The Winter 1991–1992 Earthquake Sequence at Cephalonia Island, Western Greece

—Properties of the earthquake sequence of the 23 January, 1992 (5.8 M _S ?) earthquake in Cephalonia Island, Western Greece, are investigated. The parameter b in the frequency-magnitude relation is found equal to 1.084 while the decay parameter p of the time distribution of the aftershock sequence is found equal to 0.991. The principal parameters method is applied to the aftershock sequence and the average strikes of N156°E (±20°) and N61°E (±10°) were obtained denoting also very small dips. The major strike which resulted from the aftershock epicentre distribution was NW–SE, similar to Miocene-Neogene basins on Cephalonia Island.     

Grain-size distribution in suspension over a sand-gravel bed in open channel flow

Grain-size distributions of suspended load over a sand-gravel bed at two different flow velocities were studied in a laboratory flume.The experiments had been performed to study the influence of flow velocity and suspension height on grain-size distribution in suspension over a sand-gravel bed.The experimental findings show that with an increase of flow velocity,the grain-size distribution of suspended load changed from a skewed form to a bimodal one at higher suspension heights.This study focuses on the determination of the parameter β_n which is the ratio of the sediment diffusion coefficient to the momentum diffusion coefficient of n th grain-size.A new relationship has been proposed involving β_n,the normalizing settling velocity of sediment particles and suspension height,which is applicable for widest range of normalizing settling velocity available in literature so far.A similar parameter β for calculating total suspension concentration is also developed.The classical Rouse equation is modified with β_n and β and used to compute grain-size distribution and total concentration in suspension,respectively.The computed values have shown good agreement with the measured values of experimental data.     

Sympatry and possible hybridization among species of the killifish genus Aphanius Nardo, 1827 (Teleostei: Cyprinodontidae) in Southwestern Iran

Studies of the taxonomy and present-day distribution of landlocked populations of the killifish Aphanius Nardo, 1827 (Cyprinodontidae) provide a key to understanding their zoogeographic history, and shape conservation strategies and habitat management. Here we report for the first time on the sympatric occurrence of the rare Mesopotamian tooth-carp A. mesopotamicus with a member of the widely distributed common tooth-carp (A. dispar group). Both were found in the Shadegan Wetland of the Mesopotamian drainage system (Southwestern Iran). External characters of individuals, otolith morphology and molecular data based on the cytochrome b gene confirm species identification. The otolith morphology of A. mesopotamicus, hitherto unknown, is strikingly similar to previously described otoliths of A. cf. pluristriatus from the Khonj stream (Southern Iran), which apparently reflects a close relationship between these recently diverged species. Several of the specimens recovered from the Shadegan Wetland showed intermediate characters in pigmentation, otolith morphology and some morphometric values. These specimens are interpreted as putative hybrids, which is additionally supported by a multivariate analysis of the morphometric data. Previous reports suggest that natural hybridization between species of Aphanius results largely from range overlap and range extension. A virtual distribution map derived from climatic modelling studies based on DIVA-GIS (7.5.0) indicates that sympatry of the A. dispar group and A. mesopotamicus is primarily determined by levels of precipitation during the warmest quarter, and is likely to occur only in Southwestern Iran.     

Biological enhancement of solute exchange between sediments and bottom water on the Washington continental shelf

Solute exchange between the interstitial waters and overlying waters on the Washington continental shelf was investigated based on measurements of the pore-water sulfate distribution and sulfate reduction rates as well as through models describing the distribution of sulfate in anaerobic pore waters. The depth-integrated sulfate reduction rate greatly exceeded the influx of sulfate attributable to molecular diffusion and sediment accumulation acting on the measured vertical sulfate gradients, and indicated that additional transport mechanisms must have been operating. Sediment mixing was probably not the primary mechanism since high eddy diffusivities would be required to depths of 30 cm to maintain the observed sulfate distribution, whereas previously measured²¹⁰Pb distributions indicated sediment mixing is primarily restricted to depths <7 cm. Irrigation of bottom water through animal burrows was the most likely mechanism. To describe this process, a general diffusive irrigation coefficient, B, was formulated. Vertical profiles of B showed the main irrigation zone occurred between 2 and 10 cm with reduced irrigation rates occurring below this. These coefficients calculated from the sulfate distribution were similar to ones calculated from previously published radon measurements at the same stations, indicating that this formulation of irrigation exchange may be useful in modelling the exchange of dissolved solutes between the pore water and the bottom water.     

