Frequency-size Distribution Research Articles

Spatial patterns of landslides in a modest topography of the Ozark and Ouachita Mountains, USA

Controls on landslides vary as a function of landscape and regional activity. For example, low-relief, woodland regions have slope gradients, soil types, and substrate lithologies that contrast with steeper mountainous regions prone to rock fall and debris flows. Similarly, regional variations in precipitation, earthquakes, and other impacts on landslide surfaces create regional variations in landslide properties. While the controls on landslide characteristics have been extensively studied for high-relief coastal and tectonically active regions, controls on low-relief landslides have received comparatively less attention. We focus here on a part of the Ozark and Ouachita Mountains in the US southern mid-continent to explore such characteristics of landslides and potential controls in low-relief regions. The area exhibits frequent landslides in soil-covered low-relief forested hillslopes. We evaluated the frequency-size scaling of landslides occurred during periods of different earthquake frequency and precipitation amount (pre- and post-2005). We also produced maps of landslide susceptibility based on random forest machine learning applied to remotely sensed data. We found that landslides are clustered mostly in upland hillslopes, and that small landslides dominate the area, quantified by a landslide frequency-size distribution fitting a double Pareto curve. Additionally, the overall landslide frequency, and potentially the porportion of smaller landslides relative to the larger ones, significantly increased after 2005, the period during which the area also experienced increased induced seismicity and extreme storm events. Approximately 94 % of historical landslides were within random-forest-classified high-landslide probability (probability > 0.5) zones, coinciding with moderate to steep (18° ± 9°) and convergent upland slopes underlain by shale and sandstone. Anomalously high frequency landslides appear to result from triggering by extreme weather, human-induced earthquake activity, and human-induced hillslope modification.

Viscoelastic Slider Blocks as a Model for a Seismogenic Fault.

In this work, a model is proposed to examine the role of viscoelasticity in the generation of simulated earthquake-like events. This model serves to investigate how nonlinear processes in the Earth's crust affect the triggering and decay patterns of earthquake sequences. These synthetic earthquake events are numerically simulated using a slider-block model containing viscoelastic standard linear solid (SLS) elements to reproduce the dynamics of an earthquake fault. The simulated system exhibits elements of self-organized criticality, and results in the generation of avalanches that behave similarly to naturally occurring seismic events. The model behavior is analyzed using the Epidemic-Type Aftershock Sequence (ETAS) model, which suitably represents the observed triggering and decay patterns; however, parameter estimates deviate from those resulting from natural aftershock sequences. Simulated aftershock sequences from this model are characterized by slightly larger p-values, indicating a faster-than-normal decay of aftershock rates within the system. The ETAS fit, along with realistic simulated frequency-size distributions, supports the inclusion of viscoelastic rheology to model the seismogenic fault dynamics.

Scaling properties of seismicity and faulting

The Gutenberg–Richter law and the Omori law are both characterized by a scaling behavior. However, their relation is still an open question. Although several hypotheses have been formulated, a comprehensive geophysical mechanism is still missing to explain the observed variability of the scaling exponents b-value and p-value, e.g., correlating the seismic cycle to statistical seismology and tectonic processes. In this work, a model for describing the size-frequency scaling and the temporal evolution of seismicity is proposed starting from simple assumptions. The parameter describing how the number of earthquakes decreases after a major seismic event, p, turns out to be positively correlated to the exponent of the frequency-size distribution of seismicity, b, and related to tectonics. Our findings suggest that p≈23(b+1). It implies that a relationship between fracturing regimes, “efficiency” of the seismic process, duration of the seismic sequences and geodynamic setting exists, with outstanding potential impact on seismic hazard. On the other hand, the Gutenberg–Richter law simply reflects the tendency of the segments of the Earth's crust to reach mechanical stability via constrained energy-budget optimization. Each perturbation has a probability of growing an earthquake or not, depending on disorder within the fault zone and the energy accumulated in the adjoining volume, mainly controlling the evolution of seismic sequences. The results are consistent with the different energy sources related to the tectonic settings, i.e., gravitational in extensional regimes, having higher b and p values, and generating lower maximum magnitude earthquakes with respect to strike-slip and contractional settings, which are rather fueled by elastic energy, showing lower b and p values, and they may generate higher magnitude events.

