Search NASA⌕ Search

SEARCH · Search NASA

Results for “Bayesian Analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,225 records · Page 68

Which Combinations of Environmental Conditions and Microphysical Parameter Values Produce a Given Orographic Precipitation Distribution?

This study applies an idealized modeling framework, alongside a Bayesian Markov chain Monte Carlo (MCMC) algorithm, to explore which combinations of upstream environmental conditions and cloud microphysical parameter values can produce a particular precipitation distribution over an idealized two-dimensional, bell-shaped mountain. Simulations focus on orographic precipitation produced when an atmospheric river interacts with topography. MCMC-based analysis reveals that different combinations of parameter values produce a similar precipitation distribution, with the most influential parameters being relative humidity (RH), horizontal wind speed (U), surface potential temperature (θ sfc ), and the snow fall speed coefficient (A s ). RH, U, and A s exhibit interdependence: changes in one or more of these factors can be mitigated by compensating changes in the other(s) to produce similar orographic precipitation rates. The results also indicate that the parameter sensitivities and relationships can vary for spatial subregions and given different environmental conditions. In particular, high θ sfc values are more likely to produce the target precipitation rate and spatial distribution, and thus the ensemble of simulations shows a preference for liquid precipitation at the surface. The results presented here highlight the complexity of orographic precipitation controls, and have implications for flood and water management, observational efforts, and climate change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

THREE-DIMENSIONAL VELOCITY AND DENSITY RECONSTRUCTIONS OF THE LOCAL UNIVERSE WITH COSMICFLOWS-1

This paper presents an analysis of the local peculiar velocity field based on the Wiener Filter (WF) reconstruction method. We used our currently available catalog of distance measurements containing 1797 galaxies within 3000 km s{sup -1}: Cosmicflows-1. The WF method is used to recover the full three-dimensional peculiar velocity field from the observed map of radial velocities and to recover the underlying linear density field. The velocity field within a data zone of 3000 km s{sup -1} is decomposed into a local component that is generated within the data zone and a tidal one that is generated by the mass distribution outside that zone. The tidal component is characterized by a coherent flow toward the Norma-Hydra-Centaurus (Great Attractor) region, while the local component is dominated by a flow toward the Virgo Cluster and away from the Local Void. A detailed analysis shows that the local flow is predominantly governed by the Local Void and the Virgo Cluster plays a lesser role. The analysis procedure was tested against a mock catalog. It is demonstrated that the WF accurately recovers the input velocity field of the mock catalog on the scale of the extraction of distances and reasonably recovers the velocity field on significantly larger scales. The Bayesian WF reconstruction is carried out within the {Lambda}CDM WMAP5 framework. The WF reconstruction draws particular attention to the importance of voids in proximity to our neighborhood. The prominent structure of the Local Supercluster is wrapped in a horseshoe collar of under density with the Local Void as a major component.

79 ASTRONOMY AND ASTROPHYSICS↗

Exploring soybean metabolic pathways based on probabilistic graphical model and knowledge-based methods

Soybean (Glycine max) is a major source of vegetable oil and protein for both animal and human consumption. The completion of soybean genome sequence led to a number of transcriptomic studies (RNA-seq), which provide a resource for gene discovery and functional analysis. Several data-driven (e.g., based on gene expression data) and knowledge-based (e.g., predictions of molecular interactions) methods have been proposed and implemented. In order to better understand gene relationships and protein interactions, we applied probabilistic graphical methods, based on Bayesian network and knowledgebase constraints using gene expression data to reconstruct soybean metabolic pathways. The results show that this method can predict new relationships between genes, improving on traditional reference pathway maps.

