthermore, since the joint inversion for distributed slip and fault geometry can be computed in real time, the time required to obtain a source model of the earthquake does not depend on the computational cost. Instead, the time required is controlled by the duration of the rupture and the time required for information to propagate from the source to the receivers. We apply our modeling approach, called Bayesian Evidence-based Fault Orientation and Real-time Earthquake Slip, to the 2011 Tohoku-oki earthquake, 2003 Tokachi-oki earthquake, and a simulated Hayward fault earthquake. In all three cases, the inversion recovers the magnitude, spatial distribution of slip, and fault geometry in real time. Since our inversion relies on static offsets estimated from real-time high-rate GPS data, we also present performance tests of various approaches to estimating quasi-static offsets in real time. We find that the raw high-rate time series are the best data to use for determining the moment magnitude of the event, but slightly smoothing the raw time series helps stabilize the inversion for fault geometry

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

Limits of Earthquake Early Warning Accuracy and Best Alerting Strategy

We explore how accurate earthquake early warning (EEW) can be, given our limited ability to forecast expected shaking even if the earthquake source is known. Because of the strong variability of ground motion metrics, such as peak ground acceleration (PGA) and peak ground velocity (PGV), we find that correct alerts (i.e., alerts that accurately estimate the ground motion will be above a predetermined damage threshold) are not expected to be the most common EEW outcome even when the earthquake magnitude and location are accurately determined. Infrequently, ground motion variability results in a user receiving a false alert because the ground motion turned out to be significantly smaller than the system expected. More commonly, users will experience missed alerts when the system does not issue an alert but the user experiences potentially damaging shaking. Despite these inherit limitations, EEW can significantly mitigate earthquake losses for false-alert-tolerant users who choose to receive alerts for expected ground motions much smaller than the level that could cause damage. Although this results in many false alerts (unnecessary alerts for earthquakes that do not produce damaging ground shaking), it minimizes the number of missed alerts and produces overall optimal performance

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

The limits of earthquake early warning: Timeliness of ground motion estimates

The basic physics of earthquakes is such that strong ground motion cannot be expected from an earthquake unless the earthquake itself is very close or has grown to be very large. We use simple seismological relationships to calculate the minimum time that must elapse before such ground motion can be expected at a distance from the earthquake, assuming that the earthquake magnitude is not predictable. Earthquake early warning (EEW) systems are in operation or development for many regions around the world, with the goal of providing enough warning of incoming ground shaking to allow people and automated systems to take protective actions to mitigate losses. However, the question of how much warning time is physically possible for specified levels of ground motion has not been addressed. We consider a zero-latency EEW system to determine possible warning times a user could receive in an ideal case. In this case, the only limitation on warning time is the time required for the earthquake to evolve and the time for strong ground motion to arrive at a user’s location. We find that users who wish to be alerted at lower ground motion thresholds will receive more robust warnings with longer average warning times than users who receive warnings for higher ground motion thresholds. EEW systems have the greatest potential benefit for users willing to take action at relatively low ground motion thresholds, whereas users who set relatively high thresholds for taking action are less likely to receive timely and actionable information