Changes in seismicity pattern due to the 2016 Kumamoto earthquake sequence and implications for improving the foreshock traffic-light system

Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan, that culminated in a preceding earthquake of magnitude M6.5 and a subsequent M7.3 earthquake 28 h later, caused stress perturbation on and around the causative Futagawa-Hinagu fault zone. Monitoring changes in seismicity pattern along this zone plays a role in understanding the process before and after major earthquakes. For this purpose, stress-dependent laws in statistical seismology can be used: the Gutenberg-Richter frequency-size law and the Omori-Utsu aftershock-decay law. We review the results obtained by using these laws in previous studies to show a zone of high stress near the eventual epicenters of the M6.5 and M7.3 earthquakes before the start of the Kumamoto sequence, and after it, showing a decreasing trend in stress along the Futagawa-Hinagu fault zone. Detailed analysis suggests aseismic slips along the causative fault zone. The aseismic preslip locally reduced stress just prior to the M7.3 earthquake near its epicenter. Recently, a system was proposed by Gulia and Wiemer (2019) that utilizes the Gutenberg-Richter frequency-size law to judge, immediately after a large earthquake, whether it was the mainshock or a foreshock to a future event. Based on the reviewed results and our new results, further research that takes into account the spatial variation of frequency-size distribution, allowing the exploration of the possibility of a local preslip of a future nearby earthquake, is needed to improve this system.

The Spatial Distribution of High Growth Entrepreneurship: Generative Mechanisms of Heavy Tails

Why does a disproportionate amount of high-growth entrepreneurship concentrate in a small number of geographical areas? Our research question is motivated by the heavy tails in the frequency-size distributions of high-growth entrepreneurship—the number of early-stage financing rounds, acquisitions among firms that received early-stage financing, and initial public offerings (IPOs)—in a metropolitan or micropolitan statistical area (MSA). The heavy tails could result from either of two distinct processes, but the existing research on entrepreneurship and agglomeration cannot tell the two processes apart. In this paper, we apply technical advances from complexity science and analyze which process is the more likely generative mechanism for the observed heavy tails. Using data from Crunchbase, our analysis covers 129,949 financing rounds of 58,517 unique firms across 657 MSAs, 10,145 acquisitions, and 4,614 IPOs. We find the multiplicative process to be the more likely mechanism, compared to the rich-get-richer process, which has been posited in the literature as a driver of regional advantage. For research, our finding changes the way we theorize and study agglomeration and entrepreneurship. For government policy, our research enhances the efficacy of interventions—in the form of tax breaks, business incubators, or grants aiming to stimulate entrepreneurial activity, spur innovation and create new jobs—by revealing the generative mechanism for the emergence of a region’s advantage in high-growth entrepreneurship. For entrepreneurs, our research informs whether and how the choice of where to locate the start-ups may have implications for the likelihood of obtaining early-stage financing, becoming acquired, and going public.

Frequency-size distributions of Wadati-Benioff zone and near-boundary intraplate earthquakes: Implications for intermediate and deep seismicity

We conduct a systematic analysis of the frequency-moment distribution of earthquake populations in Wadati-Benioff zones, motivated by a three-fold increase in the available GlobalCMT database since the previous study by Okal and Kirby (1995), in which some datasets may have been undersampled. We use 100-km depths bins, processed with both least-squares and maximum-likelihood algorithms, and apply an F-test methodology to assess the robustness of our results, in particular regarding multi-segment behavior within individual depth bins. Our results generally support Okal and Kirby's (1995), and the new enlarged dataset suggests the resolution of the third segment predicted by these authors for the 500–600 km bin in Tonga, in the framework of their three-tier model for two-step source saturation of seismicity generated by transformational faulting within a wedge of metastable olivine. In the 200–300 and 300–400 km depth bins, we find comparable behaviors, revealing the artificial nature of the traditional 300-km boundary between “intermediate” and “deep” earthquakes. Our view is that it may be deeper than 300 km, and fundamentally variable between distinct subduction zones.We extend our study by considering frequency-moment distributions for intraplate earthquakes in oceanic lithosphere before it subducts at trenches. Those results support the interpretation of seismicity in the shallowest portions of slabs as involving the reactivation of existing faults under a process of dehydration embrittlement. However, outer rise events occurring immediately before subduction feature different population statistics, which are probably related to the release of bending stresses of a different origin.

