Displacement Datasets Research Articles

Constraining coseismic earthquake slip using Structure from Motion from fault scarp mapping (East Helanshan Fault, China)

This study uses fault scarps to investigate past earthquakes and the potential seismic hazard of the East Helanshan Fault (EHF). The EHF is a Holocene active normal fault located at the complex transition from compression in the northeastern corner of the Tibetan Plateau to apparently east-west extension in the west margin of Ordos Block, as implied by the Yinchuan Faulted Basin and its boundary normal faults. Repeated normal faulting events, including the 1739 CE event on the EHF, offset alluvial fans of Late Pleistocene and Holocene age and formed remarkable fault scarps, especially along its Suyukou and Hongguozi segments. We selected three fault sections in the Suyukou and Hongguozi segments, where fault scarps of different heights are well preserved on different terrace surfaces. By using Structure-from-Motion-Multiview Stereo (SfM-MVS) techniques on Unmanned Aerial System (UAS) imagery, we acquired high-quality topography of the selected fault sections. Detailed mapping and surveying of the offset geomorphic features and their associated fault scarps, with distinct free faces and multiple slope breaks, suggest that surface-rupturing earthquakes occurred repeatedly along the EHF. Densely spaced cross scarp topographic profiles were extracted to evaluate the vertical slip distributions using newly acquired SfM-derived topography. Through statistical analysis of the displacement dataset, we constrain multiple earthquake events and their cumulative offsets on the Suyukou and Hongguozi segments. Large earthquakes on the EHF produced different characteristic co-seismic slips on the Suyukou segment and the Hongguozi segment of ~2.6 m and ~1.7 m, respectively. The scaling relationships between the moment magnitude, surface rupture length, and the average co-seismic slip indicate possible magnitudes within a range of Mw 6.8–7.2, and a potential magnitude of approximately Mw 7.4 as an upper bound in the case of a multi-fault rupture along the EHF. This study demonstrates the UAS-based SfM photogrammetry as an effective means for mapping fault zone topography in areas of sparse vegetation, as well as its potential for identifying and measuring subtle geomorphic features associated with past earthquakes.

Design and analysis of a computer experiment for the study of the distortion of an advanced gas-cooled reactor moderator brick

Engineering models, resolved using the finite element method, are used to model through-life changes in material properties and the resulting internal brick stresses in graphite moderator bricks within an advanced gas-cooled reactor (AGR). These models require inputs that describe the loading conditions of the moderator brick and coded relationships describing the behaviour of material properties as the brick ages. A highly multivariate spacio-temporal dataset of displacements, stresses and strains is returned as model output. In this work we describe a computer experiment conducted to study the variability in brick distortion resulting from parameter value uncertainty in the inputs to the model. We identify summary measures of brick shape and conduct global sensitivity analyses to identify the key uncertain parameters driving the variability in brick shape. Our results indicate that different measures of brick shape show sensitivities to different groups of model inputs and suggest that data obtained from core monitoring campaigns can be used to calibrate uncertain parameters in the model. Model calibration and the impact of calibration on predictions of internal brick stresses, which cannot be directly validated, are areas of current research.

Sex differences in heel pad stiffness during in vivo loading and unloading.

