Search NASA⌕ Search

SEARCH · Search NASA

Results for “sparse sampling”

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 253 records · Page 14

Optical Variability of ICRF3 Quasars in the Pan-STARRS 3Pi Survey with Functional Principal Component Analysis

We make use of individual (epoch) detection data from the Pan-STARRS “3π” survey for 2863 optical ICRF3 counterparts in the five wavelength bands g, r, i, z, and y, published as part of the Data Release 2. A dedicated method based on the Functional Principal Component Analysis is developed for these sparse and irregularly sampled data. With certain regularization and normalization constraints, it allows us to obtain uniform and compatible estimates of the variability amplitudes and average magnitudes between the passbands and objects. We find that the starting assumption of affinity of the light curves for a given object at different wavelengths is violated for several percent of the sample. The distributions of rms variability amplitudes are strongly skewed toward small values, peaking at ∼0.1 mag with tails stretching to 2 mag. Statistically, the lowest variability is found for the r band and the largest for the reddest y band. A small “brighter-redder” effect is present, with amplitudes in y greater than amplitudes in g in 57% of the sample. The variability versus redshift dependence shows a strong decline with z toward redshift 3, which we interpret as the time dilation of the dominant time frequencies. The colors of radio-loud ICRF3 quasars are correlated with redshift in a complicated, wavy pattern governed by the emergence of brightest emission lines within the five passbands.

79 ASTRONOMY AND ASTROPHYSICS↗

Development of algorithms for understanding the temporal and spatial variability of the earth's radiation balance

A brief description is given of how temporal and spatial variability in the earth's radiative behavior influences the goals of satellite radiation monitoring systems and how some previous systems have addressed the existing problems. Then, results of some simulations of radiation budget monitoring missions are presented. These studies led to the design of the Earth Radiation Budget Experiment (ERBE). A description is given of the temporal and spatial averaging algorithms developed for the ERBE data analysis. These algorithms are intended primarily to produce monthly averages of the net radiant exitance on regional, zonal, and global scales and to provide insight into the regional diurnal variability of radiative parameters such as albedo and long-wave radiant exitance. The algorithms are applied to scanner and nonscanner data for up to three satellites. Modeling of dialy shortwave albedo and radiant exitance with satellite samling that is insufficient to fully account for changing meteorology is discussed in detail. Studies performed during the ERBE mission and software design are reviewed. These studies provide quantitative estimates of the effects of temporally sparse and biased sampling on inferred diurnal and regional radiative parameters. Other topics covered include long-wave diurnal modeling, extraction of a regional monthly net clear-sky radiation budget, the statistical significance of observed diurnal variability, quality control of the analysis, and proposals for validating the results of ERBE time and space averaging.

Brooks, D. R.↗

Improving an Atlantic Fisheries DSS using Sea Surface Salinity Data from NASA's Aquarius Mission

This report assesses the capacity of incorporating NASA#s Aquarius SSS (sea surface salinity) data into the SMAST (School of Marine Science and Technology) DSS for Fisheries Science. This data will enhance the SMAST DSS by providing SSS over a large area. Aquarius is a focused satellite mission designed to measure global SSS. SSS mapping is limited because conventional in situ SSS sampling is too sparse to give a large-scale view of the salinity variability. Aquarius will resolve missing physical processes that link the water cycle, the climate, and the ocean. The SMAST Fisheries program provides a DSS for fisheries science. It collects fisheries and environmental data, integrates them into a suite of data assimilation ocean models, and provides hindcasts, nowcasts, and forecasts for fisheries research, fisheries management, and the fishery industry. Currently, SMAST is using SSS data from the National Oceanic and Atmospheric Administration#s National Data Buoy Center. The SMAST DSS would be enhanced with SSS data from the Aquarius mission.

Guest, DeNeice↗

Large Area Lunar Dust Flux Measurement Instrument

The instrument under development is designed to characterize the flux and size distribution of the lunar micrometeoroid and secondary ejecta environment. When deployed on the lunar surface, the data collected will benefit fundamental lunar science as well as enabling more reliable impact risk assessments for human lunar exploration activities. To perform this task, the instrument requirements are demanding. It must have as large a surface area as possible to sample the very sparse population of the larger potentially damage-inducing micrometeorites. It must also have very high sensitivity to enable it to measure the flux of small (<10 micron) micrometeorite and secondary ejecta dust particles. To be delivered to the lunar surface, it must also be very low mass, rugged and stow compactly. The instrument designed to meet these requirements is called FOMIS. It is a large-area thin film under tension (i.e. a drum) with multiple fiber optic displacement (FOD) sensors to monitor displacements of the film. This sensor was chosen since it can measure displacements over a wide dynamic range: 1 cm to sub-Angstrom. A prototype system was successfully demonstrated using the hypervelocity impact test facility at the University of Kent (Canterbury, UK). Based on these results, the prototype system can detect hypervelocity (approx.5 km/s) impacts by particles as small as 2 microns diameter. Additional tests using slow speeds find that it can detect secondary ejecta particles (which do not penetrate the film) with momentums as small as 15 pico-gram 100m/s, or nominally 5 microns diameter at 100 m/s.

