Gutenberg-Richter Research Articles

Frequency-Magnitude Characteristics Down to Magnitude -4.4 for Induced Seismicity Recorded at Mponeng Gold Mine, South Africa

This article aims to investigate the frequency-magnitude characteristics and lower magnitude limits of the microseismic catalog recorded with a seismic network sensitive to high frequencies at Mponeng mine, South Africa. The network, composed of one three-component accelerometer and eight acoustic emission sensors, is located at a depth of 3.5 km below the surface and covers the limited volume of approximately 300×300×300 m. The three-component accelerometer was used to estimate the moment magnitude for the limited number of 135 events ( M w ranged from -4.1 to -0.3) well recorded by the network. We use the relation between the moment magnitude estimated from accelerometer data and radiated energy/moment magnitude estimated from acoustic emission sensors to extend the catalog to lower magnitudes. The magnitude of completeness of selected spatiotemporal subsets of the catalog was estimated for: (1) an aftershock sequence of an M w 1.9 event that occurred approximately 30 m from the network, and (2) postblasting activity during working days, located more than 80 m from the network. The data follow the Gutenberg–Richter (GR) frequency-magnitude relationship with no visible deviation from self-similar behavior of seismicity between M w -4.4 and -1.9 for the aftershock sequence and between -3.5 and -1.5 for the postblasting dataset. We estimated the magnitude of completeness of selected subset as low as -4.3 ( b =1.26) for the aftershock sequence and -3.4 ( b =1.17) for the postblasting activity. Differences in magnitude of completeness are attributed to location of recorded activity and site effects.

Mapping the -Value and the Test Results on the Hyper-Gutenberg-Richter Relation for Microseismicity around the Japanese Islands

Abstract The coexistence of two earthquake groups, each following the Gutenberg–Richter (GR) relation with different b -values (hereafter called the hyper-GR group), is discussed, and an algorithm is developed to recognize them. I show how the η -value proposed in 1978 by Utsu, who introduced the parameter representing an upward or downward convex curvature of frequency-magnitude distribution (FMD), differs significantly between GR and hyper-GR groups. The spatial variation of the FMD of earthquakes down to M 2.2 in and around the Japanese islands is studied using the algorithm and the η -value. The η -value for one year preceding the M 7.4 Kii-Hanto-Oki earthquake of 2004 was high, displaying an upward convex curvature of FMD in and around the source region. The hyper-GR group was found to be a significantly better distribution model than the GR group for the seismicity greater than M 2.15, but hyper-GR was not significantly better for seismicity greater than M 3 of greater sampling radius. Further study is required to judge if it is a precursor to the event.

A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form

We study the cumulative distribution for the magnitude of earthquakes in the context of nonextensive statistical mechanics. A new modification of the Gutenberg–Richter (GR) law is introduced. We use seismic data sets which were recorded in two different regions, Iran and California, to compute the cumulative distribution of the magnitudes. The empirical data are fitted extremely well by our suggested expression for the modified GR law over the whole range of magnitudes.

Seismicity in source regions of large interplate earthquakes around Japan and the characteristic earthquake model

AbstractThe occurrence rate of the characteristic earthquake (CE) was compared with seismicity in nine source regions of interplate earthquake (i.e., the regions off Shikotan Island, off Nemuro, off Tokachi, off Northern Sanriku, off Miyagi, far off Miyagi, and the Tonankai, Nankai, and Kanto regions) by combining instrumental data and the recurrence interval of CEs evaluated by the Headquarters for Earthquake Research Promotion (HERP) in Japan. The recurrence interval of the Nankai earthquake was estimated on the basis of long historical records and found to be one of the least uncertain ones. We used the unified catalog of earthquakes obtained by the Japan Meteorological Agency (JMA) on the basis of a recently improved seismic network, together with the old JMA catalog. Seismicity of all the interplate source regions indicated that the number of observed events was much less than the number of events predicted from the Gutenberg-Richter (G-R) relation and the occurrence rate of the CE. In all regions except for far off Miyagi, the CEs occurred during the interval of the earthquake catalog. Thus, our data set included the highest seismicity period during an earthquake cycle. In the region off Tokachi where the 1952 and 2003 Tokachi-Oki earthquakes occurred, the magnitude frequency distribution (MFD) during one seismic cycle exhibited a magnitude gap of 1.1 between the CE and the other events. Therefore, our results favored the CE model. Moreover, we conversely estimated an average recurrence interval of the CEs in each region, based on the assumption that the G-R relation holds. Most estimated recurrence intervals were far longer than the evaluation given by HERP.