Significant contribution of small icebergs to the freshwater budget in Greenland fjords

Icebergs represent nearly half of the mass loss from the Greenland Ice Sheet and provide a distributed source of freshwater along fjords which can alter fjord circulation, nutrient levels, and ultimately the Meridional Overturning Circulation. Here we present analyses of high resolution optical satellite imagery using convolutional neural networks to accurately delineate iceberg edges in two East Greenland fjords. We find that a significant portion of icebergs in fjords are comprised of small icebergs that were not detected in previously-available coarser resolution satellite images. We show that the preponderance of small icebergs results in high freshwater delivery, as well as a short life span of icebergs in fjords. We conclude that an inability to identify small icebergs leads to inaccurate frequency-size distribution of icebergs in Greenland fjords, an underestimation of iceberg area (specifically for small icebergs), and an overestimation of iceberg life span.

Impact of mapping strategies on rockfall frequency-size distributions

Rockfall frequency size distributions are used in Austria for the definition of a design block for the planning of technical rockfall protection. Rockfall size datasets are often incomplete. Here, we study fifteen catalogues of rockfall size in Austria, Italy, and the USA to analyse the impact of the data collection and mapping methods on the representativeness of the catalogues and on the estimates of frequency-size statistics. To describe and compare the catalogues of rockfall size, we first use Empirical Cumulative Distribution Functions (ECDFs), followed by parametric distribution estimates in the form of Probability Density Functions (PDFs), and Cumulative Distribution Functions (CDFs). We discuss the output of Kolmogorov-Smirnov tests, the position of the frequency-size distribution rollover, and the p-value and the standard errors associated to the distribution parameters estimates to determine the reliability of our model results. In addition, we analyse the variations in the modelled CDFs for different percentiles of the frequency-size distributions to describe and discuss the representativeness of the rockfall catalogues. Our results show that different mapping strategies may affect the estimates of frequency-size distribution of rock fall volume, a relevant information when evaluating the possible impacts of rockfall processes. We conclude offering recommendations for rockfall mapping, and the use and of a non-parametric statistical method being capable to deal with small datasets, which is very typical when dealing with rockfall data. Such recommendations help for a correct dimensioning of designing rockfall mitigation measures.

Characteristic landslide distributions: An investigation of landscape controls on landslide size

Estimation of landslide erosion rates and hazard prediction require a firm understanding of the physical controls on landslide size. In this study we seek to understand how the characteristics of different landscapes and forcing events influence the distribution of landslide size at a regional scale. We explore the parameter space of a mechanically-based landslide model through a series of simulations using digital elevation data. Consistent with previous studies, we find that large slope failures are infrequent due to the scarcity of large, steep hillslopes in typical mountainous topography. On the other hand, we find that the occurrence of small landslides is limited by the cohesive strength of hillslope material, which overcomes the weaker driving forces on short slopes. We test our model results with an empirical investigation of frequency-size distributions for eight real co-seismic landslide inventories. Although empirical data are noisy, we find a positive correlation between landslide size and hillslope relief, while the effects of PGA on landslide size are less pronounced. We conclude that landslide size distributions reflect the available distribution of hillslope geometries in a given landscape, and that external forcing (e.g., seismic ground motion) determines which subset of the hillslope distribution fails during a particular event. For a given landscape and forcing event, there is a particular length-scale over which landsliding is statistically favored, leading to the concept of characteristic landslide size distributions.

Closed depressions in Kotido crater, Arabia Terra, Mars. Possible evidence of evaporite dissolution-induced subsidence

The identification of karst sinkholes in Mars may provide evidence of dissolution processes caused by liquid water and information on paleoclimatic and paleohydrological conditions. This work presents a comprehensive cartographic inventory of 513 closed depressions developed on evaporite-bearing Equatorial Layered Deposits (ELDs) within Kotido crater, Arabia Terra. Detailed mapping, morphometric analyses and spatial distribution relationships reveal a number of features supporting that the depressions correspond to collapse sinkholes related to evaporite dissolution: (1) suitable topographic and litho-structural conditions for the development of a fracture-controlled epigene evaporite karst; (2) presence of open fissures at the foot of the scarped margins; (3) dimensions and frequency-size distributions comparable with those reported on Earth; (4) spatial association with high-permeability zones (i.e., fractures). Some characteristics of the depressions indicate that they have been re-shaped and enlarged by wind erosion: (1) dominant orientation consistent with the prevalent one-directional winds; (2) differing morphological characteristics on the downwind- and upwind-sides; and (3) nested depressions associated with the upwind sector. The relatively fresh appearance of the depressions and the lack of impact craters suggest a poorly constrained Amazonian karstification phase in the region.