54 ENVIRONMENTAL SCIENCES↗

A Framework for Quantifying Measurement Uncertainties and Uncertainty Propagation in HCCI/LTGC Engine Experiments

In this study, a framework for estimating experimental measurement uncertainties for a Homogenous Charge Compression Ignition (HCCI)/Low-Temperature Gasoline Combustion (LTGC) engine testing facility is presented. Detailed uncertainty quantification is first carried out for the measurement of the in-cylinder pressure, whose variations during the cycle provide most of the information for performance evaluation. Standard uncertainties of other measured quantities, such as the engine geometry and speed, the air and fuel flow rate and the intake/exhaust dry molar fractions are also estimated. Propagating those uncertainties using a Monte Carlo simulation and Bayesian inference methods then allows for estimation of uncertainties of the mass-average temperature and composition at IVC and throughout the cycle; and also of the engine performances such as gross Integrated Mean Effective Pressure, Heat Release and Ringing Intensity. Throughout the analysis, nominal values for uncertainty inputs were taken from a well-characterized engine test facility. However, the analysis did not take into account the calibration practice of experiments run in that facility and the resulting uncertainty values are therefore not indicative of the expected accuracy of those experimental results. A future study will employ the methodology developed here to explore the effects of different calibration methods on the different uncertainty values in order to evaluate best practices for accurate engine measurements.

02 PETROLEUM↗

The 4 Ms CHANDRA Deep Field-South Number Counts Apportioned by Source Class: Pervasive Active Galactic Nuclei and the Ascent of Normal Galaxies

We present 0.5-2 keV, 2-8 keV, 4-8 keV, and 0.5-8 keV (hereafter soft, hard, ultra-hard, and full bands, respectively) cumulative and differential number-count (log N-log S ) measurements for the recently completed approx. equal to 4 Ms Chandra Deep Field-South (CDF-S) survey, the deepest X-ray survey to date. We implement a new Bayesian approach, which allows reliable calculation of number counts down to flux limits that are factors of approx. equal to 1.9-4.3 times fainter than the previously deepest number-count investigations. In the soft band (SB), the most sensitive bandpass in our analysis, the approx. equal to 4 Ms CDF-S reaches a maximum source density of approx. equal to 27,800 deg(sup -2). By virtue of the exquisite X-ray and multiwavelength data available in the CDF-S, we are able to measure the number counts from a variety of source populations (active galactic nuclei (AGNs), normal galaxies, and Galactic stars) and subpopulations (as a function of redshift, AGN absorption, luminosity, and galaxy morphology) and test models that describe their evolution. We find that AGNs still dominate the X-ray number counts down to the faintest flux levels for all bands and reach a limiting SB source density of approx. equal to 14,900 deg(sup -2), the highest reliable AGN source density measured at any wavelength. We find that the normal-galaxy counts rise rapidly near the flux limits and, at the limiting SB flux, reach source densities of approx. equal to 12,700 deg(sup -2) and make up 46% plus or minus 5% of the total number counts. The rapid rise of the galaxy counts toward faint fluxes, as well as significant normal-galaxy contributions to the overall number counts, indicates that normal galaxies will overtake AGNs just below the approx. equal to 4 Ms SB flux limit and will provide a numerically significant new X-ray source population in future surveys that reach below the approx. equal to 4 Ms sensitivity limit. We show that a future approx. equal to 10 Ms CDF-S would allow for a significant increase in X-ray-detected sources, with many of the new sources being cosmologically distant (z greater than or approx. equal to 0.6) normal galaxies.

Field-South↗

Modeling the Swift BAT trigger algorithm with machine learning

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift/BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien et al. is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of ≳97% (≲3% error), which is a significant improvement on a cut in GRB flux, which has an accuracy of 89.6% (10.4% error). These models are then used to measure the detection efficiency of Swift as a function of redshift z, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of n{sub 0}∼0.48{sub −0.23}{sup +0.41} Gpc{sup −3} yr{sup −1} with power-law indices of n{sub 1}∼1.7{sub −0.5}{sup +0.6} and n{sub 2}∼−5.9{sub −0.1}{sup +5.7} for GRBs above and below a break point of z{sub 1}∼6.8{sub −3.2}{sup +2.8}. This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling the Effect of Surface Platinum–Tin Alloys on Propane Dehydrogenation on Platinum–Tin Catalysts

