搜索结果：Magnitude

We mapped the minimum magnitude of complete reporting, M c , for Alaska, the western United States, and for the JUNEC earthquake catalog of Japan. Mc was estimated based on its departure from the linear frequency-magnitude relation of the 250 closest earthquakes to grid nodes, spaced 10 km apart. In all catalogs studied, Mc was strongly heterogeneous. In offshore areas the Mc was typically one unit of magnitude higher than onshore. On land also, Mc can vary by one order of magnitude over distance less than 50 km. We recommend that seismicity studies that depend on complete sets of small earthquakes should be limited to areas with similar Mc, or the minimum magnitude for the analysis has to be raised to the highest com- mon value of Mc. We believe that the data quality, as reflected by the Mc level, should be used to define the spatial extent of seismicity studies where Mc plays a role. The method we use calculates the goodness of fit between a power law fit to the data and the observed frequency-magnitude distribution as a function of a lower cutoff of the magnitude data. Mc is defined as the magnitude at which 90% of the data can be modeled by a power law fit. Mc in the 1990s is approximately 1.2 0.4 in most parts of California, 1.8 0.4 in most of Alaska (Aleutians and Panhandle excluded), and at a higher level in the JUNEC catalog for Japan. Various sources, such as ex- plosions and earthquake families beneath volcanoes, can lead to distributions that cannot be fit well by power laws. For the Hokkaido region we demonstrate how neglecting the spatial variability of M c can lead to erroneous assumptions about deviations from self-similarity of earthquake scaling.

In this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.

The relative importance in geomorphic processes of extreme or catastrophic events and more frequent events of smaller magnitude can be measured in terms of (1) the relative amounts of "work" done on the landscape and (2) in terms of the formation of specific features of the landscape. For many processes, above the level of competence, the rate of movement of material can be expressed as a power function of some stress, as for example, shear stress. Because the frequency distributions of the magnitudes of many natural events, such as floods, rainfall, and wind speeds, approximate log-normal distributions, the product of frequency and rate, a measure of the work performed by events having different frequencies and magnitudes will attain a maximum. The frequency at which this maximum occurs provides a measure of the level at which the largest portion of the total work is accomplished. Analysis of records of sediment transported by rivers indicates that the largest portion of the total load is carried by flows which occur on the average once or twice each year. As the variability of the flow increases and hence as the size of the drainage basin decreases, a larger percentage of the total load is carried by less frequent flows. In many basins 90 per cent of the sediment is removed by storm discharges which recur at least once every five years. Transport of sand and dust by wind in general follows the same laws. The extreme velocities associated with infrequent events are compensated for by their rarity, and it is found that the greatest bulk of sediment is transported by more moderate events. Many rivers are competent to erode both bed and banks during moderate flows. Observations of natural channels suggest that the channel shape as well as the dimensions of meandering rivers appear to be associated with flows at or near the bankfull stage. The fact that the bankfull stage recurs on the average once every year or two years indicates that these features of many alluvial rivers are controlled by these more frequent flows rather than by the rarer events of catastrophic magnitude. Because the equilibrium form of wind-blown dunes and of wave-formed beaches is quite unstable, the frequency of the events responsible for their form is less clearly definable. However, dune form and orientation are determined by both wind velocity and frequency. Similarly, a hypothetical example suggests that beach slope oscillates about a mean value related in part to wave characteristics generated by winds of moderate speed. Where stresses generated by frequent events are incompetent to transport available materials, less frequent ones of greater magnitude are obviously required. Closer observation of many geomorphic processes is required before the relative importance of different processes and of events of differing magnitude and frequency in the formation of given features of the landscape can be adequately evaluated.

