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1.
Calibration of magnitude scales for earthquakes of the Mediterranean   总被引：1，自引：1，他引：0  
In order to provide the tools for uniform size determination for Mediterranean earthquakes over the last 50-year period of instrumental seismology, we have regressed the magnitude determinations for 220 earthquakes of the European-Mediterranean region over the 1977–1991 period, reported by three international centres, 11 national and regional networks and 101 individual stations and observatories, using seismic moments from the Harvard CMTs. We calibrate M(M0) regression curves for the magnitude scales commonly used for Mediterranean earthquakes (ML, MWA, mb, MS, MLH, MLV, MD, M); we also calibrate static corrections or specific regressions for individual observatories and we verify the reliability of the reports of different organizations and observatories. Our analysis shows that the teleseismic magnitudes (mb, MS) computed by international centers (ISC, NEIC) provide good measures of earthquake size, with low standard deviations (0.17–0.23), allowing one to regress stable regional calibrations with respect to the seismic moment and to correct systematic biases such as the hypocentral depth for MS and the radiation pattern for mb; while mb is commonly reputed to be an inadequate measure of earthquake size, we find that the ISC mb is still today the most precise measure to use to regress MW and M0 for earthquakes of the European-Mediterranean region; few individual observatories report teleseismic magnitudes requiring specific dynamic calibrations (BJI, MOS). Regional surface-wave magnitudes (MLV, MLH) reported in Eastern Europe generally provide reliable measures of earthquake size, with standard deviations often in the 0.25–0.35 range; the introduction of a small (±0.1–0.2) static station correction is sometimes required. While the Richter magnitude ML is the measure of earthquake size most commonly reported in the press whenever an earthquake strikes, we find that ML has not been computed in the European-Mediterranean in the last 15 years; the reported local magnitudes MWA and ML do not conform to the Richter formula and are of poor quality and little use, with few exceptions requiring ad hoc calibrations similar to the MS regression (EMSC, ATH). The duration magnitude MD used by most seismic networks confirms that its use requires accurate station calibrations and should be restricted only to events with low seismic moments.  相似文献   

2.
—?Data sets of m b (Pn) and m b (Lg) measurements are presented for three continental regions in order to investigate scaling relationships with moment magnitude M w and event discrimination at small magnitudes. Compilations of published measurements are provided for eastern North American and central Asian earthquakes, and new measurements are reported for earthquakes located in western United States. Statistical tests on M w :m b relationships show that the m b (Lg) scale of Nuttli (1973) is transportable between tectonic regions, and a single, unified M w :m b (Lg) relationship satisfies observations for M w ～4.2–6.5 in all regions. A unified relationship is also developed for nuclear explosions detonated at the Nevada Test Site and test sites of the former Soviet Union. Regional m b for explosions scale at higher rates than for earthquakes, and of significance is the finding that m b (Pn) for explosions scales at a higher rate than m b (Lg). A model is proposed where differences in scaling rates are related to effects of spectral overshoot and near-field Rg scattering on the generation of Pn and Lg waves by explosions. For earthquakes, m b (Pn) and m b (Lg) scale similarly, showing rates near 1.0 or 2/3?·?log10 M o (seismic moment).¶M w :m b (Lg) scaling results are converted to unified M s :m b (Lg) relationships using scaling laws between log M o and M s . For earthquakes with M s greater than 3.0, the scaling rate is 0.69?·?M s , which is the same as it is for nuclear explosions if M s is proportional to 1.12?·?log M o, as determined by NTS observations. Thus, earthquake and explosion populations are parallel and separated by 0.68 m b units for large events. For small events (M s ?M s :m b (Lg) plots for stable and tectonic regions, respectively. While the scaling rate for explosions is ～0.69, this value is uncertain due to paucity of M o observations at small yields. Measurements of [m b (P)???m b (Lg)] for earthquakes in the western United States have an average value of ?0.33?±?.03 m b units, in good agreement with Nuttli's estimate of m b bias for NTS. This result suggests that Nuttli's method for estimating test site bias can be extended to earthquakes to make estimates of bias on regional scales. In addition, a new approach for quick assessments of regional bias is proposed where M s :m b (P) observations are compared with M s :m b (Lg) relationships. Catalog M s :m b (P) data suggest that m b bias is significant for tectonic regions of southern Asia, averaging about ?0.4 m b units.  相似文献   