Uncertainty analysis, reported experimental literature data, and density functional theory were synthesized to model the effect of surface tin coverage on platinum-based catalysts for nonoxidative propane dehydrogenation to propylene. Here, this study tests four different platinum–tin skin surface models as potential catalytic sites, Pt 3 Sn/Pt(100), PtSn/Pt(100), Pt 3 Sn/Pt(111), and Pt 2 Sn/Pt(211), and compares them to the corresponding pure Pt surface sites using an uncertainty analysis methodology that uses BEEF-vdW with its ensembles (BMwE) to generate the uncertainty for the energies of the intermediates and transition states. One experimental data set with two experimental observations, selectivity to propylene and turnover frequency of propylene, was used as a calibration data set to evaluate the impact of the experimental data on informing the models. This study finds that the prior model for Pt 3 Sn/Pt(100) is the most active and Pt 2 Sn/Pt(211) is the most selective toward propylene. Active sites on the (100) facet have the highest probability of being responsible for C 1 and C 2 product formations (C–C bond cleavage). Increasing the Sn coverage on the (100) surface facet to a PtSn/Pt(100) active site leads to a significantly reduced rate and might explain the experimentally observed higher selectivity of Sn-doped catalysts relative to pure Pt catalysts. Next, this study finds that for all surfaces, except PtSn/Pt(100), the rate-controlling steps are the initial dehydrogenation steps alongside some partially rate-controlling second dehydrogenation steps. For PtSn/Pt(100), only the initial terminal dehydrogenation step to CH 3 CH 2 CH 2 * and second dehydrogenation steps are rate-controlling. Next, the calibrated models for all surfaces were found to be selective toward propylene production and model the reported turnover frequency successfully. Nevertheless, Pt 2 Sn/Pt(211) emerges as the active site with some (minor) evidence as the main active site based on Jeffreys’ scale interpretation of Bayes factors. This observation agrees with prior studies that also found step sites to be most likely the most relevant active sites for pure Pt catalysts. Overall, the results indicate that tin, in addition to affecting the binding strength of the adsorbed species, prevents deeper dehydrogenation (reducing coking) and cracking reactions through increasing activation barriers for unwanted side reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a framework for sequential Bayesian design of experiments: Application to a pilot-scale solvent-based CO 2 capture process

In this paper, a methodology is developed for sequential design of experiments (SDoE) for process systems and applied to a solvent-based CO 2 capture system. In this approach, the prior knowledge of the system is used to prioritize process data collection at specific operating conditions. These data are then incorporated into a Bayesian inference methodology for updating a stochastic model by refining estimations of its underlying parameters, and the updated model is then used to generate the next set of test runs. Thus, the new knowledge obtained from the data is used to guide subsequent iterations of the experimental runs, ensuring that the overall data collection is maximally informative given that most experimental campaigns, especially at pilot or higher-scale plants, are costly, time-consuming, and resource-limited. The test run objective for this work was to minimize the maximum model prediction uncertainty for key output variables, but the methodology is generic and can be readily applied to other test run objectives. This methodology is applied to an aqueous monoethanolamine (MEA) pilot plant campaign at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama, USA. The SDoE framework was utilized for two iterations, while collecting 18 sets of data representing different process conditions, and this resulted in an overall average reduction in uncertainty of approximately 50% in the prediction of CO 2 capture percentage. Moreover, 11 additional data sets were obtained with variation of absorber packing height for further model validation. This work shows the capability of the SDoE framework to maximize learning given limited resources, allowing for the reduction of model uncertainty, which is of great importance for many applications including reduction of technical risk associated with scale-up and economic analysis.