The diurnal,annual and sunspot-cycle variations of ESFm at Huancayo compared with similar variations of spread-F occurrence at other longitudes and latitudes

Using the tabulations of spread-F data from ionosonde recordings the diurnal, annual and sunspot-cycle variations of this spread-F occurrence have been investigated for the equatorial station, Huancayo. Both R_z max and R_z min periods have been considered. The analyses suggest that some explanation of these variations can be made by involving two regimes, which have been called Regime A and Regime B. The Regime A is present throughout the night but this distribution is more obvious after midnight. This is because in the post-sunset period Regime B, which is associated with significant height rises, is dominant. The Regime A is the same as for similar distributions in mid-latitudes and is inversely related to sunspot activity. It maximizes in December solstice months. The Regime B is directly related to sunspot activity and maximizes in equinoctial months. Changes associated with the upper atmosphere neutral particle density have been found to be important, particularly for Regime A where an inverse relationship exists. The Regime A R_z min annual distributions reported here for Huancayo have been compared with similar distributions at other longitudes and latitudes.     

On the physical essence of theb value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE of rock tests and natural earthquakes has been a controversial topic during the past two decades. In the present paper the order and energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl?v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity of course covers the idea of “crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi.     

E. coli fate and transport in the Happel sphere-in-cell model

Rates of mass and gene transfer reactions involving biotic phases are often expressed as proportional to local number densities of bacteria. When the reactions involve attached bacteria, reaction rates depend on local densities of bacteria attached to surfaces. Such may be the case with microbially-facilitated redox reactions involving mineral electron donors and mineral electron receivers (e.g., Sani RK, Peyton BM, Amonette JE, Dohnalkova A. Reoxidation of uranium in the presence of iron(III)-(hydr)oxides under sulfate reducing conditions. Environ Sci Technol 2005;39:2059–66), biofilm formation induced by quorum sensing (Purevdorj B, Costerton JW, Stoodley P. Influence of hydrodynamics and cell signaling on the structure and behavior of Pseudomonas aeruginosa Biofilms. Appl Environ Microbiol 2002;68(9):4457–64) and horizontal gene transfer among attached phase bacteria (Beaudoin DL, Bryers JD, Cunningham AB, Peretti SW. Mobilization of broad host range plasmid from Pseudomonas putida to established biofilm of Bacillus azotoformans. I. Experiments. Biotech Bioeng 1998a;57(3):272–79; Beaudoin DL, Bryers JD, Cunningham AB, Peretti SW. Mobilization of broad host range plasmid from Pseudomonas putida to established biofilm of Bacillus azotoformans. II. Modeling Biotech Bioeng 1998b;57(3):280–86). Here we use the conceptual Happel sphere-in-cell model to determine the microscopic distribution of attached bacteria on idealized spherical grains of porous media, assuming azimuthal symmetry. We extend a Lagrangian model of colloid filtration to investigate the effects of motility of Escherichia coli on attachment rate and on the attachment distribution as a function of location on grain surface. The hydrodynamics of the Happel model is implicitly 3D and represented in 2D polar coordinates under the assumption of axisymmetric flow, while the motility of the E. coli cells is explicitly 3D. The model incorporates the fate and transport processes of colloid filtration theory in the particle tracking approach of Nelson and Ginn (Nelson KE, Ginn TR. Theoretical investigation of bacterial chemotaxis in porous media. Langmuir 2001;17:5636–45; Nelson KE, Ginn TR. Colloid filtration theory and the Happel sphere-in-cell model revisited with direct numerical simulation. Langmuir 2005;21:2173–84) and includes statistics reported in Biondi et al. (Biondi SA, Quinn JA, Goldfine H. Random motility of swimming bacteria in restricted geometries. AIChE J 1998;44(8):1923–29) to describe the “run & tumble” behavior of individual E. coli cells. Incorporation of the motility allowed for comparative modeling of diffusion-controlled vs. motility-controlled transport and attachment in the Happel sphere. It was found that, whereas the Lévy distribution is often associated with the distribution of run lengths for this species, the data of Biondi is better fit by a Gamma distribution due to the low frequency of short runs, and that the turn distribution is non-uniform. Further, the motility mean free path is much larger than that corresponding to Brownian diffusion and the attachment frequency is higher in the case of motile cells as a result. However the distribution of attached cells is similar in both motile and diffusive cases.     