3.
The risk formula, expressing the probability of at least one occurrence of earthquakes of greater-than-design-value magnitudes over the economic life of a structure, is modified taking into consideration the probability of no-earthquake years. The annual maximum earthquake magnitudes of three scales: Richter magnitude, also known as local magnitude (ML), body-wave magnitude (Mb), and moment magnitude (MM) in a geographical area encompassing the Bingöl Province in Turkey are taken from two sources: (1) report by Kalafat et al. (2007) [14] and (2) the web site reporting data by Kandilli Observatory which has been recording earthquakes occurring in and around Turkey since 1900. Statistical frequency analyses are applied on the three sample series using various probability distribution models, and magnitude versus average return period relationships are determined. The values of the ML, Mb, and MM series for 10% and 2% risk are computed to be around 7.2 and 8.3. The tectonic structure and seismic properties of the Bingöl region are also given briefly.  相似文献   

4.
The various useful source-parameter relations between seismic moment and common use magnitude lg(M 0) andM s,M L,m b; between magnitudesMs andM L,M s andm b,M L andm b; and between magnitudeM s and lg(L) (fault length), lg (W) (fault width), lg(S) (fault area), lg(D) (average dislocation);M L and lg(f c) (corner frequency) have been derived from the scaling law which is based on an “average” two-dimensional faulting model of a rectangular fault. A set of source-parameters can be estimated from only one magnitude by using these relations. The average rupture velocity of the faultV r=2.65 km/s, the total time of ruptureT(s)=0.35L (km) and the average dislocation slip rateD=11.4 m/s are also obtained. There are four strong points to measure earthquake size with the seismic moment magnitudeM w.
  1. The seismic moment magnitude shows the strain and rupture size. It is the best scale for the measurement of earthquake size.
  2. It is a quantity of absolute mechanics, and has clear physical meaning. Any size of earthquake can be measured. There is no saturation. It can be used to quantify both shallow and deep earthquakes on the basis of the waves radiated.
  3. It can link up the previous magnitude scales.
  4. It is a uniform scale of measurement of earthquake size. It is suitable for statistics covering a broad range of magnitudes. So the seismic moment magnitude is a promising magnitude and worth popularization.
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5.
In previous research, trace amplitudes of surface wave maxima recorded by undamped Milne seismographs were used to determine the surface-wave magnitudes Ms of large shallow earthquakes which occurred prior to 1912. For this purpose, the effective gain of these instruments was calibrated by using the surface-wave magnitudes Ms(GR) which were calculated from the unpublished worksheets for Seismicity of the Earth of Gutenberg and Richter. In this paper, the real quality of Ms(GR) is critically re-evaluated by using independent sets of data. It is found that Ms(GR) for the period 1904–1909 is considerably overestimated. The average excess from the real Ms is 0.5 units for 1904–1906, 0.4 for 1907, 0.3 for 1908–1909 and 0.0 for 1910–1912. This overestimation is so systematic and large that the previous results are all redetermined. The average effective gain of Milne instruments is revised to be 21.9; previously, the gain depended on Ms. This revision results in systematic reduction in the previously assigned magnitudes. The revised values of Ms for 264 shallow earthquakes, with Ms=6.8 and over in the period 1897–1912 inclusive, are listed. The present revision is large enough to preclude the possibility of the high activity of large shallow earthquakes around the turn of the century. The present results have a direct effect on all the magnitude catalogues of shallow earthquakes which occurred prior to 1909.  相似文献   

6.
The earthquakes in Kaliningrad, West Russia on the 21st of September 2004 were unexpected in a seismically quiet area. The main shock of magnitude mb = 5 was widely felt around the Baltic Sea. A comparison with some historic earthquakes in Northern Europe shows that its perceptibility area is smaller than that of the 1904 Oslo Graben earthquake of an estimated magnitude (ML) 5.4 but larger than those of the 1759 Kattegat and 1819 Lurøy earthquakes. The latter are claimed to have had magnitudes (MS) in the range of 5.7-6.0. An analysis of the Lg phase of the Kaliningrad earthquakes as recorded at a number of European stations accords only weakly with the macroseismic intensity pattern that shows fast attenuation towards west-northwest and southeast. The strike-slip focal mechanism of the main shock is discussed in the context of remnant glacial rebound stresses in generating present-day seismicity in N. Europe.  相似文献   

