Frequency-size Relationship Research Articles

Universal predictability of large avalanches in the Manna sandpile model.

Substantiated explanations of the unpredictability regarding sandpile models of self-organized criticality (SOC) gave way to efficient forecasts of extremes in a few models. The appearance of extremes requires a preparation phase that ends with general overloading of the system and spatial clustering of the local stress. Here, we relate the predictability of large events to the system volume in the Manna and Bak-Tang-Wiesenfeld sandpiles, which are basic models of SOC. We establish that in the Manna model, the events located to the right of the power-law segment of the size-frequency relationship are predictable and the prediction efficiency is described by the universal linear dependence on the event size scaled by a power-law function of the lattice volume. Our scaling-based approach to predictability contributes to the theory of SOC and may elucidate the forecast of extremes in the dynamics of such systems with SOC as neuronal networks and earthquakes.

Unveiling the complex canopy spatial structure of a Mediterranean old-growth beech (Fagus sylvatica L.) forest from UAV observations

In front of climate change scenarios and global loss of biodiversity, it is essential to monitor the structure of old-growth forests to study ecosystem status and dynamics to inform future conservation and restoration programmes. We propose an Unmanned Aerial Vehicle (UAV)-based framework to monitor fine-grained forest top canopy structure in a primary old-growth beech (Fagus sylvatica L.) forest in Pollino National Park, Italy, which belongs to the UNESCO World Heritage (UNESCO WH) serial site “Ancient and Primeval beech forests of the Carpathians and other regions of Europe”. Canopy profile, gap properties and their spatial distribution patterns were analysed using the canopy height model (CHM) derived from UAV surveys. Very high-resolution orthomosaic images coupled with direct field measurement data were used to assess gap detection accuracy and CHM validation. Forest canopy properties along with the vertical layering of the canopy were further explored using second-order statistics. The reconstructed canopy profile revealed a bimodal top height frequency distribution. The upper canopy layer (h > 14 m) was the most represented canopy height, with the remaining 50% split between the medium and lowest layer; 551 gaps were identified within 11.5 ha. Gap size varied between 2 m2 and 353 m2, and 19 m2was the mean gap size; the gap size-frequency relationship reflected a power-law probability distribution. About 97 % of the gaps were <100 m2 in size, showing a significant tendency to cluster. Most gaps were located in the upper and medium canopy layers; however, the highest relative gap area was found in the lowest layer. These results confirmed the high natural integrity of the ecosystem processes that distinguish the old-growth beech stands in respect to managed woodlands. Our findings demonstrate that the low-cost UAV-DAP (Digital Aerial Photogrammetry) workflow has the potential to generate realistic old-growth forest canopy attributes at a very fine scale. The proposed protocol can be adopted for monitoring the structural dynamics of high-value natural forest ecosystems as in the case of UNESCO WH sites or other old-growth stands. This approach is also helpful for mapping and deriving spatially explicit canopy structure information over confined forest areas and determining where conservation actions should be directed to preserve or restore natural ecosystem function.

The Millimeter Continuum Size–Frequency Relationship in the UZ Tau E Disk

Abstract We present high spatial resolution observations of the continuum emission from the young multiple star system UZ Tau at frequencies from 6 to 340 GHz. To quantify the spatial variation of dust emission in the UZ Tau E circumbinary disk, the observed interferometric visibilities are modeled with a simple parametric prescription for the radial surface brightnesses at each frequency. We find evidence that the spectrum steepens with radius in the disk, manifested as a positive correlation between the observing frequency and the radius that encircles a fixed fraction of the emission (R eff ∝ ν 0.34±0.08). The origins of this size–frequency relation are explored in the context of a theoretical framework for the growth and migration of disk solids. While that framework can reproduce a similar size–frequency relation, it predicts a steeper spectrum than that observed. Moreover, it comes closest to matching the data only on timescales much shorter (≤1 Myr) than the putative UZ Tau age (∼2–3 Myr). These discrepancies are direct consequences of the rapid radial drift rates predicted by models of dust evolution in a smooth gas disk. One way to mitigate that efficiency problem is to invoke small-scale gas pressure modulations that locally concentrate drifting solids. If such particle traps reach high-continuum optical depths at 30–340 GHz with a ∼30%–60% filling fraction in the inner disk (r ≲ 20 au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.