Improved Interpretation of Nuclear Magnetic Resonance T1 and T2 Distributions for Permeability Prediction: Simulation of Diffusion Coupling for a Fractal Cluster of Pores

NMR relaxometry is a powerful tool for inferring porosity and permeability data. In practice, measured magnetization decay curves are inverted for relaxation time distributions. Subsequently, one presumes a linear relationship between the pore radius distribution and the T ₁ and T ₂ distribution, for longitudinal and transverse magnetization, respectively. The fundamental equations used are based on a pore model, in which pores are assumed to be isolated from each other with respect to the NMR process and have smooth walls. The present study is based on a geometrical pore space model with connected pores and structured pore walls. The physical processes of surface relaxation, irreversible dephasing of magnetic spins and diffusive proton exchange between pores, are described by a system of differential equations. The solution yields a set of exponential functions representing the relaxation time distribution. We describe the difference between the distributions obtained for diffusion coupling and for isolated pores. With diffusion coupling on, the spectral width of the T ₁ distribution is strongly reduced, which indicates that the influence of large and small radii according to the T ₁-pore radius relationship is mixed to some extent. For a fractal pore space structure, where large pores are surrounded by adjacent minor pores, the T ₁ distribution does not resolve these substructures. Nevertheless, permeability values calculated from the logarithmic mean relaxation time T _1,LM are quite the same for diffusion coupling and for isolated pores. The T ₂ distribution for diffusion coupling is little constricted and gives a better resolution of the pore wall structures than the corresponding T ₁ distribution. The permeability values from T ₂ distributions agree with the values from longitudinal magnetization, provided that we use a corrected relaxation time T _2,corr, accounting for the dependence of the surface relaxivity ρ ₂ on pore radius. The study shows that radius distributions calculated from a T ₁ and from a T ₂ distribution differ from one another and both present an altered image of the true pore radius distribution. In practice, this has no serious influence on estimating permeability of medium- to high-permeability sandstones with the currently applied methods. The presented methodology of calculating the NMR response of pore space models with diffusion coupling may facilitate understanding porosity-permeability relationships of different rock types such as carbonate rocks with micro-porosity.     

Organic matter,sediment particle size and nutrient distributions in a sewage affected shallow channel

Sediment and seawater samples were taken in a sewage affected channel in Blanca Bay, Argentina. Protein content, ‘humic substances’ and silt-clay percentage were evaluated in the sediments; NH₄⁺, PO₄^3? and ‘dissolved organic matter’ in seawater. A highly significant correlation (r=0.747, n=59) was obtained for the relation between protein and % silt-clay. The ‘humic substances’ distribution depends more on the distance from the outfall than does the protein content, probably because of the important relation of the latter with the sediment particle size. The dissolved components showed a dilution pattern similar to that of a contaminant plume in a moving water mass, reaching normal values at 1700 m from the outfall.     

Inferring the Orientation-distribution Function from Observed Seismic Anisotropy: General Considerations and an Inversion of Surface-wave Dispersion Curves

—A general relation linking the elasticity tensor of an anisotropic medium with that of the constituting single crystals and the function describing the orientation distribution of the crystals is derived. By expanding the orientation distribution function (ODF) into tensor spherical harmonics and using canonical components of the elasticity tensors, it is shown that the elastic tensor of the medium is completely determined by a finite number of expansion coefficients, namely those with harmonic degree l≤ 4. The number of expansion coefficients actually needed to determine the elastic constants of the medium depends on the symmetry of the single crystals. For hexagonal symmetry of the single crystals it is shown that only 8 real numbers are required to fix the 13 elastic constants which are for example needed to determine the azimuthal dependence of surface wave velocities. Thus, inversions of observations of seismic anisotropy are feasible which do not make any a priori assumptions on the orientation of the crystals. As a byproduct of the derivation, a formula is given which allows the easy calculation of the elastic constants of a medium composed of hexagonal crystals obeying an arbitrary ODF. An application of the theoretical results to the inversion of surface wave dispersion curves for an anisotropic 1D-mantle model is presented. For the S-wave velocities the results are similar to those of previous inversions but the new approach also yields P-wave velocities consistent with the assumption of oriented olivine. Moreover it provides a hint of the orientation distribution of the crystals.     