Energy Balance in Avalanche Models for Solar Flares

Abstract The distributions of solar flare energies and waiting times have not been described simultaneously by a single physical model, yet. In this research, we investigate whether recent avalanche models can describe the distributions for both the released energies and waiting times of flares in an active region. Flaring events are simulated using the modified Lu and Hamilton model and also the optimized model. Applying a probability balance equation approach, we study the statistics of the simulated flaring events and investigate the origin of the observed power law in the flare frequency-size distribution. The results indicate that the power law originates in the distribution of transition rates (the distribution of the probabilities of transitions between different energies) rather than the distribution of the energy of the active region. It is also observed that the waiting-time distribution of simulated flaring events follows a q-exponential function, which approximates a simple Poisson distribution.

Exploring the frequency-size relationships of pipe collapses in different morphoclimatic regions

Piping is an important land degradation process that occurs in almost all climatic zones. This study analyses for the first time the frequency-size distribution of different types of pipe collapses (PCs): sinkholes and compound depressions related to the coalescence of sinkholes (compound sinkholes and elongated blind gullies). Exploring the frequency-size relationships of PCs provides critical morphometric information about this hazardous erosion and ground-stability process, as well as its impact on hillslope denudation, hillslope-channel coupling and landscape development. The analysis has been performed with field-based inventories of PCs from five catchments located in two different morphoclimatic environments: one in the semi-arid Ebro Depression, NE Spain (Valpalmas catchment), and four in the humid Bieszczady Mts., SE Poland. In total, 724 PCs were mapped, among which 335 PCs in Valpalmas and 389 PCs in the Bieszczady Mts. The morphometric analyses were based on the major axis (the maximum length or width) and area of the PCs. Despite differences between study areas from NE Spain and SE Poland (related to climate conditions, rainfall regime, soil water storage capacity, spatial pattern of pipe networks, vegetation cover and land use), empirical cumulative frequency curves of PCs show similar patterns in all study sites indicating similar overall effects of piping erosion. The size distribution of the inventoried PCs can be modelled satisfactorily with logarithmic functions with high goodness of fit values (R2 ≥ 0.93) for each type of PC and the combined set of PCs (sinkholes and compound sinkholes/blind gullies) mapped in each area and in the five catchments together. The PCs mapped in Valpalmas are displaced towards larger dimensions attributable to local factors. The applicability and limitations of frequency-size relationships of PCs for geomorphological studies and hazard assessment are discussed.

Topographic effects on frequency-size distribution of landslides triggered by the Hokkaido Eastern Iburi Earthquake in 2018

This study examined the frequency-size distribution of 6117 landslides spread over 440 km2 in Iburi Subprefecture, Hokkaido, Japan, induced by the Hokkaido Eastern Iburi Earthquake (Mw 6.6) on September 6, 2018. The study area is characterized by gently undulating terrain that is finely dissected by shallow streams and covered predominantly by layers of volcanic products with high water content. Most of the landslides were shallow landslides, and their slip surfaces often formed in a layer of volcanic soil called the “Ta-d,” deposited at 9000 ybp. Low ridges separating small catchments allowed individual landslides to coalesce in many locations. The average size of landslides was 7160 m2. Landslide size tended to increase with slope angle up to 20° to 25° and then decrease with further increase of slope angle. About half of the landslides occurred in a feature with both concave planform and profile curvature, and their average size was 8720 m2. In contrast, 17% of the total landslides occurred in the case of both curvatures being convex, and their average size was 5190 m2. The results indicated that the accumulation of saturated soil in concave features provided more opportunities for landslides of large sizes. The frequency-size distribution of the landslides presented high rollover, 5.0 × 10−3 km2, but the exponent of power law decay for medium to large landslides, − 2.46, was not largely different from those of studies in other locations. Compared with other seismically caused examples, the landslides triggered by the Hokkaido Eastern Iburi Earthquake can be characterized as more clustered, more numerous, and larger in size for the moment magnitude of the earthquake. Conversely, the magnitude scale for the landslide event estimated from the total landslide area was equivalent to that of a region struck by an earthquake of Mw = 7.0 to 7.4. This study demonstrated that gently undulating regions can produce unexpectedly large and frequent landslides when struck by an intense earthquake, and when soil layers vulnerable to ground shaking cover the ground.