Due to conflicting data from previous studies a new methodological approach to evaluate heel pad stiffness and soft tissue deformation has been developed. The purpose of this study was to compare heel pad (HP) stiffness in both limbs between males and females during a dynamic unloading and loading activity. Ten males and 10 females volunteered to perform three dynamic trials to unload and load the HP. The dynamic protocol consisted of three continuous phases: foot flat (baseline phase), bilateral heel raise (unloading phase) and foot flat (loading phase) with each phase lasting two seconds. Six retroreflective markers (3 mm) were attached to the skin of the left and right heels using a customised marker set. Three‐dimensional motion analysis cameras synchronised with force plates collected the kinematic and kinetic data throughout the trials. Three‐way repeated measures ANOVA together with a Bonferroni post hoc test were applied to the stiffness and marker displacement datasets. On average, HP stiffness was higher in males than females during the loading and unloading phases. ANOVA results revealed no significant differences for the stiffness and displacement outputs with respect to sex, sidedness or phase interactions (p > .05) in the X, Y and Z directions. Irrespective of direction, there were significant differences in stiffness between the baseline and unloading conditions (p < .001) but no significant differences between the baseline and loaded conditions (p = 1.000). Post hoc analyses for the marker displacement showed significant differences between phases for the X and Z directions (p < .032) but no significant differences in the Y direction (p > .116). Finally, females portrayed lower levels of mean HP stiffness whereas males had stiffer heels particularly in the vertical direction (Z) when the HP was both unloaded and loaded. High HP stiffness values and very small marker displacements could be valuable indicators for the risk of pathological foot conditions.

System Identification of a Soil Tunnel Based on a Hybrid Artificial Neural Network–Numerical Model Approach

System identification of structures is the primary goal of this study. Numerical simulation using methods such as finite element modelling or finite difference modelling is the practical solution to model the structure based on some accurate parameter values that are essential to identify the behaviour law of the structures. An optimisation method integrated with the numerical model (NM) can solve an inverse problem to provide a calibrated parameter set to improve the modelling. For this purpose, an application of artificial neural networks (ANNs) integrated with an NM with the title “hybrid ANN–NM” approach is proposed in this study so that the parameters and resulted deformations of a developed NM of the structure would enter to a designed ANN for training the network. The developed hybrid ANN–NM method to identify the system of a tunnel excavated in the soil is applied and reported in this paper. A set of variable material parameters with a set of displacement and strain data (in $$x$$ and $$y$$ directions) of critical points of the tunnel which obtained from 2D FDM in FLAC 7.00 software is provided to train the ANN. This study is divided into two methods: (1) fitting model to the displacements and strains to show the deformation behaviour of the tunnel related to the parameter changing, and (2) fitting model to the parameters related to the displacements and strains to estimate the optimum parameters for the NM. For the first method, the parameter dataset as input and the displacements and strains as the ANN’s output in one approach separately and in another approach altogether are considered to train the ANN. In the second method, the displacements and strains as input and the physical parameters of the NM as output are submitted to train the ANN. The MSE convergence of implemented ANN shows the power of ANN to model the behaviour of structure based on the token data. Also, the RMSE of residuals refers to the success of the proposed method for the fitting model. Besides, this method was able to provide the optimum parameters for the numerical model in minimum computing time regarding the implementation of the second method.

Characteristic slip distribution and earthquake recurrence along the eastern Altyn Tagh fault revealed by high-resolution topographic data

AbstractThe seismic cycle model is roughly constrained by limited offset data sets from the eastern Altyn Tagh fault with a low slip rate. The recent availability of high-resolution topographic data from the eastern Altyn Tagh fault provides an opportunity to obtain distinctly improved quantitative, dense measurements of fault offsets. In this paper, we used airborne light detection and ranging data and unmanned aircraft vehicle photogrammetry to evaluate fault offsets. To better constrain the large earthquake recurrence model, we acquired dense data sets of fault displacements using the LaDiCaoz_v2.1 software. A total of 321 offset measurements below 30 m highlight two new observations: (1) surface-slip of the most recent earthquake and multiple events exhibit both short-wavelength (m-scale) and long-wavelength (km-scale) variability; and (2) synthesis of offset frequency analysis and coefficient of variation indicate regular slip events with ∼6 m slip increment on fault segments to the west of the Shulehe triple junction. The distribution of offsets and paleoseismological data reveal that the eastern Altyn Tagh fault exhibits characteristic slip behavior, with the characteristic slip of ∼6 m and a recurrence period ranging from 1170 to 3790 years. Paleoearthquake recurrence intervals and slip increments yield mean horizontal slip-rate estimates of 2.1–2.6 mm/yr for fault segments to the west of the Shulehe triple junction. Assuming a 10 km rupture depth and a 30 GPa shear modulus, we estimated a characteristic slip event moment magnitude (Mw) of ∼7.6. Finally, we discuss the interaction mechanism between Altyn Tagh fault (strike fault) and the NW-trending thrust faults (reverse faults) that caused the sudden decrease of sinistral slip rate at the Shulehe and Subei triple junctions; our results support the eastward “lateral slip extrusion” model.