Frequency–Magnitude Distribution of −3.7 ≤ M W ≤ 1 Mining-Induced Earthquakes Around a Mining Front and b Value Invariance with Post-Blast Time

We investigated frequency-magnitude distribution (FMD) of acoustic emissions (AE) occurring near an active mining front in a South African gold mine, using a catalog developed from an AE network, which is capable of detecting AEs down to M _W  ?5. When records of blasts were removed, FMDs of AEs obeyed a Gutenberg?Richter law with similar b values, not depending on post-blasting time from the initial 1-min interval through more than 30 h. This result denies a suggestion in a previous study (Richardson and Jordan Bull Seismol Soc Am, 92:1766–1782, 2002) that new fractures generated by blasting disturb the size distribution of background events, which they interpreted as slip events on existing weak planes. Our AE catalog showed that the GR law with b ～ 1.2 was valid between M _W  ?3.7 and 0 for AEs around the mining front. Further, using the mine’s seismic catalog, which covers a longer time period of the same area, we could extend the validity range of the GR law with the same b value up to M _W 1.     

Coseismic deformation of the 2021 MW7.4 Maduo earthquake from joint inversion of InSAR,GPS, and teleseismic data

The M_W7.4 Maduo earthquake occurred on 22 May 2021 at 02:04 CST with a large-expansion surface rupture. This earthquake was located in the Bayan Har block at the eastern Tibetan Plateau, where eight earthquakes of M_S >7.0 have occurred in the past 25 years. Here, we combined interferometric synthetic aperture radar, GPS, and teleseismic data to study the coseismic slip distribution, fault geometry, and dynamic source rupture process of the Maduo earthquake. We found that the overall coseismic deformation field of the Maduo earthquake is distributed in the NWW-SEE direction along 285°. There was slight bending at the western end and two branches at the eastern end. The maximum slip is located near the eastern bending area on the northern branch of the fault system. The rupture nucleated on the Jiangcuo fault and propagated approximately 160 km along-strike in both the NWW and SEE directions. The characteristic source rupture process of the Maduo earthquake is similar to that of the 2010 M_W6.8 Yushu earthquake, indicating that similar earthquakes with large-expansion surface ruptures and small shallow slip deficits can occur on both the internal fault and boundary fault of the Bayan Har block.     

震源机制类型对近场峰值加速度(PGA)分布的影响——以唐山和汶川震区为例

利用首都圈强震台网比较密集的数字地震记录,研究2003年4月发生在唐山震区的2次4级地震。利用布设在四川、甘肃、陕西的强震台网和临时强震台网的资料,研究2008年7月和8月发生在四川汶川的2次6级地震。得到正断层和走向滑动断层、逆冲断层和走向滑动断层的地震近场PGA分布的差异。结果表明,这种差异是显著的。不仅大震的PGA近场分布复杂,中小地震也是如此。经频谱分析发现,这种影响出现差异的地震波频率较低,城市化的建筑向高层大型发展,其自振周期相应较长。近直立走向滑动地震的PGA高值区沿断层对称分布,而正断层和逆断层则集中在断层上盘,这对于破坏性地震应急救援中力量、物资的投入有借鉴意义。     

Remotely sensed assessment of water quality levels in the Pearl River Estuary, China

In this paper, a method of assessing water quality from satellite data is introduced. The composite pollution index (CPI) was calculated from measured chemical oxygen demand (COD) and nutrient concentration. The relationships between CPI and 240 band combinations of SeaWiFS water-leaving radiance were analyzed and the optimal band combination for estimating CPI was chosen from the 240 band combinations. An algorithm for retrieval of CPI was developed using the optimal band combination, (L₄₄₃ × L₅₁₀)/(L₄₁₂ + L₄₉₀). The CPI was estimated from atmospherically corrected SeaWiFS data by employing the algorithm. Furthermore, the CPI value range for each water quality level was determined based on data obtained from 850 samples taken in the Pearl River Estuary. The remotely sensed CPIs were then transferred to water quality levels and appropriate maps were derived. The remotely sensed water quality level maps displayed a similar distribution of levels based on in situ investigation issued by the State Ocean Administration, China. This study demonstrates that remote sensing can play an important role in water quality assessment.     