Rapid prediction of the magnitude scale of landslide events triggered by an earthquake

A landslide event is characterized by the distribution of landslides caused by a single triggering event. The severity of earthquake-induced landslide events can be quantified by the landslide-event magnitude, a metric derived from the frequency-size distribution of landslide inventories. However, reliable landslide inventories are not available for all earthquakes, because the preparation of a suitable inventory requires data, time, and expertise. Prediction of landslide-event magnitude immediately following an earthquake provides an estimate of the total landslide area and volume based on empirical relations. It allows to make an assessment of the severity of a landslide event in near-real time and to estimate the frequency-size distribution curve of the landslides. In this study, we used 23 earthquake-induced landslide inventories and propose a method to predict landslide-event magnitude. We selected five predictors, both morphometric and seismogenic, which are globally and readily available. We used the predictors within a stepwise linear regression and validated using the leave-one-out technique. We show that our approach successfully predicts landslide-event magnitude values and provides results along with their statistical significance and confidence levels. However, to test the validity of the approach globally, it should be calibrated using a larger and more representative dataset. A global, near real-time assessments regarding landslide-event magnitude scale can then be achieved by retrieving the readily available ShakeMaps, along with topographic and thematic information, and applying the calibrated model. The results may provide valuable information regarding landscape evolution processes, landslide hazard assessments, and contribute to the rapid emergency response after earthquakes in mountainous terrain.

Projected drought effects on the demography of Ashe juniper populations inferred from remote measurements of tree canopies

Tree mortality from drought is anticipated to increase as climate change promotes more frequent or severe water limitation. Ecosystem impacts of woody mortality depend on both the number and sizes of trees that die, but a limited capacity to predict mortality risk for individual trees hinders the capacity to forecast drought effects on tree population demography and ecosystem processes. We remotely measured leaf area of living Ashe juniper trees at three savanna sites in central Texas, USA to characterize the frequency-size distribution (FSD) of juniper populations and evaluate mortality risk from drought as a function of tree size. Mortality risk of individuals was assessed from the deviation in leaf area per tree from that of a similarly sized individual with near maximal leaf area using correlations among leaf area, growth rate, and mortality measured during a prior drought. We found that the FSD of juniper trees is bell-shaped at each site. Mortality risk from drought exceeded 25% of emergent (> 4 m height) trees in savanna juniper populations, but was highest for largest trees. Mortality risk was greatest at a grazed savanna, exceeding 50% of trees with projected canopy area > 20 m2. Results imply that severe drought could kill a large fraction (18–85%) of intermediate- to large-sized Ashe juniper trees in central Texas savannas. Our analysis demonstrates a novel use of remote measurements of canopy foliation to link mortality risk from drought to the demography of Ashe juniper populations through properties of individual trees.

Scale invariant behavior of cropping area losses

This paper shows how crop losses, display Self-Organized Critical Behavior, which implies that under a wide range of circumstances, these losses exhibit a power-law dependence on frequency in the affected area whose order of magnitude approximates those reported for extreme climate events. Self-Organized Critical Behavior has been observed in many extreme climate events, as well as in the density and distribution of pests linked to crop production. Empirical proof is provided by showing that the frequency-size distribution of the cropland loss fits the Pareto and the Weibull models with scaling exponents that are statistically similar to the expected value. In addition, the test included comparisons of the expected value and the predicted value of the scaling exponents among different subsystems and among systems of the same universality class. Results show that the Pareto model fits the heavy-tailed distribution of losses mostly caused by extreme climate events, while the Weibull model fits the whole distribution, including small events. The analyses show that crop losses adopt Self-Organized Critical Behavior regardless of the growing season and the water provision method (irrigated or rainfed). Irrigated systems show more stable behavior than rainfed systems, which display higher variability. The estimation is robust not only for calculating model parameters but also for testing the proximity to a power-law-like relationship.A long-term risk index by growing season and water provision method is derived as an application of this power-law behavior. The index is flexible, comparable between geographical units regardless of their size and provides an indirect measure of the probability of losing a cropping area of a given size.

