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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in an accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Multiparameter Methods are the New Field in Statistics

During the last decade statistical problems of a new kind have appeared more and more often, in which the dimensionality of observations is large, and the sample size is small or comparable with the dimensionality of observations. These problems may be characterized as multiparameter problems. The theory of multiparameter analysis, proposed by A.N.Kolmogorov and supported by the studies on the spectral theory of random matrices of V. A.Marchenko, L. A.Pastur, V. L.Girko, and others, revealed some specific phenomena appearing in statistics with a large number of weakly dependent variables. Particularly, there are stable relations between the principal parts of parameter set functions and the set of observed variables, which may be used to improve the statistical analysis. The use of these phenomena allows one to develop a thorough, always stable, and approximately optimal (irrespective of samples) versions of mostly used statistical procedures. The multiparameter versions of the discriminant analysis are of special interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Extension of the Concept of Invariance and Statistically Weakly Invariant Sets of Controllable Systems

We continue the study of statistically invariant and statistically weakly invariant sets with respect to controllable systems and differential inclusions launched by Prof. E. L. Tonkov. We examine properties of such statistical characteristics as the lower freq{sub *}(𝜑) and upper freq{sup *}(𝜑) relative frequencies of hitting a solution 𝜑(t) of a differential inclusion in a prescribed set. We obtain estimates and conditions of coincidence of these characteristics for functions whose difference tends to zero at infinity. We also present conditions of statistically weak invariance of a given set of a relatively controllable system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Statistically informed upscaling of damage evolution in brittle materials

The presence and growth of micro-cracks degrade the strength of brittle solids, greatly impacting the overall material response. Hence, the evolution of these micro-cracks must be accounted for in models describing the relationship between stress and strain so that accurate predictions of material failure can be made. The evolution of individual cracks and crack networks can be simulated with high-fidelity microscale models utilizing highly resolved meshes that can be computationally expensive to a point in which it limits the simulation scale. Hence, for many engineering applications that require simulations of large components, continuum-scale models, which cannot explicitly resolve individual cracks and thus lose important physical information, are required. In this work, we bridge these two scales by developing and implementing a continuum-scale effective moduli constitutive model that is informed by crack statistics generated from a high-fidelity model resolved using a finite-discrete element method (FDEM) implementation. Using statistical information describing the evolution of crack lengths and orientations, this model can capture the effects of brittle damage evolution without the need to resolve individual cracks. We have successfully captured the stress-strain behavior of the high-fidelity simulations using the statistics-based constitutive model shown through direct comparison of stress-strain curves. The curves match within error bars present in the strain-softening portions of the stress-strain curve of the high-fidelity results due to the statistical variation of the initial pre-existing crack network. In conclusion, the stress-strain curves are also compared to experimental results for similar loading conditions and show good qualitative agreement.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

Here, we statistically infer fluid flow and transport properties of porous materials based on their geometry and connectivity, without the need for detailed We summarize structure by persistent homology and then determines the similarity of structures using image analysis and statistics. Longer term, this may enable quick and automated categorization of rocks into known archetypes. We first compute persistent homology of binarized 3D images of material subvolume samples. The persistence parameter is the signed Euclidean distance from inferred material interfaces, which captures the distribution of sizes of pores and grains. Each persistence diagram is converted into an image vector. Here, we infer structural similarity by calculating image similarity. For each image vector, we compute principal components to extract features. We fit statistical models to features estimates material permeability, tortuosity, and anisotropy. We develop a Structural SIMilarity index to determine statistical representative elementary volumes.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles

In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [“An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are also compared to those based on a deterministic forcing scheme to better understand the role of large-scale forcing, relative to that of the small-scale turbulence, on turbulent collision of inertial particles. To further elucidate the correlation between the altered flow structures and dynamics of inertial particles, a conditional analysis has been performed, showing that the regions of higher collision rate of inertial particles are well correlated with the regions of lower vorticity. Regions of higher concentration of pairs at contact are found to be highly correlated with the region of high energy dissipation rate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Monte Carlo simulations of time-of-flight PET with double-ended readout: calibration, coincidence resolving times and statistical lower bounds

