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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Constructing a Simulation Surrogate with Partially Observed Output

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these surrogates. However, surrogate methods with dimension reduction generally rely on complete output training data. This article proposes a new Gaussian process surrogate method that permits the use of partially observed output while remaining computationally efficient. The new method involves the imputation of missing values and the adjustment of the covariance matrix used for Gaussian process inference. The resulting surrogate represents the available responses, disregards the missing responses, and provides meaningful uncertainty quantification. In conclusion, the proposed approach is shown to offer sharper inference than alternatives in a simulation study and a case study where an energy density functional model that frequently returns incomplete output is calibrated.

42 ENGINEERING↗
DOE OSTI2025

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius (M–R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M–R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Bayesian statistics↗
NASA NTRS2012

Using the VAHIRR Radar Algorithm to Investigate Lightning Cessation

Accurately determining the threat posed by lightning is a major area for improved operational forecasts. Most efforts have focused on the initiation of lightning within a storm, with far less effort spent investigating lightning cessation. Understanding both components, initiation and cessation, are vital to improving lightning safety. Few organizations actively forecast lightning onset or cessation. One such organization is the 45th Weather Squadron (45WS) for the Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS). The 45WS has identified that charged anvil clouds remain a major threat of continued lightning and can greatly extend the window of a potential lightning strike. Furthermore, no discernable trend of total lightning activity has been observed consistently for all storms. This highlights the need for more research to find a robust method of knowing when a storm will cease producing lightning. Previous lightning cessation work has primarily focused on forecasting the cessation of cloud-to -ground lightning only. A more recent, statistical study involved total lightning (both cloud-to-ground and intracloud). Each of these previous works has helped the 45WS take steps forward in creating improved and ultimately safer lightning cessation forecasts. Each study has either relied on radar data or recommended increased use of radar data to improve cessation forecasts. The reasoning is that radar data is able to either directly or by proxy infer more about dynamical environment leading to cloud electrification and eventually lightning cessation. The authors of this project are focusing on a two ]step approach to better incorporate radar data and total lightning to improve cessation forecasts. This project will utilize the Volume Averaged Height Integrated Radar Reflectivity (VAHIRR) algorithm originally developed during the Airborne Field Mill II (ABFM II) research project. During the project, the VAHIRR product showed a trend of increasing values with increases in the electric field magnitude above 3 kV/m. An extreme value analysis showed that VAHIRR values less than or equal to 10 dBZ-km showed that the probability of having an electric field magnitude larger than 3 kV/m was less than one in ten thousand. VAHIRR also was found to be sensitive at indicating anvil clouds that posed a threat of initiating a lightning flash. This project seeks to use VAHIRR to analyze its utility as a lightning cessation tool, particularly dealing with the threat posed by detached anvils. The results from this project will serve as a baseline effectiveness of radar ]based lightning cessation algorithms. This baseline will be used in the second, and concurrent work by the co ]author fs who are developing a lightning cessation algorithm based on dual ]polarimetric radar data. Ultimately, an accurate method for identifying lightning cessation can save money on lost manpower time as well as greatly improve lightning safety.

Stano, Geoffrey T.↗
DOE OSTI2026

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Statistical Uncertainty in Paleoclimate Proxy Reconstructions

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data-forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

58 GEOSCIENCES↗
DOE OSTI2023

Pulse profile modelling of thermonuclear burst oscillations – II. Handling variability

ABSTRACT Pulse profile modelling is a relativistic ray-tracing technique that can be used to infer masses, radii, and geometric parameters of neutron stars. In a previous study, we looked at the performance of this technique when applied to thermonuclear burst oscillations from accreting neutron stars. That study showed that ignoring the variability associated with burst oscillation sources resulted in significant biases in the inferred mass and radius, particularly for the high count rates that are nominally required to obtain meaningful constraints. In this follow-on study, we show that the bias can be mitigated by slicing the bursts into shorter segments where variability can be neglected, and jointly fitting the segments. Using this approach, the systematic uncertainties on the mass and radius are brought within the range of the statistical uncertainty. With about 106 source counts, this yields uncertainties of approximately 10 per cent for both the mass and radius. However, this modelling strategy requires substantial computational resources. We also confirm that the posterior distributions of the mass and radius obtained from multiple bursts of the same source can be merged to produce outcomes comparable to that of a single burst with an equivalent total number of counts.