Fractal analysis of damage detected in concrete structural elements under loading

In Civil Engineering materials subjected to stress or strain states a quantitative evaluation of damage is of great importance due to the critical character of this phenomenon, which at a certain point suddenly turns into a catastrophic failure. An effective damage assessment criterion is represented by the statistical analysis of the amplitude distribution of acoustic emission (AE) signals emerging from the growing microcracks. The amplitudes of such signals are distributed according to the Gutenberg–Richter (GR) law and characterised through the b-value which decreases systematically with damage growth. On the other hand, the damage process is also characterised by the progressive coalescence of microcracks to form fracture surfaces. Geometrically the fractal dimension D of the damaged domain is expected to decrease from an initial value comprised between 2 and 3 towards a final value nearly equal to 2. The b-value and the fractal analysis, are here applied to two case studies of concrete specimens loaded up to failure, and the obtained results are compared and discussed. In particular, we emphasize that a single fractal dimension does not adequately describe a crack network, since two damaged domains with the same fractal dimension could have significantly different properties.

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.

On-chip earthquake simulation model using potentials

A two-dimensional (2-D) Cellular Automata (CA) dynamic system constituted of cells-charges has been proposed for the simulation of the earthquake process. The CA model has been calibrated with the use of real data. The calibration incorporates major seismic characteristics of the area under test. The simulation results are found in good quantitative and qualitative agreement with the recorded Gutenberg–Richter (GR) scaling relations. The model is enriched with a powerful multi-parameter interface that enables the user to load real data from different regions. This paper examines the on-chip realisation of the model and its instrumentation. The CA model hardware implementation is based on Field Programmable Gate Array (FPGA) logic. It utilises an array of 32 × 32 cells. Parameters that construct the local CA rule constitute the input data. The initial seed, which to some extent corresponds to the seismic features of the area under test, is loaded in a semi-parallel way and the process is completed in a certain number of time steps. The automatic response of the processor provides the corresponding GR scaling law of the area under study. The hardware implementation of the CA-based earthquake simulation model is advantageous in terms of low-cost, high-speed, compactness and portability features. It can operate as a preliminary data-acquisition filter that accelerates the evaluation of recorded data as far as its origin time, spatial and magnitude completeness and quality are concerned. Software that performs reliable automatic phase picking, as well as data elaboration, can be assembled next to the earthquake recording instruments (the whole network) output to assure a quick and reliable iteration of the focal parameters of a recorded earthquake (epicentre coordinates, focal depth and magnitude). The dedicated processor can be accommodated right after this stage (before any manual elaboration) focusing on the near real-time development of a reliable qualitative dynamical seismic record and a mapping of the seismic characteristics of the area.

The Effect of Regional Borders when Using the Gutenberg-Richter Model, Case Study: Western Anatolia

A probabilistic seismic hazard analysis (PSHA) for Western Anatolia is presented using the Gutenberg-Richter (G-R) frequency-magnitude relation. Since the modeling is sensitive to the location of seismotectonics boundaries, to use the information content of the observed earthquake data, as a general rule the borders of the affected area are extended. In this study, the effect of the region’s definition on the G-R model is debated on the Western Anatolian region, which is one of the most seismically active and rapidly deforming regions of the world throughout the ages. Calculations are carried out for two subregions and one combined region as a whole using the seismic catalog from 1900 to 2005. The data sets are determined by the region’s borders with the parameters computed according to these data sets by the least-squares and maximum likelihood methods, and then future predictions are estimated via these parameters. Comparing the results with historical earthquake records, most appropriate regional borders for Western Anatolia are defined, and for this new region G-R model parameters are obtained.