Here, this paper demonstrates through Monte Carlo simulations that a practical positron emission tomograph with (1) deep scintillators for efficient detection, (2) double-ended readout for depth-of-interaction information, (3) fixed-level analog triggering, and (4) accurate calibration and timing data corrections can achieve a coincidence resolving time (CRT) that is not far above the statistical lower bound. One Monte Carlo algorithm simulates a calibration procedure that uses data from a positron point source. Annihilation events with an interaction near the entrance surface of one scintillator are selected, and data from the two photodetectors on the other scintillator provide depth-dependent timing corrections. Another Monte Carlo algorithm simulates normal operation using these corrections and determines the CRT. A third Monte Carlo algorithm determines the CRT statistical lower bound by generating a series of random interaction depths, and for each interaction a set of random photoelectron times for each of the two photodetectors. The most likely interaction times are determined by shifting the depth-dependent probability density function to maximize the joint likelihood for all the photoelectron times in each set. Example calculations are tabulated for different numbers of photoelectrons and photodetector time jitters for three 3 × 3 × 30 mm 3 scintillators: Lu 2 SiO 5 :Ce,Ca (LSO), LaBr 3 :Ce, and a hypothetical ultra-fast scintillator. To isolate the factors that depend on the scintillator length and the ability to estimate the DOI, CRT values are tabulated for perfect scintillator-photodetectors. For LSO with 4000 photoelectrons and single photoelectron time jitter of the photodetector J = 0.2 ns (FWHM), the CRT value using the statistically weighted average of corrected trigger times is 0.098 ns FWHM and the statistical lower bound is 0.091 ns FWHM. For LaBr 3 :Ce with 8000 photoelectrons and J = 0.2 ns FWHM, the CRT values are 0.070 and 0.063 ns FWHM, respectively. For the ultra-fast scintillator with 1 ns decay time, 4000 photoelectrons, and J = 0.2 ns FWHM, the CRT values are 0.021 and 0.017 ns FWHM, respectively. Lastly, the examples also show that calibration and correction for depth-dependent variations in pulse height and in annihilation and optical photon transit times are necessary to achieve these CRT values.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Cosmology constraints from shear peak statistics in Dark Energy Survey Science Verification data

Shear peak statistics has gained a lot of attention recently as a practical alternative to the two point statistics for constraining cosmological parameters. We perform a shear peak statistics analysis of the Dark Energy Survey (DES) Science Verification (SV) data, using weak gravitational lensing measurements from a 139 deg$^2$ field. We measure the abundance of peaks identified in aperture mass maps, as a function of their signal-to-noise ratio, in the signal-to-noise range $0<\mathcal S / \mathcal N<4$. To predict the peak counts as a function of cosmological parameters we use a suite of $N$-body simulations spanning 158 models with varying $\Omega_{\rm m}$ and $\sigma_8$, fixing $w = -1$, $\Omega_{\rm b} = 0.04$, $h = 0.7$ and $n_s=1$, to which we have applied the DES SV mask and redshift distribution. In our fiducial analysis we measure $\sigma_{8}(\Omega_{\rm m}/0.3)^{0.6}=0.77 \pm 0.07$, after marginalising over the shear multiplicative bias and the error on the mean redshift of the galaxy sample. We introduce models of intrinsic alignments, blending, and source contamination by cluster members. These models indicate that peaks with $\mathcal S / \mathcal N>4$ would require significant corrections, which is why we do not include them in our analysis. We compare our results to the cosmological constraints from the two point analysis on the SV field and find them to be in good agreement in both the central value and its uncertainty. As a result, we discuss prospects for future peak statistics analysis with upcoming DES data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations

ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Bias Correction and Statistical Downscaling of Future Solar Irradiance Projections Using the NSRDB