Astronomy & Astrophysics↗
DOE OSTI2026

pop-cosmos : redshifts and physical properties of KiDS-1000 galaxies

ABSTRACT Principled Bayesian inference of galaxy properties has not previously been performed for wide-area weak-lensing surveys with millions of sources. We address this gap by applying the pop-cosmos generative model to perform spectral energy distribution (SED) fitting for 4 million KiDS (Kilo-Degree Survey)-1000 galaxies. Calibrated on deep COSMOS2020 photometric data, pop-cosmos specifies a physically motivated prior over the galaxy population up to $z \simeq 6$ in stellar population synthesis (SPS) parameter space. Using the Speculator SPS emulator with GPU (graphics processing unit)-accelerated Markov Chain Monte Carlo sampling, we perform full posterior inference at 8.2 GPU seconds per galaxy, obtaining joint constraints on galaxy redshifts and physical properties. We validate photometric redshifts against $\sim \!185\,\!000$ KiDS galaxies cross-matched to Dark Energy Spectroscopic Instrument Data Release 1 spectroscopic samples, achieving low bias ($2\times 10^{-3}$), scatter ($\sigma _{\mathrm{MAD}}=0.03$), and outlier fraction (3.2 per cent) for the Bright Galaxy Survey, with comparable performance (bias $3\times 10^{-2}$, $\sigma _{\mathrm{MAD}}=0.05$, 1.0 per cent outliers) for luminous red galaxies (LRGs). Within the LRG sample, we identify massive, dusty, star-forming contaminants at $z \simeq 0.4$ satisfying standard colour selections for quenched populations. We infer trends in stellar mass, star formation, metallicity, and dust across five tomographic redshift bins consistent with established scaling relations. Using specific star formation rate constraints, we identify $\sim$7 per cent of KiDS-1000 galaxies as quenched, versus 37 per cent implied by conservative colour cuts. This enables the construction of weak-lensing samples defined by physical properties while mitigating intrinsic alignment systematics and preserving statistical power. Our analysis validates pop-cosmos out of sample, establishing it as a scalable approach for galaxy evolution and cosmological analyses with photometric surveys.

Halder, Anik [Institute of Astronomy and Kavli Ins↗
NASA NTRS2007

Variations in Upper-Tropospheric Humidity and Convective Processes as Seen from SSM/T-2

Water vapor feedback, particularly involving water vapor in the upper troposphere (UTH), is widely regarded as the process with the most potential to amplify anthropogenic greenhouse forcing. Yet, our ability to quantify observationally water vapor variations in the current climate and the relationships to convective processes remains rather crude. Remote sensing from polar orbiting instruments has played a major role in documenting UTH variability, supplementing highly undersampled and poorly calibrated rawinsonde measurements. Most of our observational understanding of UTH has come from the 6.7 micrometer channel measurements which are subject to cloud contamination uncertainties. In this work we examine UTH variations present in the Special Sensor Microwave Temperature Sounder 2 (SSM/T-2) sensors flying aboard Defense Military Satellite Program (DMSP) polar orbiting satellites during the period 1993 through 2001. We employ data from the the 183.3 +/- 1 GHz channel which is far less sensitive to cirrus than IR methods. Our primary focus is on obtaining more reliable statistics of interannual behavior; i.e. How close to constant RH are interannual variations in T2 UTH over the tropics? How do temperature and moisture variations contribute regionally? The 1997/1998 strong ENS0 warming event and adjacent cool periods provide a strong signal to study, albeit a perturbation of natural climate variability. Modeling the 183.3 GHz channel using reanalysis temperature data, but with climatological water vapor, allows us to infer the separate contribution by water vapor in the observations. In addition, frozen hydrometeors produced by deep convection are also captured in the 150 GHz oxygen channel, providing an opportUnity to relate the incidence of deep convection to water vapor variability. Our results indicate a much larger variation of 183.3 GHz brightness temperatures would be observed were it not for water vapor variations positively correlated with tropical SSTs. Comparisons are made with previous studies using both IR and microwave observations to characterize UTH response to tropical SSTs.

Robertson, Franklin R.↗
NASA NTRS2003

Intelligent machines in the twenty-first century: foundations of inference and inquiry

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Review↗
NASA NTRS2002

Using GEO Optical Observations to Infer Orbit Populations

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit. When observing very dim objects with small field-of-view telescopes, though, the observations are generally too short to obtain accurate orbital elements. However, it is possible to use such observations to statistically characterize the small object environment. A telescope pointed at a particular spot could potentially see objects in a number of different orbits. Inevitably, when looking at one region for certain types of orbits, there are objects in other types of orbits that cannot be seen. Observation campaigns are designed with these limitations in mind and are set up to span a number of regions of the sky, making it possible to sample all potential orbits under consideration. Each orbit is not seen with the same probability, however, so there are observation biases intrinsic to any observation campaign. Fortunately, it is possible to remove such biases and reconstruct a meaningful estimate of the statistical orbit populations of small objects in GEO. This information, in turn, can be used to investigate the nature of debris sources and to characterize the risk to GEO spacecraft. This paper describes these statistical tools and presents estimates of small object GEO populations.