Modelling earthquake activity features using cellular automata

Cellular automata (CA) are a powerful technique for modelling otherwise intractably complex systems. On the other hand, earthquake can be defined as a spatially extended dissipative dynamic system that naturally evolves into a critical state with no characteristic time or length scales. In this paper, a two-dimensional CA model capable of reproducing some prominent features of earthquake data is presented. The proposed model with continuous states and discrete time, comprises cell-charges and aims at simulating earthquake activity with the usage of potentials. Several measurements have been carried out at different critical states, leading to different paths to criticality, for various cascade (earthquake) sizes, various cell activities and different neighbourhood sizes. Most notably, the produced simulation results emulate the Gutenberg–Richter (GR) scaling law, in both quantitative and qualitative way. Furthermore, the CA model has been implemented with a user-friendly interface and the user can change several of its parameters, in order to study various hypotheses concerning the aforementioned earthquake activity features.

Richter's laws at the laboratory scale interpreted by acoustic emission

In the present work the acoustic emission (AE) technique is applied to examine some aspects influencing concrete failure in compression. By monitoring a structure by means of the AE technique, it proves possible to detect the occurrence of stress-induced cracks. Cracking, in fact, is accompanied by the emission of elastic waves that propagate within the bulk of the material. These waves can be received and recorded by transducers applied to the surface of the structural elements. This technique can be used for diagnosing structural damage phenomena. The current paper presents a mixed experimental and theoretical approach to evaluate the energy density dissipated during compression at each value of strain. Through this method, the two semi-empirical Gutenberg–Richter (GR) laws, well-known in seismology, are verified, the fractal interpretation results of which are very close to the essence of the AE phenomenon. Furthermore, the mentioned approach allows the parameter of ‘magnitude’ to be identified, appearing in the laws, with the number of oscillations larger than a given threshold measured in volts. Finally, the developed concepts are applied to the study of the compression phenomenon. In particular, by this approach, it is possible to distinguish between the energy progressively dissipated or stored in a compressed structural element.

A cellular automaton simulation tool for modelling seismicity in the region of Xanthi

Seismicity is an extended geophysical characteristic of the Greek dominion. There are certain areas of high seismic activity, as well as, regions of low seismicity where strong earthquakes are rather rare events. Consequently, it is of great interest to present a methodology concerning the earthquake process in Greece even for areas considered to be of low seismicity. In this paper, a study of the earthquake activity of an area in Northeastern Greece, centred at Xanthi, Thrace, extending over a region of radius R = 80 km, during a certain time period is presented. A two-dimensional cellular automaton (CA) dynamic system consisting of cells representing charges is used for the simulation of the earthquake process. The model has been tested as well as calibrated using the recorded events of the above-mentioned region as initial conditions. The simulation results are found in good quantitative and qualitative agreement with the Gutenberg–Richter (GR) scaling relations. Finally, the CA model has a user-friendly interface and enables the user to change several of its parameters, in order to study various hypotheses concerning the seismicity of the region under consideration.