A Tectonophysical Analysis of Earthquake Frequency—Size Relationship Types for Catastrophic Earthquakes in Central Asia

We performed a tectonophysical analysis of earthquake frequency–size relationship types for large Central Asian earthquakes in the regions of dynamical influence due to major earthquake-generating faults based on data for the last 100 years. We identified four types of frequency–size curves, depending on the presence/absence of characteristic earthquakes and the presence or absence of a downward bend in the tail of the curve. This classification by the shape of the tail in frequency–size relationships correlates well with the values of the maximum observed magnitude. Thus, faults of the first type (there are characteristic earthquakes, but no downward bend) with Mmax ≥ 8.0 are classified as posing the highest seismic hazard; faults with characteristic earthquakes and a bend, and with Mmax = 7.5–7.9, are treated as rather hazardous; faults of the third type with Mmax = 7.1–7.5 are treated as posing potential hazard; and lastly, faults with a bend, without characteristic earthquakes, and with a typical magnitude Mmax ≤ 7.0, are classified as involving little hazard. The tail types in frequency–size curves are interpreted using the model of a nonlinear multiplicative cascade. The model can be used to treat different tail types as corresponding to the occurrence/nonoccurrence of nonlinear positive and negative feedback in earthquake rupture zones, with this feedback being responsible for the occurrence of earthquakes with different magnitudes. This interpretation and clustering of earthquake-generating faults by the behavior the tail of the relevant frequency–size plot shows raises the question about the physical mechanisms that underlie this behavior. We think that the occurrence of great earthquakes is related to a decrease in effective strength (viscosity) in the interblock space of faults at a scale appropriate to the rupture zone size.

Sex-biased sound symbolism in english-language first names.

Sexual selection has resulted in sex-based size dimorphism in many mammals, including humans. In Western societies, average to taller stature men and comparatively shorter, slimmer women have higher reproductive success and are typically considered more attractive. This size dimorphism also extends to vocalisations in many species, again including humans, with larger individuals exhibiting lower formant frequencies than smaller individuals. Further, across many languages there are associations between phonemes and the expression of size (e.g. large /a, o/, small /i, e/), consistent with the frequency-size relationship in vocalisations. We suggest that naming preferences are a product of this frequency-size relationship, driving male names to sound larger and female names smaller, through sound symbolism. In a 10-year dataset of the most popular British, Australian and American names we show that male names are significantly more likely to contain larger sounding phonemes (e.g. “Thomas”), while female names are significantly more likely to contain smaller phonemes (e.g. “Emily”). The desire of parents to have comparatively larger, more masculine sons, and smaller, more feminine daughters, and the increased social success that accompanies more sex-stereotyped names, is likely to be driving English-language first names to exploit sound symbolism of size in line with sexual body size dimorphism.

Fossils come in to land

Fossils found in rocks of the Ediacaran period in Australia have been previously characterized as early marine organisms. But a report suggests that these rocks are fossilized soils. So did some of these Ediacaran organisms in fact live on land, like lichens? A palaeontologist and a geologist weigh up the evidence. See Letter p.89 The smaller the bat, the higher the frequency of its echolocation calls. Until now this scaling has been attributed either to the bat's size or to the supposition that smaller bats seeking finer prey will need to use higher frequencies to pick out smaller objects. But that doesn't explain why small bats emit such high-pitched squeaks—up to 55 kHz, when 20 kHz would do the job, carry farther and take less effort to produce. Annemarie Surlykke and colleagues compare echolocation signals from six species of vespertilionid bat over a fivefold mass range. They show that the size–frequency relationship is governed by the need to maintain a focused, highly directional beam. As sound beams narrow with increasing emitter size and signal frequency, smaller mouths impose a constraint that forces smaller bats to use higher frequencies to achieve a sufficiently narrow beam. Exceptions prove the rule: phyllostomid bats show a much weaker correlation between size and frequency, but they emit sounds through specialized nasal structures, not through the mouth, and noseleaf dimensions do not scale with body size.

Quantifying postglacial sediment storage at the mountain-belt scale

Sediment storage is an often-neglected term in sediment budgets, despite being the crucial link between rates of erosion and sediment yield. Mountain belts in particular host large valley fills that modulate fluxes of water and sediment, buffer the geomorphic coupling between hillslopes and river channels, reduce local valley relief, and protect bedrock from fluvial incision. Here we propose a region-growing algorithm based on a slope-gradient criterion to automatically extract areas of postglacial fluvial and lacustrine valley fills from digital topography at the mountain-belt scale. Applying this method to the European Alps, we find that the size-frequency relationship of 17,766 individual sediment storage units, expressed by either area or volume, follows a power law over four and five orders of magnitude with scaling exponents −1.77 and −1.71, respectively. We show that 90% of the area covered by sediment storage is in the lower quartile of the mountain belt9s elevation and below the median local relief. On average, low-gradient valley fill occupies 6% of the studied drainage basins. This fraction increases with basin size, likely reflecting the larger accommodation space of trunk valleys generated by multiple glacial-interglacial cycles. Comparison with sediment storage mapped in the Southern Alps, New Zealand, indicates that rates of uplift and precipitation control the extent and spatial distribution of sediment storage at the mountain-belt scale.