Assessing renewable energy resources under future climate scenarios has been highlighted to understand potential impacts of future climate change in renewable generation on the power sector. Climate model projection has been recognized by the renewable energy community as a useful data set to analyze the impacts of future climate change on renewable resources. However, future climate projections generated from general circulation models (GCMs) contain inherent biases that need to be corrected for accurate analysis of future projections of climate variables. In addition, the coarse spatiotemporal resolution of GCMs needs to be improved for regional climate studies. In this work, we develop statistical methods to downscale future projections of global horizontal irradiance (GHI) in a computationally efficient way. Our approach builds statistical downscaling models that correct bias of climate projection of GHI and downscale the future GHI projection from daily-scale to hourly-scale. The National Solar Radiation Database (NSRDB) is used to calibrate the statistical models and validate the downscaled GHI projections across the contiguous United State (CONUS). Preliminary results show that the statistical approach efficiently downscales climate projections of GHI with a nBIAS of 3%, nMAE of 34 % and nRMSE of 46% calculated against NSRDB for CONUS. This study describes the implemented methodology and initial results as well as future research to create high-resolution climate data sets for solar energy applications.

analytical models↗
DOE OSTI2018

Validation of a Statistical Methodology for Extracting Vegetation Feedbacks: Focus on North African Ecosystems in the Community Earth System Model

Generalized equilibrium feedback assessment (GEFA) is a potentially valuable multivariate statistical tool for extracting vegetation feedbacks to the atmosphere in either observations or coupled Earth system models. The reliability of GEFA at capturing the terrestrial impacts on regional climate is demonstrated here using the National Center for Atmospheric Research Community Earth System Model (CESM), with focus on North Africa. The feedback is assessed statistically by applying GEFA to output from a fully coupled control run. To reduce the sampling error caused by short data records, the traditional or full GEFA is refined through stepwise GEFA by dropping unimportant forcings. Two ensembles of dynamical experiments are developed for the Sahel or West African monsoon region against which GEFA-based vegetation feedbacks are evaluated. In these dynamical experiments, regional leaf area index (LAI) is modified either alone or in conjunction with soil moisture, with the latter runs motivated by strong regional soil moisture–LAI coupling. Stepwise GEFA boasts higher consistency between statistically and dynamically assessed atmospheric responses to land surface anomalies than full GEFA, especially with short data records. GEFA-based atmospheric responses are more consistent with the coupled soil moisture–LAI experiments, indicating that GEFA is assessing the combined impacts of coupled vegetation and soil moisture. Both the statistical and dynamical assessments reveal a negative vegetation–rainfall feedback in the Sahel associated with an atmospheric stability mechanism in CESM versus a weaker positive feedback in the West African monsoon region associated with a moisture recycling mechanism in CESM.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Detection of Spatiotemporal Prescription Opioid Hot Spots With Network Scan Statistics: Multistate Analysis