Corsaro, R.↗

The Role of Lightning in Controlling Interannual Variability of Tropical Tropospheric Ozone and OH and its Implications for Climate

Nitrogen oxides (NO(x) = NO + NO2) produced by lightning make a major contribution to the production of the dominant tropospheric oxidants (OH and ozone). These oxidants control the lifetime of many trace gases including long-lived greenhouse gases, and control the source-receptor relationship of inter-hemispheric pollutant transport. Lightning is affected by meteorological variability, and therefore represents a potentially important tropospheric chemistry-climate feedback. Understanding how interannual variability (IAV) in lightning affects IAV in ozone and OH in the recent past is important if we are to predict how oxidant levels may change in a future warmer climate. However, lightning parameterizations for chemical transport models (CTMs) show low skill in reproducing even climatological distributions of flash rates from the Lightning Imaging Sensor (LIS) and the Optical Transient Detector (OTD) satellite instruments. We present an optimized regional scaling algorithm for CTMs that enables sufficient sampling of spatiotemporally sparse satellite lightning data from LIS to constrain the spatial, seasonal, and interannual variability of tropical lightning. We construct a monthly time series of lightning flash rates for 1998-2010 and 35degS-35degN, and find a correlation of IAV in total tropical lightning with El Nino. We use the IAV-constraint to drive a 9-year hindcast (1998-2006) of the GEOS-Chem 3D chemical transport model, and find the increased IAV in LNO(x) drives increased IAV in ozone and OH, improving the model fs ability to simulate both. Although lightning contributes more than any other emission source to IAV in ozone, we find ozone more sensitive to meteorology, particularly convective transport. However, we find IAV in OH to be highly sensitive to lightning NO(x), and the constraint improves the ability of the model to capture the temporal behavior of OH anomalies inferred from observations of methyl chloroform and other gases. The sensitivity of OH is explained using photochemical reaction rates which show a "magnification" effect of the initial lightning NO perturbation on OH primary production, HO(x) recycling, and OH loss frequencies. This influence on OH may represent a negative feedback, if lightning increases in a warming world..

Murray, Lee T.↗

Code for multi-shape Gaussian process (GP) fitting with uncertainty quantification (UQ)

This is code associated with the publication “Nonparametric Multi-shape Modeling with Uncertainty Quantification,” authored by Hengrui Luo (Lawrence Berkeley National Laboratory) and Justin Strait (Los Alamos National Laboratory). The code is used to fit multiple-output Gaussian process (GP) models of planar closed curves to collections of ordered point sets, allowing for flexible nonlinear prediction of the underlying curve under dense or sparse point set samplings and with or without noise, as well as tractable uncertainty quantification. To do this, we employ use of a periodic kernel to account for the nonlinear input space of closed curves, and combine with coregionalization models to account for dependence both (i) between curve coordinates, and (ii) between pairs of curves. Functions in the code are capable of fitting these models, as well as performing additional tasks with the fitted curves such as (a) shape registration and alignment, (b) shape averaging, and (c) fitting for curve sub-populations / clusters.

Strait, Justin↗

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗

Estimating rates and patterns of diversification with incomplete sampling: a case study in the rosids

Premise Recent advances in generating large‐scale phylogenies enable broad‐scale estimation of species diversification. These now common approaches typically are characterized by (1) incomplete species coverage without explicit sampling methodologies and/or (2) sparse backbone representation, and usually rely on presumed phylogenetic placements to account for species without molecular data. We used empirical examples to examine the effects of incomplete sampling on diversification estimation and provide constructive suggestions to ecologists and evolutionary biologists based on those results. Methods We used a supermatrix for rosids and one well‐sampled subclade (Cucurbitaceae) as empirical case studies. We compared results using these large phylogenies with those based on a previously inferred, smaller supermatrix and on a synthetic tree resource with complete taxonomic coverage. Finally, we simulated random and representative taxon sampling and explored the impact of sampling on three commonly used methods, both parametric (RPANDA and BAMM) and semiparametric (DR). Results We found that the impact of sampling on diversification estimates was idiosyncratic and often strong. Compared to full empirical sampling, representative and random sampling schemes either depressed or inflated speciation rates, depending on methods and sampling schemes. No method was entirely robust to poor sampling, but BAMM was least sensitive to moderate levels of missing taxa. Conclusions We suggest caution against uncritical modeling of missing taxa using taxonomic data for poorly sampled trees and in the use of summary backbone trees and other data sets with high representative bias, and we stress the importance of explicit sampling methodologies in macroevolutionary studies.