A time-dependent jet model for the emission from Sagittarius A*

<i>Context. <i/>The source of emission from Sgr A*, the supermassive black hole at the Galactic Center, is still unknown. Flares and data from multiwavelength campaigns provide important clues about the nature of Sgr A* itself.<i>Aims. <i/>Here we attempt to constrain the physical origin of the broadband emission and the radio flares from Sgr A*.<i>Methods. <i/>We developed a time-dependent jet model, which for the first time allows one to compare the model predictions with flare data from Sgr A*. Taking into account relevant cooling mechanisms, we calculate the frequency-dependent time lags and photosphere size expected in the jet model. The predicted lags and sizes are then compared with recent observations.<i>Results. <i/>Both the observed time lags and size-frequency relationships are reproduced well by the model. The combined timing and structural information strongly constrain the speed of the outflow to be mildly relativistic, and the radio flares are likely to be caused by a transient increase in the matter channelled into the jets. The model also predicts light curves and structural information at other wavelengths which could be tested by observations in the near future.<i>Conclusions. <i/>We show that a time-dependent relativistic jet model can successfully reproduce: (1) the quiescent broadband spectral energy distribution of Sgr A*; (2) the observed 22 and 43 GHz light curve morphologies and time lags; and (3) the frequency-size relationship. The results suggest that the observed emission at radio frequencies from Sgr A* is most easily explained by a stratified, optically thick, mildly relativistic jet outflow. Frequency-dependent measurements of time-lags and intrinsic source size provide strong constraints on the bulk motion of the jet plasma.

Depth variation of coseismic stress drop explains bimodal earthquake magnitude‐frequency distribution

An essential part of seismic hazard analysis is the earthquake size‐frequency relationship, used to estimate earthquake recurrence time, and thus probability. A key feature of those distributions is their bimodal character: small to moderate magnitude earthquakes follow the Gutenberg‐Richter (GR) inverse power‐law relation while large magnitude (characteristic) earthquakes are more frequent than anticipated from GR, following approximately a gaussian distribution around the maximum magnitude limited by fault geometry. Using a numerical earthquake simulator, we show that the temperature dependence of friction behavior and therefore the depth‐variation of coseismic stress drop, derived from laboratory friction experiments, presents a simple and comprehensive explanation for the observed bimodal seismicity distribution. Characteristic earthquakes are the result of an abrupt increase in rupture width at the transition from small to large earthquakes.

Landslides in the Mailuu-Suu Valley, Kyrgyzstan—Hazards and Impacts

Mailuu-Suu is a former uranium mining area in Kyrgyzstan (Central Asia) at the northern border of the Fergana Basin. This region is particularly prone to landslide hazards and, during the last 50 years, has experienced severe landslide disasters in the vicinity of numerous nuclear waste tailing dams. Due to its critical situation, the Mailuu-Suu region was and still is the target area for several risk assessment projects. This paper provides a brief review of previous studies, past landslide events and a discussion on possible future risk scenarios. Various aspects of landslide hazard and related impacts in the Mailuu-Suu Valley are analyzed in detail: landslide susceptibility, historical evolution of landslide activity, size-frequency relationship, river damming and flooding as well as impacts on inhabited areas and nuclear waste storage zones. The study was carried out with standard remote sensing tools for the processing of satellite imagery and the construction of digital elevation models (DEMs). The processed inputs were combined on a GIS platform with digital landslide distribution maps of 1962, 1977, and 2003, digitized geological and geographic maps, and information from landslide monitoring and geophysical investigation.As a result, various types of landslide susceptibility maps based on conditional analysis (CA) are presented as well as predictions of future landslide activity and related damming potential and their possible impact on the population. For some risk scenarios, remediation and prevention measures are suggested.