Background: Overuse and misuse of prescription opioids have become significant public health burdens in the United States. About 11.5 million people are estimated to have misused prescription opioids for nonmedical purposes in 2016. This has led to a significant number of drug overdose deaths in the United States. Previous studies have examined spatiotemporal clusters of opioid misuse, but they have been restricted to circular shaped regions. Objective: The goal of this study was to identify spatiotemporal hot spots of opioid users and opioid prescription claims using Medicare data. Methods: We examined spatiotemporal clusters with significantly higher number of beneficiaries and rate of prescriptions for opioids using Medicare payment data from the Centers for Medicare & Medicaid Services. We used network scan statistics to detect significant clusters with arbitrary shapes, the Kulldorff scan statistic to examine the significant clusters for each year (2013, 2014, and 2015) and an expectation-based version to examine the significant clusters relative to past years. Regression analysis was used to characterize the demographics of the counties that are a part of any significant cluster, and data mining techniques were used to discover the specialties of the anomalous providers. Results: We examined anomalous spatial clusters with respect to opioid prescription claims and beneficiary counts and found some common patterns across states: the counties in the most anomalous clusters were fairly stable in 2014 and 2015, but they have shrunk from 2013. In Virginia, a higher percentage of African Americans in a county lower the odds of the county being anomalous in terms of opioid beneficiary counts to about 0.96 in 2015. For opioid prescription claim counts, the odds were 0.92. This pattern was consistent across the 3 states and across the 3 years. A higher number of people in the county with access to Medicaid increased the odds of the county being in the anomalous cluster to 1.16 in both types of counts in Virginia. A higher number of people with access to direct purchase of insurance plans decreased the odds of a county being in an anomalous cluster to 0.85. The expectation-based scan statistic, which captures change over time, revealed different clusters than the Kulldorff statistic. Providers with an unusually high number of opioid beneficiaries and opioid claims include specialties such as physician’s assistant, nurse practitioner, and family practice. Conclusions: Our analysis of the Medicare claims data provides characteristics of the counties and provider specialties that have higher odds of being anomalous. The empirical analysis identifies highly refined spatial hot spots that are likely to encounter prescription opioid misuse and overdose. The methodology is generic and can be applied to monitor providers and their prescription behaviors in regions that are at a high risk of abuse.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

To have value, comparisons of high-throughput phenotyping methods need statistical tests of bias and variance

The gap between genomics and phenomics is narrowing. The rate at which it is narrowing, however, is being slowed by improper statistical comparison of methods. Quantification using Pearson’s correlation coefficient ( r ) is commonly used to assess method quality, but it is an often misleading statistic for this purpose as it is unable to provide information about the relative quality of two methods. Using r can both erroneously discount methods that are inherently more precise and validate methods that are less accurate. These errors occur because of logical flaws inherent in the use of r when comparing methods, not as a problem of limited sample size or the unavoidable possibility of a type I error. A popular alternative to using r is to measure the limits of agreement (LOA). However both r and LOA fail to identify which instrument is more or less variable than the other and can lead to incorrect conclusions about method quality. An alternative approach, comparing variances of methods, requires repeated measurements of the same subject, but avoids incorrect conclusions. Variance comparison is arguably the most important component of method validation and, thus, when repeated measurements are possible, variance comparison provides considerable value to these studies. Statistical tests to compare variances presented here are well established, easy to interpret and ubiquitously available. The widespread use of r has potentially led to numerous incorrect conclusions about method quality, hampering development, and the approach described here would be useful to advance high throughput phenotyping methods but can also extend into any branch of science. The adoption of the statistical techniques outlined in this paper will help speed the adoption of new high throughput phenotyping techniques by indicating when one should reject a new method, outright replace an old method or conditionally use a new method.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

AN EXPLORATION OF THE STATISTICAL SIGNATURES OF STELLAR FEEDBACK

All molecular clouds are observed to be turbulent, but the origin, means of sustenance, and evolution of the turbulence remain debated. One possibility is that stellar feedback injects enough energy into the cloud to drive observed motions on parsec scales. Recent numerical studies of molecular clouds have found that feedback from stars, such as protostellar outflows and winds, injects energy and impacts turbulence. We expand upon these studies by analyzing magnetohydrodynamic simulations of molecular clouds, including stellar winds, with a range of stellar mass-loss rates and magnetic field strengths. We generate synthetic {sup 12}CO(1–0) maps assuming that the simulations are at the distance of the nearby Perseus molecular cloud. By comparing the outputs from different initial conditions and evolutionary times, we identify differences in the synthetic observations and characterize these using common astrostatistics. We quantify the different statistical responses using a variety of metrics proposed in the literature. We find that multiple astrostatistics, including the principal component analysis, the spectral correlation function, and the velocity coordinate spectrum (VCS), are sensitive to changes in stellar mass-loss rates and/or time evolution. A few statistics, including the Cramer statistic and VCS, are sensitive to the magnetic field strength. These findings demonstrate that stellar feedback influences molecular cloud turbulence and can be identified and quantified observationally using such statistics.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