Structural heterogeneity of the media and macroseismic field formation: Racha,April 29, 1991 earthquake

The points with normal, anomalously low, and anomalously high shaking intensities are recognized in the spatial distribution of macroseismic effects from the 1991 Racha earthquake, Greater Caucasus. Distribution of these points in the epicentral area is not random. Comparison between this distribution and the results of local tomography reveals that seismic wave velocities do not increase in the upper layers (from 0 to 3 km) beneath the points with anomalously high intensity, while a sharp increase in velocity is observed in the depth interval from 6 to 9 km. An original method of b-value mapping is suggested. Application of the method demonstrates that anomalously low intensities correlate to high b-values. This likely reflects higher intensity attenuation associated with higher b-value.     

A Dislocation Model of Seismic Wave Attenuation and Micro-creep in the Earth: Harold Jeffreys and the Rheology of the Solid Earth

—A microphysical model of seismic wave attenuation is developed to provide a physical basis to interpret temperature and frequency dependence of seismic wave attenuation. The model is based on the dynamics of dislocation motion in minerals with a high Peierls stress. It is proposed that most of seismic wave attenuation occurs through the migration of geometrical kinks (micro-glide) and/or nucleation/migration of an isolated pair of kinks (Bordoni peak), whereas the long-term plastic deformation involves the continuing nucleation and migration of kinks (macro-glide). Kink migration is much easier than kink nucleation, and this provides a natural explanation for the vast difference in dislocation mobility between seismic and geological time scales. The frequency and temperature dependences of attenuation depend on the geometry and dynamics of dislocation motion both of which affect the distribution of relaxation times. The distribution of relaxation times is largely controlled by the distribution in distance between pinning points of dislocations, L, and the observed frequency dependence of Q, Q, Q∝ω^α is shown to require a distribution function of P(L)∝L ^-m with m=4-2α The activation energy of Q ^?1 in minerals with a high Peierls stress corresponds to that for kink nucleation and is similar to that of long-term creep. The observed large lateral variation in Q ^?1 strongly suggests that the Q ^?1 in the mantle is frequency dependent. Micro-deformation with high dislocation mobility will (temporarily) cease when all the geometrical kinks are exhausted. For a typical dislocation density of ～ 10⁸ m^?2, transient creep with small viscosity related to seismic wave attenuation will persist up to the strain of ～ 10^?6, thus even a small strain (～ 10^?6?10^?4) process such as post-glacial rebound is only marginally affected by this type of anelastic relaxation. At longer time scales continuing nucleation of kinks becomes important and enables indefinitely large strain, steady-state creep, causing viscous behavior.     

Improved earthquake resistant design of eccentric steel buildings

Recently, a design modification has been proposed for eccentric, torsionally stiff, braced steel buildings, designed according to the current Eurocodes 3 and 8, that improves noticeably their inelastic response under the action of design level earthquakes. The improvement consists in a more uniform distribution of ductility demands throughout the building. In the present paper, a similar, though differently derived, modification is applied to torsionally flexible eccentric buildings and their response is again evaluated under pairs of design earthquake motions. A substantial improvement of their inelastic response is also observed, similar to what had been obtained for torsionally stiff buildings. The new approach is also tested with torsionally stiff buildings and leads to similarly satisfactory results. Thus it may be recommended for general application.     