Displacement Prediction Model for Concrete Dam Based on PSO-GBDT

Displacement plays a vital role in concrete dam safety monitoring data. It is affected by a multitude of factors such as water pressure, temperature, structure stiffness, and bottom bedrock settlement. A displacement prediction model based on gradient boosting decision tree (GBDT) is proposed to make accurate predictions. Meanwhile, particle swarm optimization (PSO) algorithm is used to optimize the model parameters, including learning rate, the trees’number, the maximum optional variables, and the maximum depth of each tree. Finally, a real-world radial displacement dataset is used to compare the performance of the PSO-GBDT model, the multiple linear regression model (MLR), and the stepwise regression model (SR). The results indicate that the PSO-GBDT model achieves the best performance. Moreover, the model can also analyse the importance of each variable, which has substantial practical value.

Probabilistic Evaluation of Off-Fault Displacements of the 2016 Kumamoto Earthquake

The 2016 Kumamoto earthquake occurred on April 16, 2016, and induced the complex distribution of surface ruptures and fault displacements, which revealed the difficulty of evaluating off-fault displacement hazards. The evaluation of off-fault displacements is necessary for the site investigation of an important facility, such as nuclear installations, but is difficult because off-fault displacements are thought to occur on unmapped or small-scale structures. A probabilistic fault displacement hazard analysis (PFDHA) assesses an off-fault displacement hazard as well as an on-fault one. Several PFDHA models have been developed from fault displacement datasets parsed by global-specific and Japanese-various faulting types. We developed a procedure to assess off-fault displacement hazards based on probabilistic and numerical simulation approaches. In the probabilistic approach, we constructed strike-slip and reverse-slip PFDHA models from a dataset of Japanese fault displacements. The off-fault components in PFDHA had a probability of non-zero off-fault displacement and an attenuation relationship. In the case of evaluating the site of an important facility, detailed field surveys were performed to collect numerous site-specific information. There is little site-specific data of off-fault displacements in Japan. The trench surveys were performed at off-fault displacement sites from the 2016 Kumamoto earthquake. The two trench sites were selected based on a linear low-coherence zone derived from the InSAR analysis, which emphasizes small-scale displacements. The excavation survey result at one site suggests a shorter recurrence interval than that of the active fault long-term evaluation. We also performed a probabilistic fault hazard analysis (PFDHA) of the trench sites by using the global strike-slip model and Japanese PFDHA models with and without the site-specific data. For the PFDHA results without site-specific data, the difference in the annual rates of exceedance between the global strike-slip and Japanese models increased with increasing fault displacements. This is because of the reduced decrease in the attenuation relationship of Japanese models. The differences in the annual rates of exceedance constrained with the site-specific data are independent of fault displacements due to variation in the probability of non-zero off-fault displacement between the global strike-slip and Japanese PFDHA models. These results suggest that the off-fault PFDHA models have high variability. In the case of PFDHA evaluation with several models, the individual PFDHA components are carefully selected by considering the individual effects. The site-specific short recurrence interval revealed by the trench survey leads to higher annual rates of exceedance.