7.
The time variations in the Gutenberg–Richter b-value are minutely studied based on the data of highly accurate seismological observations at the Garm prognostic site, Tajikistan, where a stationary network of seismic stations of the Complex Seismological Expedition (CSE) of Schmidt Institute of Physics of the Earth (IPE) of the USSR (Russian) Academy of Sciences was in operation from 1955 to 1992. A total of 93035 local earthquakes ranging from 0.0 to 6.3 in the Ml magnitudes are considered. The spatiotemporal fluctuations in the minimal magnitude of completeness of the earthquakes, Mc, are analyzed. The study considers a 25-year interval of the observations at the center of the observation system within which Mc = 0.9. It is shown that in most cases, the b-value and log10E2/3 experience characteristic time variations before the earthquakes with magnitudes higher than the minimal magnitude of the predicted earthquake (MPE). The 6-year anomaly in the parameters’ b-value, log10E2/3, and log10N associated with the single strongest earthquake with M = 6.3 that occurred in the observation region on October 26, 1984 is revealed. The inversely proportional relationship is established between the time variations in the b-value and the time variations in the velocities of seismic waves Vp and Vp/Vs. It is shown that the exponent p in the power function which links the time variations of the b-value and log10E2/3 is higher in the zones of crustal compression than in the zones of extension. It is simultaneously confirmed that the average b-value in the zones of compression is lower than in the zones of extension. It is established that in the case of earthquakes with M ≥ 2.6, the time series of seismic activity log10Ni and the time series of the b-value are highly cross correlated with a coefficient of r ≈ 0.75, whereas in the case of earthquakes with M ≥ 0.9, the coefficient of cross correlation between these time series is close to zero (r ≈ 0.06). The law of variations in the slope of the lines approximating the relationship between the log10Ni time series in the different magnitude ranges (M ≥ Mci) and b-value time series is obtained. It is hypothesized that the seismic activity of the earthquakes with high magnitudes can be estimated provided that the parameters of the time series of the b-value and time series of the number of earthquakes logN(ΔMi) in the range of low magnitudes are known. It is concluded that using the parameter log10N for prognostic estimates of the strong earthquakes only makes sense for earthquakes having moderate and large magnitudes. It is inferred that the time variations in the b-value are predominantly contributed by the time variations of the earthquakes with relatively large magnitudes.  相似文献   

8.
In the light of the single scattering model of coda originating from local earthquakes, and based on the aftershock coda registered respectively at the 4 short period stations installed near the foci shortly after theM7.6 Lancang andM7.2 Gengma earthquakes, this paper has tentatively calculated the rate of amplitude attenuation and theQ c-value of the coda in the Lancang and Gengma areas using a newly-founded synthetic determination method. Result of the study shows the rate of coda amplitude attenuation demonstrates remarkable regional differences respectively in the southern and northern areas. The southern area presents a faster attenuation (Q c=114), whereas the northern area shows a slower attenuation (Q c=231). The paper also discusses the reasons causing such differences. Result of the study also suggests a fairly good linear relation between the coda source factorA o(f) and the seismic moment and the magnitude. Using the earthquake scaling law, the following formulas can be derived: lgM 0=lgA 0(f)+17.6,M D=0.67lgA 0(f)+1.21 and logM 0=1.5M D+15.79. In addition, the rates of amplitude attenuationβ s andβ m are respectively calculated using the single scattering and multiple scattering models, and the ratioβ s/βm=1.20−1.50 is found for the results respectively from the two models. Finally, the mean free pathL of the S-wave scattering in the southern and northern areas are determined to be 54 km and 122 km respectively by the relations which can distinguish between the inherentQ i and scatteringQ s, testify to this areas having lowQ-values correspond to stronger scatterings. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 71–82, 1992. This study is partly supported by the Seismological Science Foundation of the State Seismological Bureau of China, and the present English version of the paper is translated from its Chinese original by Wenyi Xia, Seismological Bureau of Yunnan Province.  相似文献   