Equivalent diffusion coefficient of clay-rich geological formations: comparison between numerical and analytical estimates

Laboratory experiments in rock samples collected from clay-rich formations indicate that the effective molecular diffusion coefficient (D) is a heterogeneous and anisotropic property. Since laboratory measurements of D are representative of a very small volume, upscaling is necessary in order to incorporate these data in large-scale numerical models of diffusive transport. In this work we address the problem of the estimating the equivalent diffusion coefficient (D _eq ), in terms of total diffusive flux, in a three-dimensional domain characterized by a heterogeneous and anisotropic spatial distribution of D. D _eq was estimated from the results of steady-state diffusive transport simulations through several realizations of the D field. The ensemble averages of D _eq from fields with different degrees of heterogeneity and anisotropy were then compared with estimates from analytical upscaling expressions based on stochastic as well as power-averaging approaches. These expressions are largely based on similar expressions developed for calculating the effective hydraulic conductivity in heterogeneous and anisotropic domains. Comparisons showed that stochastic expressions provide accurate estimates of D _eq only for fields characterized by low heterogeneity. Within the range of heterogeneity and anisotropy considered, our results showed that a power-averaging expression is very accurate in predicting D _eq especially when the parameter p _i is estimated through fitting of the numerical results. Nonetheless, the relationship between this parameter and the anisotropy ratio is linear.     

Alcohol compounds in <Emphasis Type="Italic">Azolla imbricata</Emphasis> and potential source implication for marine sediments

This study investigated the composition of long-chain alkyl diols, triols, sec-alcohols, hydroxyl acids, and other hydroxylated compounds in Azolla imbricata and compared the organic alcohol components of Azolla filiculoides, Azolla microphylla, and South China Sea (SCS) sediments in order to investigate the possible indication of Azolla being the biological source of diols and triols in SCS sediment. Large amounts of diols, monohydroxy acids, and sec-alcohols with internal hydroxy groups at ω20 were detected in the three types of Azolla. Among these, 1,ω20-diol and ω20-hydroxy acid exhibited strong even-odd predominance distribution, whereas ω20-sec-alcohol exhibited strong odd-even predominance distribution. In addition, small amounts of diols, triols, and dihydroxy acids with internal hydroxy groups at 9, 10 or ω9, ω10 were detected, among which the chain length of C₂₉ was predominate. Compounds having similar structures as those in Azolla reflected a similar biosynthetic pathway: ω20-hydroxy acid exhibiting even-odd predominance distribution is decarboxylated to ω20-sec-alcohol exhibiting odd-even predominance distribution and converted to 1, ω20-diol with even-odd predominance distribution by acyl reduction; ω9, ω10-hydroxy acid is converted to 1,20,21(1, ω9, ω10)-triol by acyl reduction, and then converted to 9,10-diol by hydrogenation and dehydration. The alcohol components in A. imbricata were clearly not the biological source of 1,13/1,14/1,15-C_{28, 30, 32} diols and 1,3,4-C_27-29 triols in the SCS sediment. Certain marine diatoms might be the source of 1,14-C_{28, 30} diol in inshore sediment, but the biological source of diols and triols in the SCS sediment requires further investigation.     

Representation and Analysis of the Earthquake Size Distribution: A Historical Review and Some New Approaches

—The size distribution of earthquakes has been investigated since the early 20th century. In 1932 Wadati assumed a power-law distribution n(E) = kE ^?w for earthquake energy E and estimated the w value to be 1.7 ～ 2.1. Since the introduction of the magnitude-frequency relation by Gutenberg and Richter in 1944 in the form of log n(M) = a?bM, the spatial or temporal variation (or stability) of b value has been a frequently discussed subject in seismicity studies. The log n(M) versus M plots for some data sets exhibit considerable deviation from a straight line. Many modifications of the G-R relation have been proposed to represent such character. The modified equations include the truncated G-R equation, two-range G-R equation, equations with various additional terms to the original G-R equation. The gamma distribution of seismic moments is equivalent to one of these equations.¶In this paper we examine which equation is the most suitable to magnitude data from Japan and the world using AIC. In some cases, the original G-R equation is the most suitable, however in some cases other equations fit far better. The AIC is also a powerful tool to test the significance of the difference in parameter values between two sets of magnitude data under the assumption that the magnitudes are distributed according to a specified equation. Even if there is no significant difference in b value between two data sets (the G-R relation is assumed), we may find a significant difference between the same data sets under the assumption of another relation. To represent a character of the size distribution, there are indexes other than parameters in the magnitude-frequency distribution. The η value is one of such numbers. Although it is certain that these indexes vary among different data sets and are usable to represent a certain feature of seismicity, the usefulness of these indexes in some practical problems such as foreshock discrimination has not yet been established.