The 2016 M7 Kumamoto, Japan, Earthquake Slip Field Derived From a Joint Inversion of Differential Lidar Topography, Optical Correlation, and InSAR Surface Displacements

AbstractObservations of surface deformation within 1–2 km of a surface rupture contain invaluable information about the coseismic behavior of the shallow crust. We investigate the oblique strike‐slip 2016 M7 Kumamoto, Japan, earthquake, which ruptured the Futagawa‐Hinagu Fault. We solve for variable fault slip in an inversion of differential lidar topography, satellite optical image correlation, and Interferometric Synthetic Aperture Radar (InSAR)‐derived surface displacements. The near‐fault differential lidar pose several challenges. The model fault geometry must follow the surface trace at the sub‐kilometer scale. Integration of displacement datasets with different sensitivities to the 3D deformation field and varying spatial distribution permits additional complexity in the inferred slip but introduces ambiguity that requires careful selection of the regularization. We infer a Mw earthquake. The maximum slip of 6.9 m occurred at 4.5‐km depth, suggesting an on‐fault slip deficit in the upper several kilometers of the crust that likely reflects distributed and inelastic deformation within the shallow fault zone.

Mapping ground displacement by a multiple phase difference-based InSAR approach: with stochastic model estimation and turbulent troposphere mitigation

Tropospheric delay is one of the dominant error sources of interferometric synthetic aperture radar when measuring ground displacement. Although many methods have been presented for the correction of tropospheric effects, a large portion of them (such as the numerical weather models and the topography-correlated analysis methods) can only be used to correct the stratified delays (i.e., topography-related delays), and it is still intractable for mitigating the turbulent effects. Considering that the approximate displacement extent over an interested region often can be known based on some prior geophysical or geological information, we present here a new method to mitigate the effects of atmospheric turbulence by fusing multiple phase differences (MPDs) between the pixel of interest and those pixels whose displacement can be ignored or can be known based on external displacement datasets (e.g., from other geodetic observations). Our method involves estimating the stochastic model, i.e., variance–covariance matrix, of the MPDs for each pixel and then reconstructing the ground displacement pixel by pixel using a proposed minimum variance-based linear estimator. Two advantages of the proposed method are that: (1) no external atmospheric data are required; (2) uncertainties of the reconstructed displacements can be provided as well. In addition, our method is implemented interferogram by interferogram, so we do not need time series of InSAR datasets. The performance of the proposed approach is tested by using both simulated datasets and the real data over Mexico City regions, and the experimental results show that our method can mitigate the turbulent atmosphere efficiently and robustly, which is of great interest to a wide community of geodesists and geophysicists.

An Improved Long Short‐Term Memory Model for Dam Displacement Prediction

Displacement plays a vital role in dam safety monitoring data, which adequately responds to security risks such as the flood water pressure, extreme temperature, structure deterioration, and bottom bedrock damage. To make accurate predictions, former researchers established various models. However, these models’ input variables cannot efficiently reflect the delays between the external environment and displacement. Therefore, a long short‐term memory (LSTM) model is proposed to make full use of the historical data to reflect the delays. Furthermore, the LSTM model is improved to optimize the performance by making variables more physically reasonable. Finally, a real‐world radial displacement dataset is used to compare the performance of LSTM models, multiple linear regression (MLR), multilayer perceptron (MLP) neural networks, support vector machine (SVM), and boosted regression tree (BRT). The results indicate that (1) the LSTM models can efficiently reflect the delays and make the variables selection more convenient and (2) the improved LSTM model achieves the best performance by optimizing the input form and network structure based on a clearer physical meaning.

Investigating paleoseismicity using fault scarp morphology of the Dushanzi Reverse Fault in the northern Tian Shan, China

This study uses the morphology of fault scarps to study the paleoseismic history of the Dushanzi Reverse Fault (DRF) in the northern Tian Shan region, China. Using high-resolution LiDAR DEMs to create a large number of scarp profiles, we detected slope breaks in the fault scarp morphology to quantify the number of paleoearthquakes that occurred on the scarps and obtained the along-strike scarp height distribution to determine the cumulative and single-event vertical displacements. Our results revealed four surface-rupturing events with similar co-seismic vertical displacements of ~1.4 m via the statistical analysis of displacement datasets and slope breaks, which were in agreement with the findings from paleoseismic trenching. We then assessed the paleomagnitudes using the empirical scaling relationships between moment magnitude and rupture parameters and the recurrence interval for surface-rupturing events using the formation ages of the displaced terrace surfaces. The results indicate that the possible magnitudes range from Mw 6.5 to 6.7, even reaching Mw ~7.2 in the case of a multi-fault rupture of the entire anticline-fault belt, with an average recurrence interval of ~2.4–3.0 ka. This study also demonstrates the importance of using high-resolution topographic data in paleoseismic investigations, which enables the determination of fine-scale tectono-geomorphic interpretations and detailed offset measurements over large regions along the fault.