20 FOSSIL-FUELED POWER PLANTS↗

ZEM: Integrated Framework for Real-Time Data and Model Analyses for Robust Environmental Management Decision Making - 16438

Typically environmental management (EM) problems require analysis of large and complex data sets originating from concurrent data streams with different data collection frequencies and pedigree. These big data sets require on-the-fly analysis, assimilation and integration into a series of models with different complexity for various types of model-based analyses. This is needed to provide fast iterative model analyses based on the latest available data to guide decision-making. Furthermore, the data and model are associated with uncertainties. The uncertainties are probabilistic (e.g. measurement errors) and non-probabilistic (unknowns, e.g. alternative conceptual models characterizing site conditions). To address all of these issues, we have developed an integrated framework for real-time data and model analyses for environmental decision-making called ZEM. The framework allows for seamless and on-the-fly integration of data and modeling results for robust and scientifically-defensible decision-making applying advanced decision analyses tools such as Bayesian-Information-Gap Decision Theory (BIG-DT). The framework also includes advanced methods for optimization that are capable of dealing with a large number of unknown model parameters, and surrogate (reduced order) modeling capabilities based on support vector regression techniques. The framework is predominantly coded in Julia, a state-of-the-art high-performance programing language (http://julialang.org) and incorporates the MADS computational tools (Model Analysis and Decision Support; http://mads.lanl.gov). We demonstrate the application of ZEM for data and model analyses at the LANL Chromium site. The ZEM framework will be released as open-source code and can be applied to any environmental management site. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Integrating GLL-Weibull Distribution Within a Bayesian Framework for Life Prediction of Shape Memory Alloy Spring Undergoing Thermo-mechanical Fatigue

The present paper tackles an important but unmapped problem of the reliability estimations of smart materials. First, an experimental setup is developed for accelerated life testing of the shape memory alloy (SMA) springs. Generalized log-linear Weibull (GLL-Weibull) distribution-based novel approach is then developed for SMA spring life estimation. Applied stimulus (voltage), elongation and cycles of operation are used as inputs for the life prediction model. The values of the parameter coefficients of the model provide better interpretability compared to artificial intelligence based life prediction approaches. In addition, the model also considers the effect of operating conditions, making it generic for a range of the operating conditions. Moreover, a Bayesian framework is used to continuously update the prediction with the actual degradation value of the springs, thereby reducing the uncertainty in the data and improving the prediction accuracy. In addition, the deterioration of material with number of cycles is also investigated using thermogravimetric analysis and scanning electron microscopy.

36 MATERIALS SCIENCE↗

THE 4 Ms CHANDRA DEEP FIELD-SOUTH NUMBER COUNTS APPORTIONED BY SOURCE CLASS: PERVASIVE ACTIVE GALACTIC NUCLEI AND THE ASCENT OF NORMAL GALAXIES

We present 0.5-2 keV, 2-8 keV, 4-8 keV, and 0.5-8 keV (hereafter soft, hard, ultra-hard, and full bands, respectively) cumulative and differential number-count (log N-log S) measurements for the recently completed Almost-Equal-To 4 Ms Chandra Deep Field-South (CDF-S) survey, the deepest X-ray survey to date. We implement a new Bayesian approach, which allows reliable calculation of number counts down to flux limits that are factors of Almost-Equal-To 1.9-4.3 times fainter than the previously deepest number-count investigations. In the soft band (SB), the most sensitive bandpass in our analysis, the Almost-Equal-To 4 Ms CDF-S reaches a maximum source density of Almost-Equal-To 27,800 deg{sup -2}. By virtue of the exquisite X-ray and multiwavelength data available in the CDF-S, we are able to measure the number counts from a variety of source populations (active galactic nuclei (AGNs), normal galaxies, and Galactic stars) and subpopulations (as a function of redshift, AGN absorption, luminosity, and galaxy morphology) and test models that describe their evolution. We find that AGNs still dominate the X-ray number counts down to the faintest flux levels for all bands and reach a limiting SB source density of Almost-Equal-To 14,900 deg{sup -2}, the highest reliable AGN source density measured at any wavelength. We find that the normal-galaxy counts rise rapidly near the flux limits and, at the limiting SB flux, reach source densities of Almost-Equal-To 12,700 deg{sup -2} and make up 46% {+-} 5% of the total number counts. The rapid rise of the galaxy counts toward faint fluxes, as well as significant normal-galaxy contributions to the overall number counts, indicates that normal galaxies will overtake AGNs just below the Almost-Equal-To 4 Ms SB flux limit and will provide a numerically significant new X-ray source population in future surveys that reach below the Almost-Equal-To 4 Ms sensitivity limit. We show that a future Almost-Equal-To 10 Ms CDF-S would allow for a significant increase in X-ray-detected sources, with many of the new sources being cosmologically distant (z {approx}> 0.6) normal galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Fables of reconstruction: controlling bias in the dark energy equation of state