Matney, Mark↗
DOE OSTI2025

Joint cosmic density reconstruction from photometric and spectroscopic samples

ABSTRACT We reconstruct the dark matter density field from spatially overlapping spectroscopic and photometric redshift catalogues through a field-level forward modelling approach. Instead of directly inferring the underlying density field, we find the best-fitting initial Gaussian fluctuations that will evolve into the observed cosmic volume. To account for the substantial uncertainty of photometric redshifts we employ a differentiable continuous Poisson process. As an initial test, we construct a mock based on the upcoming Prime Focus Spectrograph combined with photometric sample modelled on the Subaru Hyper Suprime-Cam. Depending on the statistic of interest, we find improvements in cosmic structure classification equivalent to 50–100 per cent more spectroscopic targets by combining relatively sparse spectroscopic with dense photometric samples.

Horowitz, B.↗
NASA NTRS1989

Bayesian learning

In 1983 and 1984, the Infrared Astronomical Satellite (IRAS) detected 5,425 stellar objects and measured their infrared spectra. In 1987 a program called AUTOCLASS used Bayesian inference methods to discover the classes present in these data and determine the most probable class of each object, revealing unknown phenomena in astronomy. AUTOCLASS has rekindled the old debate on the suitability of Bayesian methods, which are computationally intensive, interpret probabilities as plausibility measures rather than frequencies, and appear to depend on a subjective assessment of the probability of a hypothesis before the data were collected. Modern statistical methods have, however, recently been shown to also depend on subjective elements. These debates bring into question the whole tradition of scientific objectivity and offer scientists a new way to take responsibility for their findings and conclusions.

Denning, Peter J.↗
DOE OSTI2020

STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408−5354

We present a blind time-delay cosmographic analysis for the lens system DES J0408−5354. This system is extraordinary for the presence of two sets of multiple images at different redshifts, which provide the opportunity to obtain more information at the cost of increased modelling complexity with respect to previously analysed systems. We perform detailed modelling of the mass distribution for this lens system using three band Hubble Space Telescope imaging. We combine the measured time delays, line-of-sight central velocity dispersion of the deflector, and statistically constrained external convergence with our lens models to estimate two cosmological distances. We measure the ‘effective’ time-delay distance corresponding to the redshifts of the deflector and the lensed quasar |$D_{\Delta t}^{\rm eff}=$||$3382_{-115}^{+146}$| Mpc and the angular diameter distance to the deflector D_d = |$1711_{-280}^{+376}$| Mpc, with covariance between the two distances. From these constraints on the cosmological distances, we infer the Hubble constant H_0= |$74.2_{-3.0}^{+2.7}$| km s^−1 Mpc^−^1 assuming a flat ΛCDM cosmology and a uniform prior for Ω_m as |$\Omega _{\rm m} \sim \mathcal {U}(0.05, 0.5)$|⁠. This measurement gives the most precise constraint on H_0 to date from a single lens. Our measurement is consistent with that obtained from the previous sample of six lenses analysed by the H_0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) collaboration. It is also consistent with measurements of H_0 based on the local distance ladder, reinforcing the tension with the inference from early Universe probes, for example, with 2.2σ discrepancy from the cosmic microwave background measurement.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Inference of the Mass Composition of Cosmic Rays with Energies from 10 18.5 to 10 20 eV Using the Pierre Auger Observatory and Deep Learning

We present measurements of the atmospheric depth of the shower maximum X max , inferred for the first time on an event-by-event level using the surface detector of the Pierre Auger Observatory. Using deep learning, we were able to extend measurements of the X max distributions up to energies of 100 EeV ( 10 20 eV ), not yet revealed by current measurements, providing new insights into the mass composition of cosmic rays at extreme energies. Gaining a 10-fold increase in statistics compared to the fluorescence detector data, we find evidence that the rate of change of the average X max with the logarithm of energy features three breaks at 6.5 ± 0.6 ( stat ) ± 1 ( syst ) EeV , 11 ± 2 ( stat ) ± 1 ( syst ) EeV , and 31 ± 5 ( stat ) ± 3 ( syst ) EeV , in the vicinity to the three prominent features (ankle, instep, suppression) of the cosmic-ray flux. The energy evolution of the mean and standard deviation of the measured X max distributions indicates that the mass composition becomes increasingly heavier and purer, thus being incompatible with a large fraction of light nuclei between 50 and 100 EeV. Published by the American Physical Society 2025

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Evidence for Suppression of Structure Growth in the Concordance Cosmological Model

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the ``growth index'' γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat ΛCDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield γ = 0.633$^{+0.025}_{–0.024}$, excluding γ = 0.55 at a statistical significance of 3.7σ. The combination of fσ8 and Planck measurements prefers an even higher growth index of γ = 0.639$^{+0.024}_{–0.025}$, corresponding to a 4.2σ-tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. Furthermore, a higher γ leads to a higher matter fluctuation amplitude S 8 inferred from galaxy clustering and weak lensing measurements, and a lower S 8 from Planck data, effectively resolving the S 8 tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