We analyse the bivariate distribution, in color versus absolute magnitude (u-r vs. M_r), of a low redshift sample of galaxies from the Sloan Digital Sky Survey (SDSS; 2400 deg^2, 0.004<z<0.08, -23.5<M_r<-15.5). We trace the bimodality of the distribution from luminous to faint galaxies by fitting double-Gaussians to the color functions separated in absolute magnitude bins. Color-magnitude (CM) relations are obtained for red and blue distributions (early- and late-type, predominantly field, galaxies) without using any cut in morphology. Instead, the analysis is based on the assumption of normal Gaussian distributions in color. We find that the CM relations are well fit by a straight line plus a tanh function. Both relations can be described by a shallow CM trend (slopes of about -0.04, -0.05) plus a steeper transition in the average galaxy properties over about two magnitudes. The midpoints of the transitions (M_r=-19.8 and -20.8 for the red and blue distributions, respectively) occur around 2x10^10 M_solar after converting luminosities to stellar mass. Separate luminosity functions are obtained for the two distributions. The red distribution has a more luminous characteristic magnitude and a shallower faint-end slope (M^*=-21.5, alpha=-0.8) compared to the blue distribution (alpha=-1.3 depending on the parameterization). These are approximately converted to galaxy stellar mass functions. The red distribution galaxies have a higher number density per magnitude for masses greater than about 3x10^10 M_solar. Using a simple merger model, we show that the differences between the two functions are consistent with the red distribution being formed from major galaxy mergers.

A study of a sample provides only an estimate of the true (population) value of an outcome statistic. A report of the study therefore usually includes an inference about the true value. Traditionally, a researcher makes an inference by declaring the value of the statistic statistically significant or nonsignificant on the basis of a P value derived from a null-hypothesis test. This approach is confusing and can be misleading, depending on the magnitude of the statistic, error of measurement, and sample size. The authors use a more intuitive and practical approach based directly on uncertainty in the true value of the statistic. First they express the uncertainty as confidence limits, which define the likely range of the true value. They then deal with the real-world relevance of this uncertainty by taking into account values of the statistic that are substantial in some positive and negative sense, such as beneficial or harmful. If the likely range overlaps substantially positive and negative values, they infer that the outcome is unclear; otherwise, they infer that the true value has the magnitude of the observed value: substantially positive, trivial, or substantially negative. They refine this crude inference by stating qualitatively the likelihood that the true value will have the observed magnitude (eg, very likely beneficial). Quantitative or qualitative probabilities that the true value has the other 2 magnitudes or more finely graded magnitudes (such as trivial, small, moderate, and large) can also be estimated to guide a decision about the utility of the outcome.

abstract During the deformation of rock in laboratory experiments, small cracking events, i.e., microfractures, occur which radiate elastic waves in a manner similar to earthquakes. These radiations were detected during uniaxial and triaxial compression tests and their frequency-magnitude relation studied. They were found to obey the Gutenberg and Richter relation log N = a + b M Where N is the number of events which occurred of magnitude M, and a and b constants. The dependence of the parameter b on rock type, stress, and confining pressure was studied. It was found to depend primarily on stress, in a characteristic way. The frequency-magnitude relation for events which accompanied frictional sliding and deformation of a ductile rock was found to have a much higher b value than that observed in brittle rock. The Gutenberg and Richter formulation of the frequency-magnitude relation was derived from a statistical model of rock and crustal deformation. This analysis demonstrates the basis of similarity between rock deformation experiments in the laboratory and deformation of the crust.

Nine experiments of timed odd-even judgments examined how parity and number magnitude are accessed from Arabic and verbal numerals. With Arabic numerals, Ss used the rightmost digit to access a store of semantic number knowledge. Verbal numerals went through an additional stage of transcoding to base 10. Magnitude information was automatically accessed from Arabic numerals. Large numbers preferentially elicited a rightward response, and small numbers a leftward response. The Spatial-Numerical Association of Response Codes (SNARC) effect depended only on relative number magnitude and was weaker or absent with letters or verbal numerals. Direction did not vary with handedness or hemispheric dominance but was linked to the direction of writing, as it faded or even reversed in right-to-left writing Iranian Ss

Absolute magnitudes in the B, V, and I bands are derived for nine well-observed Type Ia supernovae using host galaxy distances estimated via the surface brightness fluctuations or Tully-Fisher methods. These data indicate that there is a significant intrinsic dispersion in the absolute magnitudes at maximum light of Type Ia supernovae, amounting to +/- 0.8 mag in B, +/- 0.6 mag in V, and +/- 0.5 mag in I. Moreover, the absolute magnitudes appear to be tightly correlated with the initial rate of decline of the B light curve, with the slope of the correlation being steepest in B and becoming progressively flatter in the V and I bands. This implies that the intrinsic B - V colors of Type Ia supernovae at maximum light are not identical, with the fastest declining light curves corresponding to the intrinsically reddest events. Certain spectroscopic properties may also be correlated with the initial decline rate. These results are most simply interpreted as evidence for a range of progenitor masses, although variations in the explosion mechanism are also possible. Considerable care must be exercised in employing Type Ia supernovae as cosmological standard candles, particularly at large redshifts where Malmquist bias could be an important effect.