We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully to minimise variance and bias in the reconstruction. Using a principal component analysis, we show how a correlated prior can be used to create a smooth reconstruction and also avoid bias in the mean behaviour of w(z). We test our method using Wiener reconstructions based on Fisher matrix projections, and also against more realistic MCMC analyses of simulated data sets for Planck and a future space-based dark energy mission. While the accuracy of our reconstruction depends on the smoothness of the assumed w(z), the relative error for typical dark energy models is ∼<10% out to redshift z = 1.5.

79 ASTRONOMY AND ASTROPHYSICS↗

Vibration-Based Techniques for Concrete Structural Health Monitoring. Light Water Reactor Sustainability Program report

The objectives of this ongoing research project focus on health monitoring and data analytics of concrete slabs containing reactive aggregates and thus subjected to degradation due to alkali-silica reaction (ASR). A controlled concrete slab with four pockets of reactive aggregates (pure silica, and reactive aggregates from three different quarries) was cast at Vanderbilt University and cured in representative conditions to accelerate degradation due to ASR. A set of four concrete samples were also cast and cured at the University of Alabama for ASR testing. Of these four samples, two slabs contained reactive aggregates while the other two had the non-reactive aggregate counterparts mixed throughout the samples. Four additional slabs were cast and cured at the University of Nebraska- Lincoln. Of these four samples; one contained non-reactive aggregates and no reinforcement, one contained reactive aggregates and no reinforcement, one contained reactive aggregates and rebar reinforcement in one direction, and the last contained reactive aggregates and reinforcement in two directions. Single frequency and dual frequency tests were used on these slabs to locate ASR damage within the specimens containing reactive aggregates. The vibration tests were conducted with different sensor and actuator configurations to facilitate damage detection and localization. The results from the data analysis of the dynamic testing on concrete slabs are discussed in detail in this report. Results for damage localization are dependent on multiple parameters used in the tests. This report investigates different methods of data fusion including voting, raw averaging, damage index averaging, and Bayesian fusion.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Shape Optimization by Bayesian-Validated Computer-Simulation Surrogates

A nonparametric-validated, surrogate approach to optimization has been applied to the computational optimization of eddy-promoter heat exchangers and to the experimental optimization of a multielement airfoil. In addition to the baseline surrogate framework, a surrogate-Pareto framework has been applied to the two-criteria, eddy-promoter design problem. The Pareto analysis improves the predictability of the surrogate results, preserves generality, and provides a means to rapidly determine design trade-offs. Significant contributions have been made in the geometric description used for the eddy-promoter inclusions as well as to the surrogate framework itself. A level-set based, geometric description has been developed to define the shape of the eddy-promoter inclusions. The level-set technique allows for topology changes (from single-body,eddy-promoter configurations to two-body configurations) without requiring any additional logic. The continuity of the output responses for input variations that cross the boundary between topologies has been demonstrated. Input-output continuity is required for the straightforward application of surrogate techniques in which simplified, interpolative models are fitted through a construction set of data. The surrogate framework developed previously has been extended in a number of ways. First, the formulation for a general, two-output, two-performance metric problem is presented. Surrogates are constructed and validated for the outputs. The performance metrics can be functions of both outputs, as well as explicitly of the inputs, and serve to characterize the design preferences. By segregating the outputs and the performance metrics, an additional level of flexibility is provided to the designer. The validated outputs can be used in future design studies and the error estimates provided by the output validation step still apply, and require no additional appeals to the expensive analysis. Second, a candidate-based a posteriori error analysis capability has been developed which provides probabilistic error estimates on the true performance for a design randomly selected near the surrogate-predicted optimal design.