Gender in medical education: The Nijmegen pilot-project

The main purpose of this study is to apply an innovative approach to assess simultaneously the median annual seismicity rates and their dispersions for Taiwan earthquakes in different depth ranges. In this approach an alternative Gutenberg-Richter (G-R) relation is explicitly expressed in terms of both the logarithmic mean annual seismicity rate and its standard deviation, instead of only by the arithmetic mean in the conventional G-R relation. Seismicity data from 1975 to 2014 in a Taiwan earthquake catalog with homogenized Mw moment magnitudes are used in this study. This catalog consists of high-quality earthquake data originally obtained by the Institute of Earth Sciences (IES) and the Central Weather Bureau (CWB). The selected seismicity data set is shown to be complete for Mw⩾3.0. The logarithmic mean annual seismicity rate and its standard deviation from the observed annual seismicity rates of individual years are obtained initially for different Mw ranges. It is shown subsequently that the logarithmic annual seismicity rates indeed possess a well-behaved lognormal distribution. It is further shown that our new approach has an added merit that tends to suppress the influences of anomalously high annual seismicity rates due to large numbers of aftershocks from major earthquake sequences. Finally, the observed logarithmic mean annual seismicity rates with their standard deviations for 3.0 ⩽ Mw ⩽ 5.0 are used to obtain the alternative Gutenberg-Richter relations for different depth ranges. The results are as follows:log10N=5.75-0.90Mw±(0.25-0.01Mw) for focal depth 0–300 km;log10N=5.78-0.94Mw±(0.20+0.01Mw) for focal depth 0–35 km;log10N=4.72-0.89Mw±(-0.08+0.08Mw) for focal depth 35–70 km;log10N=4.69-0.88Mw±(-0.47+0.16Mw) for focal depth 70–300 km.In above equations log10N represents the logarithmic annual seismicity rate. These G-R relations give distinctly different values of the parameters a and b for Taiwan earthquakes in different depth ranges. These analytical equations can be readily used to obtain both the mean logarithmic annual seismicity rate and its standard deviation for any given Mw. As an example, a numerical table presenting the corresponding median annual seismicity rates and their upper and lower bounds at median ± one standard deviation levels, is given at the end. This table offers a concise glance at the annual seismicity rates for Taiwan earthquakes of various magnitudes and focal depths. It is interesting to point out that the seismicity rate of crustal earthquakes, which tends to contribute most hazards, accounts for only about 74% of the overall seismicity rate in Taiwan. Accordingly, direct use of the entire earthquake catalog without differentiating focal depth ranges may result in substantial overestimates of potential seismic hazards.

Characteristic scales of earthquake rupture from numerical models

Abstract. Numerical models of earthquake rupture are used to investigate characteristic length scales and size distributions of repeated earthquakes on vertical, planar fault segments. The models are based on exact solutions of static three-dimensional (3-D) elasticity. Dynamical rupture is approximated by allowing the static stress field to expand from slip motions at a single velocity. To show how the vertical fault width affects earthquake size distributions for a broad range of fault behaviors, two different fault strength models are used; a smooth model and a heterogeneous asperity model. The smooth model is a simplified version of the Dieterich-Ruina rate and state dependent friction law. The heterogeneous asperity model uses a slip-dependent random powerlaw strength distribution. It is shown that the characteristic scale of fault segmentation is proportional to the vertical width of a seismogenic fault. This conclusion holds for both the smooth and the heterogeneous models. For the smooth models characteristic quake distributions result, with populations of large events that are obviously distinct from smaller events. The distributions of large events have well-defined mean lengths and moments. The heterogeneous models result in Gutenberg-Richter (GR) powerlaw distributions of event sizes up to a characteristic quake size. Quakes larger than the characteristic size fall off the GR distribution such that the powerlaw would greatly overestimate the probability of occurrence of the larger events.

Båth's law derived from the Gutenberg‐Richter law and from aftershock properties

The empirical Båth's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere‐Jones' [1969] and Console et al. [2003], we show that the origin of Båth's law is to be found in the selection procedure used to define mainshocks and aftershocks rather than in any difference in the mechanisms controlling the magnitude of the mainshock and of the aftershocks. We use the ETAS model of seismicity, which provides a more realistic model of aftershocks, based on (i) a universal Gutenberg‐Richter (GR) law for all earthquakes, and on (ii) the increase of the number of aftershocks with the mainshock magnitude. Using numerical simulations of the ETAS model, we show that this model is in good agreement with Båth's law in a certain range of the model parameters.

Aftershock activity of Bhuj earthquake of january 26th, 2001

Following a large-sized Bhuj earthquake (M s = 7.6) of January 26th, 2001, a small aperture 4-station temporary local network was deployed, in the epicentral area, for a period of about three weeks and resulted in the recording of more than 1800 aftershocks (-0.07 ≤M L <5.0). Preliminary locations of epicenters of 297 aftershocks (2.0 ≤M L <5.0) have brought out a dense cluster of aftershock activity, the center of which falls 20 km NW of Bhachau. Epicentral locations of after-shocks encompass a surface area of about 50 × 40 km2 that seems to indicate the surface projection of the rupture area associated with the earthquake. The distribution of aftershock activity above magnitude 3, shows that aftershocks are nonuniformly distributed and are aligned in the north, northwest and northeast directions. The epicenter of the mainshock falls on the southern edge of the delineated zone of aftershock activity and the maximum clustering of activity occurs in close proximity of the mainshock. Well-constrained focal depths of 122 aftershocks show that 89% of the aftershocks occurred at depths ranging between 6 and 25 km and only 7% and 4% aftershocks occur at depths less than 5 and more than 25 km respectively. The Gutenberg-Richter (GR) relationship, logN = 4.52 - 0.89ML, is fitted to the aftershock data (1.0<-M L<5.0) and theb-value of 0.89 has been estimated for the aftershock activity.