Estimates of inbreeding depression obtained from the literature were used to evaluate the association between inbreeding depression and the degree of self-fertilization in natural plant populations. Theoretical models predict that the magnitude of inbreeding depression will decrease with inbreeding as deleterious recessive alleles are expressed and purged through selection. If selection acts differentially among life history stages and deleterious effects are uncorrelated among stages, then the timing of inbreeding depression may also evolve with inbreeding. Estimates of cumulative inbreeding depression and stage-specific inbreeding depression (four stages: seed production of parent, germination, juvenile survival, and growth/reproduction) were compiled for 79 populations (using means of replicates, N = 62) comprising 54 species from 23 families of vascular plants. Where available, data on the mating system also were collected and used as a measure of inbreeding history. A significant negative correlation was found between cumulative inbreeding depression and the primary selfing rate for the combined sample of angiosperms (N = 35) and gymnosperms (N = 9); the correlation was significant for angiosperms but not gymnosperms examined separately. The average inbreeding depression in predominantly selfing species (δ = 0.23) was significantly less (43%) than that in predominantly outcrossing species (δ = 0.53). These results support the theoretical prediction that selfing reduces the magnitude of inbreeding depression. Most self-fertilizing species expressed the majority of their inbreeding depression late in the life cycle, at the stage of growth/reproduction (14 of 18 species), whereas outcrossing species expressed much of their inbreeding depression either early, at seed production (17 of 40 species), or late (19 species). For species with four life stages examined, selfing and outcrossing species differed in the magnitude of inbreeding depression at the stage of seed production (selfing δ = 0.05, N = 11; outcrossing δ = 0.32, N = 31), germination (selfing δ = 0.02, outcrossing δ = 0.12), and survival to reproduction (selfing δ = 0.04, outcrossing δ = 0.15), but not at growth and reproduction (selfing δ = 0.21, outcrossing δ = 0.27); inbreeding depression in selfers relative to outcrossers increased from early to late life stages. These results support the hypothesis that most early acting inbreeding depression is due to recessive lethals and can be purged through inbreeding, whereas much of the late-acting inbreeding depression is due to weakly deleterious mutations and is very difficult to purge, even under extreme inbreeding.

Abstract We introduce a new method to determine the magnitude of completeness M c and its uncertainty. Our method models the entire magnitude range (EMR method) consisting of the self-similar complete part of the frequency-magnitude distribution and the incomplete portion, thus providing a comprehensive seismicity model. We compare the EMR method with three existing techniques, finding that EMR shows a superior performance when applied to synthetic test cases or real data from regional and global earthquake catalogues. This method, however, is also the most computationally intensive. Accurate knowledge of M c is essential for many seismicity-based studies, and particularly for mapping out seismicity parameters such as the b-value of the Gutenberg-Richter relationship. By explicitly computing the uncertainties in M c using a bootstrap approach, we show that uncertainties in b-values are larger than traditionally assumed, especially when considering small sample sizes. As examples, we investigated temporal variations of M c for the 1992 Landers aftershock sequence and found that it was underestimated on average by 0.2 with former techniques. Mapping M c on a global scale, M c reveals considerable spatial variations for the Harvard Centroid Moment Tensor (CMT) (5.3 � M c � 6.0) and the International Seismological Centre (ISC) catalogue (4.3 � M c � 5.0).

Previous research has shown that two components of the event-related brain potential, the P300 and feedback negativity, are sensitive to information about rewards and penalties. The present study investigated the properties of these components in a simple gambling game that required participants to choose between cards that were unpredictably associated with monetary gains and losses of variable magnitude. The aim was to determine the sensitivity of each component to two critical features of reward stimuli: magnitude (small or large) and valence (win or loss). A double dissociation was observed, with the P300 sensitive to reward magnitude but insensitive to reward valence and the feedback negativity showing the opposite pattern, suggesting that these two fundamental features of rewarding stimuli are evaluated rapidly and separately in the human brain. Subsequent analyses provided additional evidence of functional dissociations between the feedback negativity and P300. First, the P300 (but not the feedback negativity) showed sensitivity to the reward value of alternative, nonselected stimuli. Second, individual differences in the amplitude of the feedback negativity correlated with individual differences in risk-taking behavior observed after monetary losses, whereas individual differences in P300 amplitude were related to behavioral adjustments observed in response to alternative, unchosen outcomes.