59 BASIC BIOLOGICAL SCIENCES↗

The stellar density profile of the distant galactic halo

We use extensive gravity-sensitive DDO 51 photometry over 5100 square degrees, combined with Sloan Digital Sky Survey broadband photometry, to select a catalog of ∼4000 giant stars covering a large fraction of the high Galactic latitude sky and reaching out to ∼80 kpc in the Galactic halo. This sample of bright and unbiased tracers enables us to measure the radial profile and 3D structure of the stellar halo to large distances, which had previously only been measured with sparse tracers or small samples. Using population synthesis models to reproduce the observed giant star luminosity function, we find that the halo maintains a r{sup −3.5} profile from 30 to 80 kpc with no signs of a truncation or sharp break over this range. The radial profile measurement is largely insensitive to individual halo substructure components, but we find that attempting to measure the shape of the halo is overwhelmed by the Sagittarius stream such that no elliposidal shape is a satisfactory description in this region. These measurements allow us to begin placing the Milky Way in context with the growing sample of external galaxies where similar halo profile measurements are available, with the goal of further linking the properties of stellar halos to the accretion histories that formed them.

79 ASTRONOMY AND ASTROPHYSICS↗

Stochastic Gradients for Large-Scale Tensor Decomposition

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of loss functions such as Bernoulli loss for binary data or Huber loss for robust estimation. Here, the stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor times Khatri--Rao product tensor kernel. For dense tensors, we simply use uniform sampling. For sparse tensors, we propose two types of stratified sampling that give precedence to sampling nonzeros. Numerical results demonstrate the advantages of the proposed approach and its scalability to large-scale problems.

97 MATHEMATICS AND COMPUTING↗

Micro-imaging of Brain Cancer Radiation Therapy Using Phase-contrast Computed Tomography

Experimental neuroimaging provides a wide range of methods for the visualization of brain anatomic morphology down to subcellular detail. Still, each technique-specific detection mechanism presents compromises among the achievable field-of-view size, spatial resolution, and nervous tissue sensitivity, leading to partial sample coverage, unresolved morphologic structures, or sparse labeling of neuronal populations and often also to obligatory sample dissection or other sample invasive manipulations. X-ray phase-contrast imaging computed tomography (PCI-CT) is an experimental imaging method that simultaneously provides micrometric spatial resolution, high soft-tissue sensitivity, and ex vivo full organ rodent brain coverage without any need for sample dissection, staining or labeling, or contrast agent injection. In the present study, we explored the benefits and limitations of PCI-CT use for in vitro imaging of normal and cancerous brain neuromorphology after in vivo treatment with synchrotron-generated x-ray microbeam radiation therapy (MRT), a spatially fractionated experimental high-dose radiosurgery. The goals were visualization of the MRT effects on nervous tissue and a qualitative comparison of the results to the histologic and high-field magnetic resonance imaging findings.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Parallel Environment for the Creation of Stochastics 1.0

PECOS is a computational library for creating and manipulating realizations of stochastic quantities, including scalar uncertain variables, random fields, and stochastic processes. It offers a unified interface to univariate and multivariate polynomial approximations using either orthogonal or interpolation polynomials; numerical integration drivers for Latin hypercube sampling, quadrature, cubature, and sparse grids; and fast Fourier transforms using third party libraries. The PECOS core also offers statistical utilities and transformations between various representations of stochastic uncertainty. PECOS provides a C++ API through which users can generate and transform realizations of stochastic quantities. It is currently used by Sandia's DAKOTA, Stokhos, and Encore software packages for uncertainty quantification and verification. PECOS generates random sample sets and multi-dimensional integration grids, typically used in forward propagation of scalar uncertainty in computational models (uncertainty quantification (UQ)). PECOS also generates samples of random fields (RFs) and stochastic processes (SPs) from a set of user-defined power spectral densities (PSDs). The RF/SP may be either Gaussian or non-Gaussian and either stationary or nonstationary, and the resulting sample is intended for run-time query by parallel finite element simulation codes. Finally, PECOS supports nonlinear transformations of random variables via the Nataf transformation and extensions.