Exploring Feature-Based Learning for Data-Driven Haptic Rendering.

In this work we extend ideas of machine learning to the domain of data-driven haptic rendering. The proposed approach facilitates the processing of high-dimensional haptic interaction signals, which so far proved too difficult for existing data-driven methods. The key idea is to construct a compact feature space in the frequency domain which allows for efficient data reduction via a feature selection process. First, in a recording stage, extensive force and displacement datasets are acquired in automated measurements on deformable sample objects. These data are then transformed into a dimensionally reduced, compact frequency space representation. Next, feature-based learning is carried out in this feature space to significantly reduce the size of the original dataset. Based on this, time-domain haptic models capable of real-time performance are finally generated to encode the forces arising from bimanual object interactions. The presented processing chain is generally applicable and extendable to more complex interactions with even higher-dimensional data. The resulting haptic models are directly usable for data-driven haptic rendering. We illustrate the improved performance in comparison with previously existing data-processing approaches.

Monitoring the Earthquake Cycle in the Northern Andes from the Ecuadorian cGPS Network

The continuous Global Positioning System (cGPS) network operating in the northern Andes (Ecuador and Colombia) for about a decade has the main objectives of quantifying interseismic coupling along the subduction interface, detecting occurrence of transient aseismic episodic slip, detailing the rupture kinematics of large earthquakes, recording long‐term movements along crustal faults, as well as recording swelling or deflation on the flanks of volcanoes. An opportunity to test the network’s timely registry of surface coseismic offsets was provided by the 16 April 2016 Mw 7.8 Pedernales, Ecuador, earthquake whose epicenter was along the western margin of central Ecuador, South America. This large earthquake was the biggest to occur in the northern Andes since 1979 and produced static surface offsets that were recorded by the cGPS stations operating at distances out to ∼400 km from source. Near‐field stations, operating along the Ecuadorian littoral recorded static horizontal surface displacements up to 80 cm and high‐rate GPS (HRGPS) stations recorded dynamic peak‐to‐peak displacements reaching 2 m. These measurements, together with seismic data, revealed the southward propagation of the seismic rupture, its spatial extent, and the successive breaking of two main asperities (Nocquet et al., 2017). Here, we provide the complete data set of static coseismic displacements recorded from Ecuador to southern Colombia out to 400 km from the rupture. North of the Pedernales earthquake’s foci, in the adjoining Esmeraldas‐Narino segment, some patches show high interseismic coupling and rapid strain accumulation is ongoing. In the 200‐km‐long Esmeraldas‐Narino segment, the seismic potential is particularly high. cGPS data suggest that the Esmeraldas‐Narino segment is likely a zone of future rupture.

GPS Recovery of Daily Hydrologic and Atmospheric Mass Variation: A Methodology and Results From the Australian Continent