9.
This paper presents the review of the experience in applying the approach based on the limiting distributions of the extreme value theory (the generalized Pareto distribution, GPS, and generalized extreme value distribution, GEV) for deriving the distributions of maximal magnitudes and related ground accelerations from the earthquakes on the future time intervals of a given duration. The results of analyzing the global and regional earthquake catalogs and the ground peak accelerations during the earthquakes are described. It is shown that the magnitude of the strongest possible earthquake M max (and analogous characteristics for other types of data), which is often used in seismic risk assessment, is potentially unstable. We suggest a stable alternative for M max in the form of quantiles Q q (τ) of the maximal possible earthquake, which could occur during the future time interval of length τ. The quantity of the characteristic maximal event M c, which has been introduced in our previous publications, is another helpful robust scalar parameter. All the cases of approximation of the tails of empirical distributions, which were studied in our works, turned out to be finite (bounded); however, the rightmost point of these distributions, M max, is often poorly detectable and unstable. Therefore, the M max parameter has a low practical value.  相似文献   

10.
Summary TheGumbel's theory of largest values has been applied to the estimation of probability of occurrence and of return periods of largest earthquakes in the European area. For this study shallow shocks from the period 1901–1955 and from 15 earthquake zones were used. For each zone the largest magnitudes corresponding to one-year intervals were arranged in order of increasingM, grouped in classes and then the probabilitiesF(x j) were calculated. The data plotted on the probability paper fit a straight line fairly well. The extrapolated lines yield the possibility of estimating large magnitudes which will be exceeded with a given probability, e.g. 1%. Such values were compared with largest magnitudes observed during the period 1901–1955. Their return periods indicate that in most regions the largest probable shock already occurred. Following the procedure ofEpstein-Lomnitz the coefficients and were calculated and compared with corresponding values ofa andb of the magnitude-frequency relation.  相似文献   

11.
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12.
Abstract

We have contrived a model E(αω) α μ?1ω?p+1(ω 2?ω i 2)?+ for the distribution of internal wave energy in horizontal wavenumber, frequency-space, with wavenumber α extending to some upper limit μ(ω) α ω r-1 (ω 2?ω i 2)½, and frequency ω extending from the inertial frequency ω i to the local Väisälä frequency n(y). The spectrum is portrayed as an equivalent continuum to which the modal structure (if it exists) is not vital. We assume horizontal isotropy, E(α, ω) = 2παE(α1, α2, ω), with α1, α2 designating components of α. Certain moments of E(α1, α2, ω) can be derived from observations. (i) Moored (or freely floating) devices measuring horizontal current u(t), vertical displacement η(t),…, yield the frequency spectra F (u,η,…)(ω) = ∫∫ (U 2, Z 2,…)E(α1, ∞2, ω) dα1 dα2, where U, Z,… are the appropriate wave functions. (ii) Similarly towed measurements give the wavenumber spectrum F (…)(α1) = ∫∫… dα2 dω. (iii) Moored measurements horizontally separated by X yield the coherence spectrum R(X, ω) which is related to the horizontal cosine transform ∫∫ E(α1, α2 ω) cos α1 Xdα1 dα1. (iv) Moored measurements vertically separated by Y yield R(Y, ω) and (v) towed measurements vertically separated yield R(Y, α1), and these are related to similar vertical Fourier transforms. Away from inertial frequencies, our model E(α, ω) α ω ?p-r for α ≦ μ ω ω r, yields F(ω) ∞ ω ?p, F(α1) ∞ α1 ?q, with q = (p + r ? 1)/r. The observed moored and towed spectra suggest p and q between 5/3 and 2, yielding r between 2/3 and 3/2, inconsistent with a value of r = 2 derived from Webster's measurements of moored vertical coherence. We ascribe Webster's result to the oceanic fine-structure. Our choice (p, q, r) = (2, 2, 1) is then not inconsistent with existing evidence. The spectrum is E(∞, ω) ∞ ω ?1(ω 2?ω i 2 ?1, and the α-bandwith μ ∞ (ω 2?ω i 2)+ is equivalent to about 20 modes. Finally, we consider the frequency-of-encounter spectra F([sgrave]) at any towing speed S, approaching F(ω) as S ≦ S o, and F(α1) for α1 = [sgrave]/S as S ≧ S o, where S o = 0(1 km/h) is the relevant Doppler velocity scale.  相似文献   