Maximum earthquake magnitudes in the Aegean area constrained by tectonic moment release rates

SUMMARY Seismic moment release is usually dominated by the largest but rarest events, making the estimation of seismic hazard inherently uncertain. This uncertainty can be reduced by combining long-term tectonic deformation rates with short-term recurrence rates. Here we adopt this strategy to estimate recurrence rates and maximum magnitudes for tectonic zones in the Aegean area. We first form a merged catalogue for historical and instrumentally recorded earthquakes in the Aegean, based on a recently published catalogue for Greece and surrounding areas covering the time period 550 BC‐2000 AD, at varying degrees of completeness. The historical data are recalibrated to allow for changes in damping in seismic instruments around 1911. We divide the area up into zones that correspond to recent determinations of deformation rate from satellite data. In all zones we find that the Gutenberg‐Richter (GR) law holds at low magnitudes. We use Akaike’s information criterion to determine the best-fitting distribution at high magnitudes, and classify the resulting frequency‐magnitude distributions of the zones as critical (GR law), subcritical (gamma density distribution) or supercritical (‘characteristic’ earthquake model) where appropriate. We determine the ratio η of seismic to tectonic moment release rate. Low values of η ( 1.0). The seismic and tectonic moment release rates are then combined to constrain recurrence rates and maximum credible magnitudes (in the range 6.7‐ 7.6 m W where the results are well constrained) based on extrapolating the short-term seismic data. With current earthquake data, many of the tectonic zones show a characteristic distribution that leads to an elevated probability of magnitudes around 7, but a reduced probability of larger magnitudes above this value when compared with the GR trend. A modification of the generalized gamma distribution is suggested to account for this, based on a finite statistical second moment for the seismic moment distribution.

Constraints on the frequency-magnitude relation and maximum magnitudes in the UK from observed seismicity and glacio-isostatic recovery rates

Earthquake populations have recently been shown to have many similarities with critical-point phenomena, with fractal scaling of source sizes (energy or seismic moment) corresponding to the observed GutenberG-Richter (G-R) frequency—magnitude law holding at low magnitudes. At high magnitudes, the form of the distribution depends on the seismic moment release rate M˙ and the maximum magnitude mmax. The G-R law requires a sharp truncation at an absolute maximum magnitude for finite M˙ . In contrast, the gamma distribution has an exponential tail which allows a soft or ‘credible’ maximum to be determined by negligible contribution to the total seismic moment release. Here we apply both distributions to seismic hazard in the mainland UK and its immediate continental shelf, constrained by a mixture of instrumental, historical and neotectonic data. Tectonic moment release rates for the seismogenic part of the lithosphere are calculated from a flexural-plate model for glacio-isostatic recovery, constrained by vertical deformation rates from tide-gauge and geomorphological data. Earthquake focal mechanisms in the UK show near-vertical strike-slip faulting, with implied directions of maximum compressive stress approximately in the NNW-SSE direction, consistent with the tectonic model. Maximum magnitudes are found to be in the range 6.3–7.5 for the G-R law, or 7.0–8.2 mL for the gamma distribution, which compare with a maximum observed in the time period of interest of 6.1 mL. The upper bounds are conservative estimates, based on 100 per cent seismic release of the observed vertical neotectonic deformation. Glacio-isostatic recovery is predominantly an elastic rather than a seismic process, so the true value of mmax is likely to be nearer the lower end of the quoted range.