Field Jr, Richard↗

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

Bacteriophage Tail-Tube Assembly Studied by Proton-Detected 4D Solid-State NMR

Obtaining unambiguous resonance assignments remains a major bottleneck in solid-state NMR studies of protein structure and dynamics. Particularly for supramolecular assemblies with large subunits (>150 residues), the analysis of crowded spectral data presents a challenge, even if three-dimensional (3D) spectra are used. Here, we present a proton-detected 4D solid-state NMR assignment procedure that is tailored for large assemblies. The key to recording 4D spectra with three indirect carbon or nitrogen dimensions with their inherently large chemical shift dispersion lies in the use of sparse non-uniform sampling (as low as 2 %). As a proof of principle, we acquired 4D (H)COCANH, (H)CACONH, and (H)CBCANH spectra of the 20 kDa bacteriophage tail-tube protein gp17.1 in a total time of two and a half weeks. These spectra were sufficient to obtain complete resonance assignments in a straightforward manner without use of previous solution NMR data.

59 BASIC BIOLOGICAL SCIENCES↗

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

97 MATHEMATICS AND COMPUTING↗

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

Objectives: Sepsis affects nearly 1 million people in the United States per year, has a mortality rate of 28–50% and requires more than $20 billion a year in hospital costs. Over a quarter century of research has not yielded a single reliable diagnostic test or a directed therapeutic agent for sepsis. Central to this insufficiency is the fact that sepsis remains a clinical/physiological diagnosis representing a multitude of molecularly heterogeneous pathological trajectories. Advances in computational capabilities offered by High Peformance Computing (HPC) platforms call for an evolution in the investigation of sepsis to attempt to define the boundaries of traditional research (bench, clinical and computational) through the use of computational proxy models. We present a novel investigatory and analytical approach, derived from how HPC resources and simulation are used in the physical sciences, to identify the epistemic boundary con- ditions of the study of clinical sepsis via the use of a proxy agent-based model of systemic inflammation. Design: Current predictive models for sepsis use correlative methods that are limited by patient heterogeneity and data sparseness. We address this issue by using an HPC version of a system-level validated agent-based model of sepsis, the Innate Immune Response ABM (IIRBM), as a proxy system in order to identify boundary conditions for the possible behavioral space for sepsis. We then apply advanced analysis derived from the study of Random Dynamical Systems (RDS) to identify novel means for characterizing system behavior and providing insight into the tractability of traditional investigatory methods. Results: The behavior space of the IIRABM was examined by simulating over 70 million sepsis patients for up to 90 days in a sweep across the following parameters: cardio-respiratory-metabolic resilience; microbial invasiveness; microbial toxigenesis; and degree of nosocomial exposure. In addition to using established methods for describing parameter space, we developed two novel methods for characterizing the behavior of a RDS: Probabilistic Basins of Attraction (PBoA) and Stochastic Trajectory Analysis (STA). Computationally generated behavioral landscapes demonstrated attractor structures around stochastic re- gions of behavior that could be described in a complementary fashion through use of PBoA and STA. The stochasticity of the boundaries of the attractors highlights the challenge for correlative attempts to characterize and classify clinical sepsis. Conclusions: HPC simulations of models like the IIRABM can be used to generate approximations of the behavior space of sepsis to both establish “boundaries of futility” with respect to existing investi- gatory approaches and apply system engineering principles to investigate the general dynamic properties of sepsis to provide a pathway for developing control strategies. Here, the issues that bedevil the study and treatment of sepsis, namely clinical data sparseness and inadequate experimental sampling of system behavior space, are fundamental to nearly all biomedical research, manifesting in the “Crisis of Reproducibility” at all levels. HPC-augmented simulation-based research offers an investigatory strategy more consistent with that seen in the physical sciences (which combine experiment, theory and simulation), and an opportunity to utilize the leading advances in HPC, namely deep machine learning and evolutionary computing, to form the basis of an iterative scientific process to meet the full promise of Precision Medicine (right drug, right patient, right time).

59 BASIC BIOLOGICAL SCIENCES↗

Characterization and Geological Implications of Precambrian Calcite-Hosted Phosphate

Constraints on marine phosphate availability and cycling directly inform our understanding of long-term biological evolution. However, early Earth phosphate records are sparse, biased toward siliciclastic samples, and susceptible to post-depositional modification. Well-preserved shallow marine inorganic carbonate precipitates provide a complementary yet understudied record of phosphate cycling. We combined micro-X ray fluorescence mapping, X-ray absorption, and Nuclear Magnetic Resonance spectroscopy on samples of Precambrian syndepositional herringbone calcite (HBC) and microspar to characterize phosphorus speciation and distribution in these carbonate fabrics. Phosphorus spectroscopy from synthetic calcite, HBC, and microspar, is qualitatively consistent with a disordered distribution of phosphate. These characteristics are diagnostic of calcite-hosted phosphate, which is pervasive at low concentrations in HBC and microspar. This study provides evidence that ancient, well-preserved carbonate fabrics retain phosphate sourced from seawater and highlights the potential for an unaltered archive of marine phosphate concentration over geologic time.

58 GEOSCIENCES↗