This paper is in continuation of previous investigations (Gutenberg and Richter, Paper I, 1942; Paper I I , 1956). The earthquake magnitude has statistical and other uses independent of the relation between magnitude and energy. Indeed, it is possible that there is no complete one-to-one correlation between magnitude and energy for large and complex tectonic events. Even so, a mean or representative relation is a legitimate object of inquiry.

The nearly coincident forms of the relations between seismic moment M 0 and the magnitudes M L , M S , and M w imply a moment magnitude scale M = ⅔ log M 0 ‐ 10.7 which is uniformly valid for 3 ≲ M L ≲ 7, 5 ≲ M s ≲ 7½, and M w ≳ 7½.

Analysis of numerous case histories of earthquake sequences induced by fluid injection at depth reveals that the maximum magnitude appears to be limited according to the total volume of fluid injected. Similarly, the maximum seismic moment seems to have an upper bound proportional to the total volume of injected fluid. Activities involving fluid injection include (1) hydraulic fracturing of shale formations or coal seams to extract gas and oil, (2) disposal of wastewater from these gas and oil activities by injection into deep aquifers, and (3) the development of enhanced geothermal systems by injecting water into hot, low-permeability rock. Of these three operations, wastewater disposal is observed to be associated with the largest earthquakes, with maximum magnitudes sometimes exceeding 5. To estimate the maximum earthquake that could be induced by a given fluid injection project, the rock mass is assumed to be fully saturated, brittle, to respond to injection with a sequence of earthquakes localized to the region weakened by the pore pressure increase of the injection operation and to have a Gutenberg-Richter magnitude distribution with a b value of 1. If these assumptions correctly describe the circumstances of the largest earthquake, then the maximum seismic moment is limited to the volume of injected liquid times the modulus of rigidity. Observations from the available case histories of earthquakes induced by fluid injection are consistent with this bound on seismic moment. In view of the uncertainties in this analysis, however, this should not be regarded as an absolute physical limit.

In recent years, the magnitude, consistency, and stability across time of cognitive sex differences have been questioned. The present study examined these issues in the context of spatial abilities. A meta-analysis of 286 effect sizes from a variety of spatial ability measures was conducted. Effect sizes were partitioned by the specific test used and by a number of variables related to the experimental procedure in order to achieve homogeneity. Results showed that sex differences are significant in several tests but that some intertest differences exist. Partial support was found for the notion that the magnitude of sex differences has decreased in recent years. Finally, it was found that the age of emergence of sex differences depends on the test used. Results are discussed with regard to their implications for the study of sex differences in spatial abilities.

Single-channel, speaker-independent speech separation methods have recently seen great progress. However, the accuracy, latency, and computational cost of such methods remain insufficient. The majority of the previous methods have formulated the separation problem through the time-frequency representation of the mixed signal, which has several drawbacks, including the decoupling of the phase and magnitude of the signal, the suboptimality of time-frequency representation for speech separation, and the long latency of the entire system. To address these shortcomings, we propose a fully-convolutional time-domain audio separation network (Conv-TasNet), a deep learning framework for end-to-end time-domain speech separation. Conv-TasNet uses a linear encoder to generate a representation of the speech waveform optimized for separating individual speakers. Speaker separation is achieved by applying a set of weighting functions (masks) to the encoder output. The modified encoder representations are then inverted back to the waveforms using a linear decoder. The masks are found using a temporal convolutional network (TCN) consisting of stacked 1-D dilated convolutional blocks, which allows the network to model the long-term dependencies of the speech signal while maintaining a small model size. The proposed Conv-TasNet system significantly outperforms previous time-frequency masking methods in separating two- and three-speaker mixtures. Additionally, Conv-TasNet surpasses several ideal time-frequency magnitude masks in two-speaker speech separation as evaluated by both objective distortion measures and subjective quality assessment by human listeners. Finally, Conv-TasNet has a significantly smaller model size and a much shorter minimum latency, making it a suitable solution for both offline and real-time speech separation applications. This study therefore represents a major step toward the realization of speech separation systems for real-world speech processing technologies.