Patera, Anthony T.↗

A Differentiable Hydrology Approach for Modeling With Time-Varying Parameters

In the analysis of observational data with mathematical models, it is often desirable to let one or more model parameters vary with time to account for changing environmental conditions or to offer more flexibility. A standard approach for dynamic models is to allow for the number of parameters to grow as a function of time, leading to a high-dimensional inference problem for long data records. We propose using Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo (MCMC) method, to perform Bayesian inference for time-varying parameters (TVP) in hydrology models. As derivatives of model error functions with regard to parameters are not available in closed form, we implemented the GR4J rainfall-runoff models in Theano/PyMC3, and Jax/NumPyro, allowing for the application of automatic differentiation techniques. A simulation experiment assessing the viability of these methods for recovering underlying temporal variation in parameters indicates that a discrete Gaussian random walk-based prior appears to be best suited across a range of scenarios while the continuous-time Gaussian process compares relatively poorly. In an analysis of 20 years of daily real-world streamflow records from the Model Parameter Estimation Experiment (MOPEX) hydrology data set with increasing data sparsity and at multiple temporal resolutions, we find that TVP inference with gradient-based MCMC is a flexible and reliable approach for analyzing hydrology models with dynamic parameter sets.

54 ENVIRONMENTAL SCIENCES↗

Stan : A Probabilistic Programming Language

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.

97 MATHEMATICS AND COMPUTING↗

Assessing and benchmarking the fidelity of posterior inference methods for astrophysics data analysis

In this era of large and complex astronomical survey data, interpreting, validating, and comparing inference techniques becomes increasingly difficult. This is particularly critical for emerging inference methods like Simulation-Based Inference (SBI), which offer significant speedup potential and posterior modeling flexibility, especially when deep learning is incorporated. We present a study to assess and compare the performance and uncertainty prediction capability of Bayesian inference algorithms – from traditional MCMC sampling of analytic functions to deep learning-enabled SBI. We focus on testing the capacity of hierarchical inference modeling in those scenarios. Before we extend this study to cosmology, we first use astrophysical simulation data to ensure interpretability. We demonstrate a probabilistic programming implementation of hierarchical and non-hierarchical Bayesian inference using simulations derived from the DeepBench software library, a benchmarking tool developed by our group that generates simple and controllable astrophysical objects from first principles. This study will enable astronomers and physicists to harness the inference potential of these methods with confidence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Bayesian Monte Carlo inversion of spatial auto-correlation (SPAC) for near-surface Vs structure applied to both broad-band and geophone data

SUMMARY We propose a new Bayesian method to reveal the Vs structure of the near surface of the earth using spatial autocorrelation (SPAC) functions and apply this new method to synthetic, broad-band and geophone data sets. The principle of SPAC is introduced, and an implementation of the Bayesian Monte Carlo inversion (BMCI) for modelling SPAC coherency functions is described. To demonstrate its effectiveness, BMCI is applied to synthetic tests, data from 14 SPAC array sites in the Salt Lake Valley (SLV), Utah, and two arrays (one broad-band and one geophone) located in south central Utah. The Vs models derived from previous SPAC analysis of the 14 SLV sites differ by 10 per cent at most from those determined by BMCI and lie within uncertainties determined for the BMCI models. These agreements demonstrate the effectiveness of the BMCI method. The synthetic tests and applications to the SLV SPAC data show BMCI has great potential to resolve Vs structure down to at least 400 m. To achieve resolution for deeper Vs structure, longer duration deployments, wider array apertures, and additional seismometers or geophones can be used. Additionally, when the target frequencies are greater than 0.1 Hz, there is no apparent disadvantage in using geophone data for BMCI compared to broad-band data. Most significantly, BMCI places a quantifiable constraint on the uncertainties of the Vs models as well as Vs30.

58 GEOSCIENCES↗