AbstractWe present a methodology to invert a regional set of vertical displacement data from Global Positioning System (GPS) to determine the surface mass redistribution. It is assumed that GPS deformation is a result of the Earth's elastic response to the surface mass load of hydrology, atmosphere, and/or ocean. We develop an algorithm to estimate the spectral information of displacements from “regional” GPS data through regional spherical (Slepian) basis functions and apply the load Love numbers to estimate the mass load. The same approach is applied to determine global mass changes from “global” geopotential change data of Gravity Recovery and Climate Experiment (GRACE). We rigorously examine all systematic errors caused by various truncations (spherical harmonic series and Slepian series) and the smoothing constraint applied to the GPS inversion. We demonstrate the technique by processing 16 years of daily vertical motions determined from 114 GPS stations in Australia. The GPS‐inverted surface mass changes are validated against GRACE data, atmosphere and ocean models, and a land surface model. Seasonal and interannual terrestrial mass variations from GPS are in good agreement with GRACE data and the water storage models. The GPS recovery compares better with the water storage model around the smaller coastal basins than two different GRACE solutions. The submonthly mass changes from GPS provide meaningful results agreeing with atmospheric mass changes in central Australia. Finally, it is suggested to integrate GPS and GRACE data to draw a comprehensive picture of daily mass changes on different continents.

A complex elastographic hyperbolic solver (CEHS) to recover frequency dependent complex shear moduli in viscoelastic models utilizing one or more displacement data-sets

In this paper, we present a linear marching scheme to recover frequency-dependent complex shear moduli in viscoelastic models utilizing two sets of single component displacement data. The proposed method is designed to provide stable and accurate estimation of the tissue viscoelastic stiffness parameters by solving a first-order complex partial differential equation. To control the exponential growth of the numerical error resulting from one of the complex coefficients in the inverse equation, a modified upwind discretization is utilized on the first-order derivative terms of the target parameter. The algorithm is fully stablized when: (1) carefully chosen multiple data-sets are combined to eliminate the remaining complex coefficient that contributes to exponential error growth; and (2) a modified Tikhonov regularization is applied to the inversion method. We obtain the stability result in the norm so that the numerical scheme is convergent at fractional 1 / 2 order. Its performance is compared with the performance of the Algebraic Inversion Model previously investigated. We present shear modulus reconstructions from synthetic data, from laboratory phantom data and match frequency-dependent complex moduli from phantom data to several viscoelastic models. Since we have previously presented phase wave speed images from interference patterns, we exhibit those images here for comparison.

Mechanics Based Tomography: A Preliminary Feasibility Study.

We present a non-destructive approach to sense inclusion objects embedded in a solid medium remotely from force sensors applied to the medium and boundary displacements that could be measured via a digital image correlation system using a set of cameras. We provide a rationale and strategy to uniquely identify the heterogeneous sample composition based on stiffness (here, shear modulus) maps. The feasibility of this inversion scheme is tested with simulated experiments that could have clinical relevance in diagnostic imaging (e.g., tumor detection) or could be applied to engineering materials. No assumptions are made on the shape or stiffness quantity of the inclusions. We observe that the novel inversion method using solely boundary displacements and force measurements performs well in recovering the heterogeneous material/tissue composition that consists of one and two stiff inclusions embedded in a softer background material. Furthermore, the target shear modulus value for the stiffer inclusion region is underestimated and the inclusion size is overestimated when incomplete boundary displacements on some part of the boundary are utilized. For displacements measured on the entire boundary, the shear modulus reconstruction improves significantly. Additionally, we observe that with increasing number of displacement data sets utilized in solving the inverse problem, the quality of the mapped shear moduli improves. We also analyze the sensitivity of the shear modulus maps on the noise level varied between 0.1% and 5% white Gaussian noise in the boundary displacements, force and corresponding displacement indentation. Finally, a sensitivity analysis of the recovered shear moduli to the depth, stiffness and the shape of the stiff inclusion is performed. We conclude that this approach has potential as a novel imaging modality and refer to it as Mechanics Based Tomography (MBT).

Test Suite for Image-Based Motion Estimation of the Brain and Tongue.