Analysis of landslide susceptibility in the Suusamyr region, Tien Shan: statistical and geotechnical approach

The Suusamyr region is located in the northern part of the Tien Shan Range in Central Asia. In 1992, this region was hit by the Ms = 7.3 Suusamyr earthquake triggering several large landslides along the Suusamyr Valley and on the southern slopes of the adjacent Suusamyr Range. One of these landslides had been investigated by geophysical and geotechnical methods in order to determine local trigger factors. The present paper focuses on the influence of geological and morphological factors upon landslide occurrence on a regional scale. The analysis is based on a digital data set including landslides triggered in 1992 and several older landslides as well as various types of digital elevation models (DEMs), ASTER image data, and geological and active fault maps. These data were combined to compute landslide susceptibility (LS) maps using statistical methods, Landslide Factor and Conditional Analyses (LFA, CA), as well as a geotechnical one, the Newmark's Method (NM). The landslide data set was also analyzed with respect to the size–frequency relationship.

A model of characteristic earthquakes and its implications for regional seismicity

AbstractRegional seismicity (i.e. that averaged over large enough areas over long enough periods of time) has a size–frequency relationship, the Gutenberg–Richter law, which differs from that found for some seismic faults, the Characteristic Earthquake relationship. But all seismicity comes in the end from active faults, so the question arises of how one seismicity pattern could emerge from the other. The recently introduced Minimalist Model of Vázquez‐Prada et al. of characteristic earthquakes provides a simple representation of the seismicity originating from a single fault. Here, we show that a Characteristic Earthquake relationship together with a fractal distribution of fault lengths can accurately describe the total seismicity produced in a region. The resulting earthquake catalogue accounts for the addition of both all the characteristic and all the non‐characteristic events triggered in the faults. The global accumulated size–frequency relationship strongly depends on the fault length fractal exponent and, for fractal exponents close to 2, correctly describes a Gutenberg–Richter distribution with a b exponent compatible with real seismicity.

Possible evidence for the disc origin for the powering of jets in Sgr A* and nearby elliptical galaxies

Recent VLBA observation indicates the existence of an elongated (jet) structure in the compact radio source Sgr A*. This is hard to explain in the context of advection-dominated accretion flow (ADAF) model for this source. On the other hand, the mass accretion rate favoured by ADAF is 10–20 times smaller than that favoured by the hydrodynamical simulation based on Bondi capture. If the latter were adopted, the predicted radio flux would significantly exceed the observation. A similar situation exists in the case of nearby giant ellipticals, where the canonical ADAF model — the widely assumed standard model for these sources — also significantly overpredicts the radio flux. Based on these facts, in this paper we propose a truncated ADAF model for Sgr A* and three ellipticals M87, NGC 4649 and NGC 4636. We assume that the accretion disc is truncated at a certain radius Rtr within which the jet forms by extracting the energy of the disc. The radio flux is greatly suppressed owing to the radiative truncation of the disc and the fits to the observational data are excellent. For example, for Sgr A*, the model fits the observational spectrum very well from radio including the ‘excess’ below the break frequency to hard X-ray under a high accretion rate near the simulation value, and the predicted size-frequency relationship is also in excellent agreement with the observation; for M87, the predicted upper limit of the jet location is 24Rg, in excellent agreement with the observational result that the jet is formed on scales smaller than 30Rg, and the ≈20 per cent variability at ∼1 keV — which is hard to explain in another model that succeeded in explaining the low radio flux of M87 — is also marginally interpreted. The success of the model supplies possible evidence for the disc rather than the hole origin for the powering of jets.

Performance assessment of parallel spectral analysis: towards a practical performance model for parallel medical applications

We present the first parallel medical application for the analysis of dynamic positron emission tomography (PET) images together with a practical performance model. The parallel application may improve the diagnosis for a patient (e.g. in epilepsy surgery) because it enables the fast computation of parametric images on a pixel level as opposed to the traditionally used region of interest (ROI) approach which is applied to determine an average parametric value for a particular anatomic region of the brain. We derive the performance model from the application context and show its relation to abstract machine models. We demonstrate the accuracy of the model to predict the runtime of the application on a network of workstations and use it to determine an optimal value in the message frequency–size relationship.