13.
The problem of discriminating between earthquakes and underground nuclear explosions is formulated as a problem in pattern recognition. As such it may be separated into two stages, feature extraction and classification. The short-period (SP) features consist of mb and autoregressive parameters characterising the preceding noise, signal and coda. The long-period (LP) features consist of LP power spectral estimates taken within various group velocity windows. Contrary to common usage we have extracted features from horizontal Rayleigh waves and Love waves as well as vertical Rayleigh waves. The classification is performed by approximating the statistical distribution of earthquake and explosion feature vectors by multivariate normal distributions.The method has been tested on a data base containing 52 explosions and 73 earthquakes from Eurasia recorded at NORSAR between 1971 and 1975. Several of these events are difficult on the mb : Ms diagram [mb(PDE) and Ms (NORSAR) have been used]. The data set was divided into a learning and an independent data set. All of the events both from the learning data set and the independent data set were correctly classified using the new procedures. Furthermore, the increase in separation as compared to the mb : Ms discriminant is significant.  相似文献   

14.
Uncertainties in the estimation of earthquake magnitudes in Greece   总被引：1，自引：0，他引：1  
Instrumental magnitudes in Greece have been reported as: a) Mmagnitudes based on the records of the Wiechert or Mainka seismographs,b) MLGR magnitudes based on the records of the Wood-Anderson(WA) seismographs (To = 0.8 sec, Veffective 1000) or othershort period seismographs calibrated against WA records and,c) MLSM magnitudes based on strong motion records(accelerograms). Comparison of such magnitudes with momentmagnitudes, Mw, for 329 earthquakes, with epicenters in thebroader Aegean area, performed in this study, showedthat M, MLGR+0.5 and MLSM are practically equalto Mw, with a small overall standard error ( = 0.23).Therefore, equivalent moment magnitudes, Mw *,estimated from these magnitudes and reported in the catalogues of theGeophysical Laboratory of the University of Thessaloniki are equal tomoment magnitudes for all practical purposes with reasonable uncertainties.It has been further shown that surface wave magnitudes, Ms,for Ms <6.0, can be also transferred into momentmagnitudes, Mw *, but the larger uncertaintiesencountered make its use rather problematic.  相似文献   

15.
We suggest supplementing the MLH magnitude with the threshold (M thr) values of MPV, MSH, and MLH magnitudes (Russian scales), as well as M S and M W now in wide international use, for issuing tsunami alerts for hazards emanating from the main tsunamigenic zones of the Pacific Ocean. Relations are given to connect the MLH to these magnitudes. A comparative analysis applied to a catalog of large (M ≥ 6) earthquakes in the North Pacific and to the associated tsunami catalog gave the probabilities of false alerts and unpredicted tsunamis as functions of the threshold magnitude value (M thr). A two-step decision rule is proposed to issue tsunami alerts due to the tsunamigenic zones situated close to the Far East coast of Russia.  相似文献   

16.
According to the fact that the Xinfengjiang reservoir earthquakes are caused mainly by water seepage, this paper using the data ofM s?2. 0 earthquakes, studies the hydraulic diffusivity of the mainshock zone by the expansion of the distribution area of epicenters. It is indicated thatin-situ hydraulic diffusivity during the preshock activity of the Xinfengjiang reservoir region was about 6. 2 m2/s. However, after the main shock, thein-situ hydraulic diffusivity in the main shock region increased by fifty percent, that is to say, to 9. 7 m2/s. During the long period after main shock occurrence thein-situ hydraulic diffusivity was affected by significant anisotropy of the medium and fluctuation of water level. No regularity can be found. In addition, we compare the diffusivity found by experiment with rock samples collected with thein-situ hydraulic diffusivity estimated. It is shown that the diffusivity of rock samples with fractures is about the same as the diffusivity estimatedin-situ. However, the diffusivity of whole rock samples is 3 orders of magnitudes smaller than that estimatedin-situ. Finally, we discuss the limits on the method by the expansion of distribution area of epicenters in the study of reservoir induced seismicity.  相似文献   