Noninvasive analysis of motion has important uses as qualitative markers for organ function and to validate biomechanical computer simulations relative to experimental observations. Tagged MRI is considered the gold standard for noninvasive tissue motion estimation in the heart, and this has inspired multiple studies focusing on other organs, including the brain under mild acceleration and the tongue during speech. As with other motion estimation approaches, using tagged MRI to measure 3D motion includes several preprocessing steps that affect the quality and accuracy of estimation. Benchmarks, or test suites, are datasets of known geometries and displacements that act as tools to tune tracking parameters or to compare different motion estimation approaches. Because motion estimation was originally developed to study the heart, existing test suites focus on cardiac motion. However, many fundamental differences exist between the heart and other organs, such that parameter tuning (or other optimization) with respect to a cardiac database may not be appropriate. Therefore, the objective of this research was to design and construct motion benchmarks by adopting an "image synthesis" test suite to study brain deformation due to mild rotational accelerations, and a benchmark to model motion of the tongue during speech. To obtain a realistic representation of mechanical behavior, kinematics were obtained from finite-element (FE) models. These results were combined with an approximation of the acquisition process of tagged MRI (including tag generation, slice thickness, and inconsistent motion repetition). To demonstrate an application of the presented methodology, the effect of motion inconsistency on synthetic measurements of head-brain rotation and deformation was evaluated. The results indicated that acquisition inconsistency is roughly proportional to head rotation estimation error. Furthermore, when evaluating non-rigid deformation, the results suggest that inconsistent motion can yield "ghost" shear strains, which are a function of slice acquisition viability as opposed to a true physical deformation.

Experimental analysis of the shear behaviour of prestressed and reinforced concrete beams

This paper presents the detailed experimental results of 23 full-scale rectangular and I-shaped prestressed and reinforced concrete beams. All beams were designed to fail in shear and were subjected to a four-point bending test with monotonically increasing load until failure. The main investigated parameters were the amount of prestressing, the amount of longitudinal and shear reinforcement ratio and the shear span-to-effective depth ratio respectively. An extensive set of displacement and deformation data were gathered during the experiments using both traditional mechanical measurement devices and advanced optical(-numerical) measurement techniques. The experimentally measured failure loads are compared to analytical predictions obtained from current Eurocode 2 shear design equations. In general, a poor correlation was found between the reported experimental results and analytical predictions (mean experimental to predicted failure load ratio equal to 1.77; coefficient of variation equal to 31.6%). Based on the measured deformation fields, it was observed that, in the case of rectangular beams and prestressed I-shaped beams with shear reinforcement, the applied load is primarily carried by means of a direct compression strut which significantly increased the failure load.

A nonlinear population Monte Carlo scheme for the Bayesian estimation of parameters of [formula omitted]-stable distributions

The class of α-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general α-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an α-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the α-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of α, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided.

Robust and Fast Probabilistic Source Parameter Estimation from Near‐Field Displacement Waveforms Using Pattern Recognition

The robust and automated determination of earthquake source parameters on a global and regional scale is important for many applications in seismology. We present a novel probabilistic method to invert a wide variety of (waveform) data for point‐source parameters in real time using pattern recognition. Inferences are made in the form of marginal probability density functions for point‐source parameters and incorporate realistic posterior uncertainty estimates. The neural‐network‐based method is calibrated using samples from the prior distribution, which are synthetic data vectors, and corresponding sources located in a predefined monitoring volume. Once a set of trained neural networks is available, inversions are fast with very moderate demands on computational resources: an inversion takes less than a second on a standard desktop computer. Uncertainties in the layered Earth model are taken into account in the Bayesian framework and increase the robustness of the results with respect to neglected 3D heterogeneities. Moreover, we find that the method is very robust with respect to perturbations such as observational noise and missing data and therefore is potentially well suited for automated and real‐time tasks, such as earthquake monitoring and early warning. We demonstrate the method by means of synthetic tests and by inverting an observed high‐rate Global Positioning System displacement dataset for the 2010 M w 7.2 El Mayor–Cucapah event. Our results are compatible with published point‐source estimates for this event within the respective uncertainty bounds. Online Material: Additional information on the neural network methodology and implementation details, tables on neural network parameters, crustal model and reference double‐couple solution, and figures showing prediction error, crustal models, normalized displacements, and histograms of weighted parameters.