Oceanic mega-impacts and crustal evolution

Lunar mare crater counts, the terrestrial impact flux, and astronomical observations of asteroids and comets define a consistent impact rate of 4–6 ṁ 10 −15 km −2 ṁ yr −1 within the inner solar system since the end of the late heavy bombardment ∼3.8 Ga. Coupled with the observed crater size vs. cumulative crater size frequency relationship of N ∝ D c −1.8 ( N = cumulative number of craters of diameter > D c ), these rates imply formation on Earth of more than 450 D c ≥ 100-km-diameter craters, more than 50 D c ≥ 300-km-diameter craters, and more than 20 D c ≥ 500-km-diameter craters. Geochemical and isotopic constraints require that more than 80% of the projectiles impacted on time-integrated oceanic crust since the late heavy bombardment. The injection of shock energies calculated at >10 8 Mt TNT equivalent by a D p >10-km-diameter projectile may result in propagating fractures and rift networks, thermal perturbations, and ensuing magmatic activity. Examinations of the geologic record for correlated impact and magmatic fingerprints of such events remain inconclusive in view of isotopic age uncertainties. Potential but unproven connections may be represented by the (1) Cretaceous-Tertiary boundary (ca. 65 Ma) impact(s), onset of the Carlsberg Ridge spreading, Deccan volcanism, and onset of the mantle plume of the Emperor-Hawaii chain; (2) Jurassic-Cretaceous boundary (ca. 145 Ma) impacts, onset of Gondwana breakup, including precursors of the East African rift structures; (3) Permian-Triassic boundary (ca. 251 Ma) impact(s), Siberian Norilsk traps, and Early Triassic rifting; and (4) the 3.26 Ga basal Fig Tree Group (east Transvaal) Ir-rich and Ni-rich quench spinel-bearing impact spherules and contemporaneous igneous-tectonic activity. Tests of the theory require further identification and isotopic dating of distal ejecta, impact spherule condensates, and meteoritic geochemical anomalies.

Mass and energy budgets of explosive volcanic eruptions

Analysis of the frequency‐size relationship of explosive volcanic eruptions for the past 2000 years reveals that the time‐averaged eruptive mass flux of tephra from subaerial explosive eruptions is 3×104 kg s−1. This mass flux corresponds to a thermal energy release of 4×1010 W. Half of the long‐term (&gt;10³ year) mass and thermal energy release from explosive volcanic eruptions is accounted for by eruptions of &gt;10 km³ of tephra.

Fault scaling laws and the temporal evolution of fault systems

Through an analysis of the temporal evolution of duplex fault systems, this contribution shows that it is unlikely that all faults in a deformed area will conform to a single frequency-size scaling relationship. The development of a duplex leads to different size—frequency relationships for the faults that compose the duplex and those confined to individual horses. The faults that compose the duplex define segments with relatively steep stopes on a log N (number of faults, i.e. frequency) vs log D (displacement magnitude, i.e. size) plot; faults within individual horses define segments with relatively shallow slopes on a log N vs log D plot. The distinction between these two types of faults in a duplex is akin to the distinction between large active faults, which cut the entire seismogenic layer, and small active faults, which do not extend across the seismogenic layer. If, as is often the case, the faults that compose a duplex do not extend across the seismogenic layer, the stepped nature of the resulting log N vs log D plot may make it particularly difficult to assess the contribution of these ‘small’ faults to regional deformation. Since duplex geometries result in part from anisotropies present in deforming rocks, the anisotropy present in nearly all crustal rocks will affect the size-frequency relationship observed for systems of faults. Different parts of a deforming rock mass are likely to have different initial anisotropies. Combining data on fault systems from markedly different portions of a deforming region may, then, obscure the unique characteristics of the size-frequency relationship in either area and may lead to inaccurate assessments of the relative contributions of ‘small’ and ‘large’ faults to regional fault-accommodated strains.

Changes in frequency–size relationship from small to large earthquakes

THE constant 'b value' observed in frequency–magnitude distributions of earthquakes has been taken as an indication of self-similarity at all magnitudes. Hence, earthquake properties should scale uniformly in the same way from small to large earthquakes. It has often been observed, however, that the seismic moment released in small earthquakes scales differently with rupture length than it does for large events1,2, where the crossover between small and large events is defined at a rupture dimension equal to the down-dip width of the seismogenic zone. A possible explanation for this contradiction is that frequency–size distributions are biased by small earthquakes. Small events dominate most global earthquake catalogues because of the short time-period covered. Another source of bias in size distributions is the saturation of earthquake magnitudes for large events. Here we correct biases in calculations of b values and present evidence for a change in b value in frequency–size distributions. We find that a break in self-similarity, from small to large earthquakes, occurs at a point where the dimension of the event equals the down-dip width of the seismogenic layer.

Venusian impact craters on Magellan images: View from Venera 15/16

The review of the data of the analysis of images of Venera 15/16 mission is done. These data are used to make some predictions of how many impact craters the MAGELLAN space probe would see on Venus and how they would look. The possible trends of crater areal distribution and characteristic features of the size-frequency relationship are discussed.