Knowledge of the frequencies of highly explosive, moderately explosive, and nonexplosive eruptions would be useful in a variety of volcano studies. Historical records are generally incomplete, however, and contain very little quantitative data from which explosive magnitude can be estimated. Only the largest eruptions have a complete record back to the early 19th Century; other important explosive events went unrecorded prior to about 1960. Only a handful of the very biggest eruptions are represented in the geologic record, so it will be impossible to augment historical records post facto. A composite estimate of the magnitude of past explosive eruptions, termed the Volcanic Explosivity Index (VEI), is proposed as a semiquantitative compromise between poor data and the need in various disciplines to evaluate the record of past volcanism. The VEI has been assigned to over 8000 historic and prehistoric eruptions, and a complete list is available in a companion document.

It is an important task to faithfully evaluate the perceptual quality of output images in many applications, such as image compression, image restoration, and multimedia streaming. A good image quality assessment (IQA) model should not only deliver high quality prediction accuracy, but also be computationally efficient. The efficiency of IQA metrics is becoming particularly important due to the increasing proliferation of high-volume visual data in high-speed networks. We present a new effective and efficient IQA model, called gradient magnitude similarity deviation (GMSD). The image gradients are sensitive to image distortions, while different local structures in a distorted image suffer different degrees of degradations. This motivates us to explore the use of global variation of gradient based local quality map for overall image quality prediction. We find that the pixel-wise gradient magnitude similarity (GMS) between the reference and distorted images combined with a novel pooling strategy-the standard deviation of the GMS map-can predict accurately perceptual image quality. The resulting GMSD algorithm is much faster than most state-of-the-art IQA methods, and delivers highly competitive prediction accuracy. MATLAB source code of GMSD can be downloaded at http://www4.comp.polyu.edu.hk/~cslzhang/IQA/GMSD/GMSD.htm.

Summary The paper investigates the principal physical elements of earthquakes: the magnitude M, energy E, intensity I, acceleration a, and their relation to the depth h and radius of perceptibility r. (r2 + h2 = R2. Subscript zero (0) refers to the epicenter.) Equations log ⁡ a = I 3 − 1 2 and A D 2 T 2 = constant (A = ground amplitude, T = period, D = hypocentral distance for a given shock) are established empirically for California shocks. Equation (9) holds very generally, and offers a basis for a more accurate definition of I, like that suggested by Cancani. Equation (4) is here used very generally at short distances; but it is approximate only, may differ regionally, and bridges over the probably discontinuous transition of the maximum acceleration from S̄ to some other transverse wave, with increasing distance. However, consequences derived from (4) nowhere conflict seriously with observation. The instrumental earthquake-magnitude scale has been extended to cover short distances. The results enter into an empirical relation M = 2.2 + 1.8 log ⁡ a 0 from which and (9) follows M = 1.3 + 0.6 I 0 These two equations are established and verified for the California region; they should also hold in other regions of similar structure for earthquakes originating at about the same depth (which is roughly 18 km.). The simplest possible assumptions (constant velocity, negligible absorption, sinusoidal waves) lead to the general equation log ⁡ E = 14.9 + 2 log ⁡ h + log ⁡ t 0 + 2 log ⁡ T 0 + 2 log ⁡ a 0 (t0 = duration, T0 = period, of sinusoidal wave train at the epicenter). Equations (27), (9), and (4) give the generally applicable results a 0 h 2 = a D 2 = a r R 2 I 1 − I 2 = 6 log ⁡ D 2 D 1 I 0 − 1.5 = 6 log ⁡ R h ar, the minimum perceptible acceleration, is approximately 1 gal. For shocks at the usual depth in California log ⁡ E = 11.3 + 1.8 M For other depths, and probably for other regions, log ⁡ E = 9.5 + 3.2 log ⁡ h + 1.1 I 0 log ⁡ E = 11.1 + 6.4 log ⁡ R − 3.2 log ⁡ h A summary of the physical elements for shocks in California is given in table 10. Equation (13) is used to calculate apparent depths for earthquakes in the United States and Europe. The results tend to confirm the relatively shallow origin of shocks on the Pacific Coast compared with those occurring elsewhere, particularly under the Canadian Shield, the central Mississippi Valley, and the southern Appalachians.