State-to-State Molecular Reactions in the Ultracold Regime (Final Scientific Report)

We have achieved the proposed goal to experimentally probe the AB + CD and AB + C types of reactions with state-to-state resolution, which we also compared to advanced theoretical calculations to help elucidate the role of quantum mechanics in the processes of bond breakage and formation. Our approach uses reactants that are prepared at ultracold temperatures (< 1µK) such that the quantum effects of translational motion are an important factor. Specific example reactions, including the potassium-rubidium metathesis reaction KRb + KRb → K 2 + Rb 2 as well as the atom exchange reaction Rb + KRb → Rb2 + K, are chosen because the technology of quantum internal and motional state control of these types of molecules is particularly advanced. The results for the entire funding period are fruitful. For the majority of this grant, we have constructed a one-of-the-kind quantum degenerate gas apparatus that integrates ion detection and velocity map imaging capabilities, allowing us to explore the KRb + KRb → K 2 + Rb 2 bimolecular reaction in detail. Specifically, we first verified such a reaction indeed proceed at ultracold temperatures by direct detection of reaction products. We then mapped out the complete product state distribution, which was compared to a state-counting model based on statistical theory. Our results show an overall agreement with the statistical state counting model, but also reveal several deviating state-pairs. An exact quantum calculation for molecule-molecule collisions, that is needed to understand these deviations, is however beyond the current state-of-the-art. Beside scrutinizing the reaction products, we also directly observe the reaction intermediate complex, which was quite a surprise to us. The intermediate complexes are long-lived and can interact with the inferred light that we use to trap the ultracold gas. After molecule-molecule collisions, we then explored the more theoretically tractable Rb + KRb reaction, which is endothermic. Surprisingly, we observed an exceedingly long-lived KRb$^*_2$ collisional complexes, with our experimentally measured complex lifetime deviating from conventional theoretical calculations by five orders of magnitude. This discrepancy has motivated many explorations of possible underlying causes, though no model yet captures this phenomenon completely. In the final year and the work that continues today, we extend upon these atom-molecule collision experiments to explore the origin of the long-lived KRb$^*_2$ complex lifetime and develop means to control the outcome of the reaction complex. The 5-year funded work advanced our understanding of chemical reactions at the lowest possible temperatures and at the same time opened up many new questions that are beyond our initial imaginations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Computing Nonlinear Power Spectra Across Dynamical Dark Energy Model Space with Neural ODEs

I show how to compute the nonlinear power spectrum across the entire $w(z)$ dynamical dark energy model space. Using synthetic ΛCDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear matter power spectrum as a function of the background expansion and mean matter density across ∼9 Gyr of cosmic evolution. After training, the model generalises to any dynamical dark energy model parameterised by $w(z)$. With little optimisation, the neural ODE is accurate to within 4% up to $k = 5\, h\, {\mathrm Mpc}^{−1}$. Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.

cosmology↗
NASA NTRS1988

The cratering record in the inner solar system: Implications for earth

Internal and external processes have reworked the Earth's surface throughout its history. In particular, the effect of meteorite impacts on the early history of the earth is lost due to fluvial, aeolian, volcanic and plate tectonic action. The cratering record on other inner solar system bodies often provides the only clue to the relative cratering rates and intensities that the earth has experienced throughout its history. Of the five major bodies within the inner solar system, Mercury, Mars, and the Moon retain scars of an early episode of high impact rates. The heavily cratered regions on Mercury, Mars, and the Moon show crater size-frequency distribution curves similar in shape and crater density, whereas the lightly cratered plains on the Moon and Mars show distribution curves which, although similar to each other, are statistically different in shape and density from the more heavily cratered units. The similarities among crater size-frequency distribution curves for the Moon, Mercury, and Mars suggest that the entire inner solar system was subjected to the two populations of impacting objects but Earth and Venus have lost their record of heavy bombardment impactors. Thus, based on the cratering record on the Moon, Mercury, and Mars, it can be inferred that the Earth experienced a period of high crater rates and basin formation prior to about 3.8 BY ago. Recent studies have linked mass extinctions to large terrestrial impacts, so life forms were unable to establish themselves until impact rates decreased substantially and terrestrial conditions became more benign. The possible periodicity of mass extinctions has led to the theory of fluctuating impact rates due to comet showers in the post heavy bombardment period. The active erosional environment on the Earth complicates attempts to verify these showers by erasing geological evidence of older impact craters. The estimated size of the impactor purportedly responsible for the Cretaceous-Tertiary mass extinctions is 10 km in diameter. Thus impactors greater than or equal to the size postulated for K-T impactor are rare within the inner solar system since the end of heavy bombardment.

Barlow, N. G.↗