The effects of slope length and slope gradient on the size distributions of loess slides: Field observations and simulations

In this study, we characterize and consider the effects of slope length and slope gradient on the size distributions of loess slides. To carry out this study, we employ data on 275 loess slides within Zhidan County, Central Loess Plateau, China. These data were collected in the field and supplemented by the interpretation of remote sensing images. Both the field observations and slope stability analysis show that loess slide size increases with the slope length. Slide sizes is significantly correlated with slope length, showing a power law relationship in both cases. However, the simulation results show that slope gradient is not associated with loess slide size. The main part of the link between slope gradient and slide size seen in the observations is only apparent, as indicated by the strong connection between slope gradient and length. Statistical analysis of the field observations reveals that slope gradient decreases with increasing slope length, and this correlation interferes with the potential relationship between landslide sizes and slope gradient seen in the field observations. In addition, the probability densities of the areas of loess slides occurring on slopes of different slope lengths are determined using kernel density estimation. This analysis shows that slope length controls the rollover of the frequency-size distribution of loess slides. The scaling exponent increases with slope length.

The Time-Scaling Analysis of Chinese Stock Market Based on Fractal Methods

Detrended fluctuation analysis (DFA), detrended cross-correlation fluctuation analysis (DCCA) and multifractal methods are applied to the time-scaling properties analysis of daily closing prices of Shanghai composite index (SHCI) and Shenzhen composite index (SZCI) of Chinese stock market. The results show that these index series are characterised by long-term memory, multifractal scaling and power-law behavior, and these characteristics have obvious differences between the SHCI and SZCI. The comparison results suggest that heterogeneity (disordered state) characterises of the SHCI dynamics owing to the wider fluctuation of the power of impulsion and suppression outside to stock, and other related factors in Shanghai stock market than that of SZCI in Shenzhen stock market. Furthermore, we investigated the frequency-size distribution of SHCI and SZCI series. This work can be helpful to improvement of modelling of Chinese stock market.

The 2015 Mw 7.8 Gorkha Earthquake in Nepal and its aftershocks: analysis of strong ground motion

Various aspects of the 2015 Gorkha Earthquake and its aftershocks are presented, and different hypotheses about the nature of long period pulses observed in ground motion record in Kathmandu Valley are critically discussed and reviewed. The frequency-size distribution of aftershocks, as well as the temporal distribution within one year of the mainshock is discussed. Some interesting features of the strong ground motion of the mainshock recorded at different places in Kathmandu Valley are discussed. Although the root-mean-square horizontal ground accelerations recorded at rock and soft sites were similar, the peak accelerations varied significantly. Elastic response spectra of the mainshock near the centre of the Valley (KATNP station operated by USGS) contained two very distinct peaks: a narrower and larger peak at ~0.4 s and a smaller, but very wide, peak at ~5 s. The peak of the spectra was significantly larger than what is commonly adopted in design codes. The latest published uniform hazard spectra for a 475-year return period were found to significantly over-estimate seismic demands on stiff structures (fundamental period less than ~0.5 s,) and underestimate the demands on more flexible structures. The resonant site frequencies computed from microseismic recordings, as reported in published literature, are found to be much larger than what was observed in the spectral ratio of ground motion recorded in soft sediments and exposed bedrock in Kathmandu. Response spectra of aftershock motions recorded at two stations lacked the peculiar peak at 5 s observed in the spectra of mainshock motion. The relatively high Fourier spectral amplitudes (at frequencies near 0.2–0.3 Hz) of ground acceleration recorded at the rock site indicate that the long-period pulse prominent at the soft site was not entirely due to site effects. The polarization pattern of the 5 s pulse at the rock site and at soft site KATNP were found to be very different. Comparison of polarization patterns of mainshock ground motion at rock and soft sites indicate that the 5 s pulse observed at some locations in Kathmandu Valley is a combination of shear waves (the amplitudes of which were amplified by the basin layers) and Love waves.

Bayesian estimation of the Modified Omori Law parameters for the Iranian Plateau

The forecasting of large aftershocks is a preliminary and critical step in seismic hazard analysis and seismic risk management. From a statistical point of view, it relies entirely on the estimation of the properties of aftershock sequences using a set of laws with well-defined parameters. Since the frequentist and Bayesian approaches are common tools to assess these parameter values, we compare the two approaches for the Modified Omori Law and a selection of mainshock–aftershock sequences in the Iranian Plateau. There is a general agreement between the two methods, but the Bayesian appears to be more efficient as the number of recorded aftershocks decreases. Taking into account temporal variations of the b-value, the slope of the frequency-size distribution, the probability for the occurrence of strong aftershock, or larger main shock has been calculated in a finite time window using the parameters of the Modified Omori Law observed in the Iranian Plateau.