Preliminary Statistical Maneuver Analysis for A Low-Thrust NRHO to DRO Transfer

To understand practical implications of implementing transfers that leverage multibody dynamics, a statistical analysis is performed on an Earth-Moon Near Rectilinear Halo Orbit (NRHO) to distant retrograde orbit (DRO) transfer using solar electric propulsion. The statistical analysis includes perturbations due to maneu- ver execution and orbit determination error to understand operational character- istics of the transfer such as statistical ∆V and statistical state targeting errors at the final DRO. We explore the need for low-thrust trajectory correction maneuver (TCM) opportunities as well as the delivery accuracy to the final target. Finally, we explore options for long-term-stable target DROs.

low thrust↗
DOE OSTI2015

North American extreme temperature events and related large scale meteorological patterns: A review of statistical methods, dynamics, modeling, and trends

This paper reviews research approaches and open questions regarding data, statistical analyses, dynamics, modeling efforts, and trends in relation to temperature extremes. Our specific focus is upon extreme events of short duration (roughly less than 5 days) that affect parts of North America. These events are associated with large scale meteorological patterns (LSMPs). Methods used to define extreme events statistics and to identify and connect LSMPs to extreme temperatures are presented. Recent advances in statistical techniques can connect LSMPs to extreme temperatures through appropriately defined covariates that supplements more straightforward analyses. A wide array of LSMPs, ranging from synoptic to planetary scale phenomena, have been implicated as contributors to extreme temperature events. Current knowledge about the physical nature of these contributions and the dynamical mechanisms leading to the implicated LSMPs is incomplete. There is a pressing need for (a) systematic study of the physics of LSMPs life cycles and (b) comprehensive model assessment of LSMP-extreme temperature event linkages and LSMP behavior. Generally, climate models capture the observed heat waves and cold air outbreaks with some fidelity. However they overestimate warm wave frequency and underestimate cold air outbreaks frequency, and underestimate the collective influence of low-frequency modes on temperature extremes. Climate models have been used to investigate past changes and project future trends in extreme temperatures. Overall, modeling studies have identified important mechanisms such as the effects of large-scale circulation anomalies and land-atmosphere interactions on changes in extreme temperatures. However, few studies have examined changes in LSMPs more specifically to understand the role of LSMPs on past and future extreme temperature changes. Even though LSMPs are resolvable by global and regional climate models, they are not necessarily well simulated so more research is needed to understand the limitations of climate models and improve model skill in simulating extreme temperatures and their associated LSMPs. Furthermore, the paper concludes with unresolved issues and research questions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Statistical tests on clustered global earthquake synthetic data sets

Abstract We study the ability of statistical tests to identify nonrandom features of earthquake catalogs, with a focus on the global earthquake record since 1900. We construct four types of synthetic data sets containing varying strengths of clustering, with each data set containing on average 10,000 events over 100 years with magnitudes above M = 6. We apply a suite of statistical tests to each synthetic realization in order to evaluate the ability of each test to identify the sequences of events as nonrandom. Our results show that detection ability is dependent on the quantity of data, the nature of the type of clustering, and the specific signal used in the statistical test. Data sets that exhibit a stronger variation in the seismicity rate are generally easier to identify as nonrandom for a given background rate. We also show that we can address this problem in a Bayesian framework, with the clustered data sets as prior distributions. Using this new Bayesian approach, we can place quantitative bounds on the range of possible clustering strengths that are consistent with the global earthquake data. At M = 7, we can estimate 99th percentile confidence bounds on the number of triggered events, with an upper bound of 20% of the catalog for global aftershock sequences, with a stronger upper bound on the fraction of triggered events of 10% for long‐term event clusters. At M = 8, the bounds are less strict due to the reduced number of events. However, our analysis shows that other types of clustering could be present in the data that we are unable to detect. Our results aid in the interpretation of the results of statistical tests on earthquake catalogs, both worldwide and regionally.

Daub, Eric G.↗