17.
Forward seismic problems are solved for elastic media by rigorous methods (i.e., methods with controllable accuracy). Analysis of the current state of research on this subject suggests that the most promising methods are based on integral and integro-differential equations, notwithstanding the rather modest results of their application to solving forward problems in the theory of elastic vibrations. The second Green integral theorem for seismic waves, formulated and proven in the paper, yields a system of two boundary (surface) integral equations for the displacement vector u(M 0) and the normal (to the boundary surface) vector component of the stress tensor tn(M 0). The integrands of the surface integrals in terms of which the function tn(M 0) is expressed on both sides of the interface between the medium and the heterogeneity contain the second derivatives of the Green’s tensor functions ? e (M 0, M) and ? i (M 0, M), respectively, which are responsible for a cubic singularity (third-order singularity) if the integration point M coincides with the observation point M 0. An original method of eliminating the cubic singularity proposed in the paper involves special tensor normalization of the integrals on the outer and inner sides of the interface and subsequent subtraction of one integral from another in order to construct the second integral equation.  相似文献   

18.
Results are reported from the ongoing 2007–2008 work using the method of long-term earthquake prediction for the Kuril-Kamchatka arc based on the patterns of seismic gaps and the seismic cycle. This method was successful in predicting the M S = 8.2 Simushir I. (Middle Kuril Is.) earthquake occurring in the Simushir I. area on November 15, 2006. An M S = 8.1 earthquake occurred in the same area on January 13, 2007. We consider the evolution of the seismic process and determine the common rupture region of the two earthquakes. The sequence of M ≥ 6.0 aftershocks and forecasts for these are given. We provide a long-term forecast for the earthquake-generating zone of the Kuril-Kamchatka arc for the next five years, April 2008 to March 2013. Explanations are given for the method of calculation and prediction. The probable locations of future M ≥ 7.7 earthquakes are specified. For all segments of the earthquake-generating zone we predict the expected phases of the seismic cycle, the rate of low-magnitude seismicity (A10), the magnitudes of moderate-sized earthquakes to be expected, with probabilities of 0.8, 0.5, and 0.15, their maximum possible magnitudes, and the probabilities of occurrence of great (M ≥ 7.7) earthquakes. The results of these forecasts are used to enhance seismic safety.  相似文献   

19.
By linear regression and orthogonal regression methods, comparisons are made between different magnitudes (lo-cal magnitude ML, surface wave magnitudes MS and MS7, long-period body wave magnitude mB and short-period body wave magnitude mb) determined by Institute of Geophysics, China Earthquake Administration, on the basis of observation data collected by China Seismograph Network between 1983 and 2004. Empirical relations between different magnitudes have been obtained. The result shows that: 1 As different magnitude scales reflect radiated energy by seismic waves within different periods, earthquake magnitudes can be described more objectively by using different scales for earthquakes of different magnitudes. When the epicentral distance is less than 1 000 km, local magnitude ML can be a preferable scale; In case M<4.5, there is little difference between the magnitude scales; In case 4.5MS, i.e., MS underestimates magnitudes of such events, therefore, mB can be a better choice; In case M>6.0, MS>mB>mb, both mB and mb underestimate the magnitudes, so MS is a preferable scale for deter-mining magnitudes of such events (6.08.5, a saturation phenomenon appears in MS, which cannot give an accurate reflection of the magnitudes of such large events; 2 In China, when the epicentral distance is less than 1 000 km, there is almost no difference between ML and MS, and thus there is no need to convert be-tween the two magnitudes in practice; 3 Although MS and MS7 are both surface wave magnitudes, MS is in general greater than MS7 by 0.2~0.3 magnitude, because different instruments and calculation formulae are used; 4 mB is almost equal to mb for earthquakes around mB4.0, but mB is larger than mb for those of mB≥4.5, because the periods of seismic waves used for measuring mB and mb are different though the calculation formulae are the same.  相似文献   

20.
The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω i is characterized by a system of random variables, viz., energy class ki, latitude φ i , longitude λ i , and depth h i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k 0) is the basic data [Bogdanov, 2006] rather than the seismic activity A 0, we proceed to show that for different intervals of coordinates and time the distribution f elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f full(k), which corresponds to the full catalog. It follows from our calculations that f 0(k) takes on nearly identical numeral values for different initial values of energy class k 0 (8 ≤ k 0 ≤ 12) f(k 0). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k 0) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k 0) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods  相似文献   

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