Beno Gutenberg contribution to seismic hazard assessment and recent progress in the European–Mediterranean region

The fundamental work of Beno Gutenberg has inspired and guided an appreciable part of research in modern seismology, both from the experimental and the theoretical point of view. Among the several topics of seismology that have benefited from the fundamental contribution of Gutenberg, we consider particularly relevant the description of the asthenospheric low-velocity channel, the definition of the surface waves magnitude and the Gutenberg–Richter law, since they are pivotal tools for seismic hazard assessment. The quite revolutionary model for the lithosphere–asthenosphere system in the European area predicts the existence of almost aseismic lithospheric roots. These roots are located in correspondence of most of the orogenic belts and interrupt the asthenosphere low velocity channel that has been identified by Beno Gutenberg in 1948. The model of the European upper mantle, proposed for the first time in 1979 and subsequently refined, has stimulated a considerable amount of research, which has nicely confirmed the major innovative features of the early model. At present, the subduction of the lithosphere at continent–continent collisions, supported not only by seismological data, is a widely accepted concept within the community of Earth scientists, even if it contradicts one of the basic dogmas of the original formulation of plate tectonics. The proposed model for the Alpine–Apennines area supplies a new and unifying framework for the interpretation of the Quaternary magmatism, at present generally accepted by petrologists and geochemists. The theoretical basis for the Gutenberg's surface-wave magnitude calibration function has been supplied by the use of complete synthetic seismograms, and thus it has been possible to formulate the theoretical M S depth correction. The introduction of the depth correction for M S enables the computation of surface wave magnitude for all earthquakes, regardless of their focal depth. This is especially important for the quantification of subcrustal historical earthquakes, for which the seismic moment may be difficult to estimate from recordings of early mechanical seismographs. The new M S calibrating function yield both distance- and depth-independent magnitude estimates. The analysis of the global seismicity, using the seismotectonic regionalization in subduction zones, mid oceanic ridge zones, island arcs, shows that a single Gutenberg–Richter (GR) relation is not universally applicable and that a multiscale seismicity model can reconcile two apparently conflicting paradigms: the Self-Organized Criticality mechanism and the Characteristic Earthquake concept. The multiscale representation has been applied to Italy, where the zones at the space scale of 400–500 km quite well reproduce the shapes of the regions used to apply the, globally tested, CN intermediate term earthquake prediction algorithm.

Using Artificial Neural Networks and the Gutenberg-Richter Power Law to "Rightsize" a Behavioral Health Care System

The authors propose a new paradigm for designing and managing behavioral health care systems by using artificial neural networks to measure quality of care (Q), using length-of-stay (LOS) prediction and the variation in LOS prediction, and subsequently using the variation of Q to obtain a measure of uncertainty in treatment. The paper proposes that mental illness is fractal in nature (self-similar at all scales) and conforms to power laws like the Gutenberg-Richter (G-R) law, whereby there is a log-log relationship between frequency of episodes (i.e., admissions) and the severity of those episodes. The paper also hypothesizes that 28% is the average uncertainty (residual or excess entropy) in the treatment of mental illness. The authors use the G-R paradigm to calculate the severity of admission and, subsequently, the minimum number of beds for different behavioral health care facilities and propose the optimal partition of beds between community and state services, thereby "balancing" the delivery system. The data presented support the notion that mental illness manifests complexity and "self-organized criticality." The authors hypothesize that correcting deviations from the theoretical G-R curve for each level of care will allow optimum resource distribution, improve quality of care, and reduce costs.

The Almighty Earthquake

Discussion on the characteristic earthquake model vs. the Gutenberg-Richter (G-R) relationship leaves me with some uneasiness. The Gutenberg-Richter relation is a traditional, basic one of seismology with an origin that can be traced back to Ishimoto and Iida's empirical power law formula in 1939 describing the frequency of maximum amplitudes of observed seismic waves. The G-R relationship is unambiguously defined by a simple formula, but some ambiguities about the G-R relation exist as well. For example, possible sources of ambiguity are how to define the maximum magnitude since we have an Earth of finite size (and hence the maximum possible magnitude must be finite also), and how to truncate the relationship at the maximum magnitude. On the other hand, the relatively new idea of the characteristic earthquake model appears to have many loose ends. Does it include any specification on the temporal earthquake distribution, or does it specify only a...