Earthquake Size Distribution: Power-Law with Exponent Beta = 1/2?

We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter beta of the power-law distribution of earthquake sizes. In particular, we find that estimated beta-values may be inflated by 1-3% because relative moment uncertainties decrease with increasing earthquake size. Moreover, earthquake clustering greatly influences the beta-parameter. If clusters (aftershock sequences) are taken as the entity to be studied, then the exponent value for their size distribution would decrease by 5-10%. The complexity of any earthquake source also inflates the estimated beta-value by at least 3-7%. The centroid depth distribution also should influence the beta-value, an approximate calculation suggests that the exponent value may be increased by 2-6%. Taking all these effects into account, we propose that the recently obtained beta-value of 0.63 could be reduced to about 0.52--0.56: near the universal constant value (1/2) predicted by theoretical arguments. We also consider possible consequences of the universal beta-value and its relevance for theoretical and practical understanding of earthquake occurrence in various tectonic and Earth structure environments. Using comparative crystal deformation results may help us understand the generation of seismic tremors and slow earthquakes and illuminate the transition from brittle fracture to plastic flow.Comment: 46 pages, 2 tables, 11 figures 53 pages, 2 tables, 12 figure

Synthesis of 1-diazo-3-methoxy-3-phenyl-2-propanone and reaction with boron trifluoride etherate

It has been found that the normal reaction of diazoketones with an acid to form substituted methyl ketones is often subverted by cyclization to form closed chain cyclic ketones. Some work has been done with aromatic diazoketones but very little has been done with the aliphatic diazoketones. The object of this research was to bring about ring closure of a four membered ring from an aliphatic diazoketone. It was decided to put a phenyl group on the aliphatic chain in order to obtain crystalline derivatives. Specifically, the object of this work was to bring about the cyclization of 1-diazo-3-methoxy-3-phenyl-2-propane. The diazoketone must be synthesized from the respective acid, D, L – phenyl-2-methoxy-acetic acid, by a series of steps which involve: (1) the conversion of the acid to the acid chloride upon treatment with thionyl chloride, (2) the conversion of the acid chloride to the diazoketone upon treatment with diazo methane. Diazomethane will be written: CH2N2. It is actually a resonance hybrid of the two forms

Importance of small earthquakes for stress transfers and earthquake triggering

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as \~10^(Dm/2). The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future event as well as earthquake triggering. If earthquake magnitudes follow the Gutenberg-Richter law with b>D/2, small earthquakes collectively dominate stress transfer and earthquake triggering, because their greater frequency overcomes their smaller individual triggering potential. Using a Southern-California catalog, we observe that the rate of seismicity triggered by an earthquake of magnitude m increases with m as 10^(alpha m), where alpha=1.00+-0.05. We also find that the magnitude distribution of triggered earthquakes is independent of the triggering earthquake magnitude m. When alpha=b, small earthquakes are roughly as important to earthquake triggering as larger ones. We evaluate the fractal correlation dimension of hypocenters D=2 using two relocated catalogs for Southern California, and removing the effect of short-term clustering. Thus D=2alpha as predicted by assuming that earthquake triggering is due to static stress. The value D=2 implies that small earthquakes are as important as larger ones for stress transfers between earthquakes.Comment: 14 pages, 7 eps figures, latex. In press in J. Geophys. Re

Regional variations in the diffusion of triggered seismicity

[1] We determine the spatiotemporal characteristics of interearthquake triggering in the International Seismological Centre catalogue on regional and global scales. We pose a null hypothesis of spatially clustered, temporally random seismicity, and determine a residual pair correlation function for triggered events against this background. We compare results from the eastern Mediterranean, 25 Flinn-Engdahl seismic regions, and the global data set. The null hypothesis cannot be rejected for distances greater than 150 km, providing an upper limit to triggering distances that can be distinguished from temporally uncorrelated seismicity in the stacked data at present. Correlation lengths L andmean distances between triggered events hri are on the order of 10–50 km, but can be as high as 100 km in subduction zones. These values are not strongly affected by magnitude threshold, but are comparable to seismogenic thicknesses, implying a strong thermal control on correlation lengths. The temporal evolution of L and hri is well fitted by a power law, with an exponent H 0.1 ± 0.05. This is much lower than the value H = 0.5 expected for Gaussian diffusion in a homogenous medium. We observe clear regional variations in L, hri and H that appear to depend on tectonic setting. A detectable transition to a more rapid diffusion regime occurs in some cases at times greater than 100–200 days, possibly due to viscoelastic processes in the ductile lower crust

Importance of direct and indirect triggered seismicity

Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source. We show that, in this model, the fraction of earthquakes in the population that are aftershocks is equal to the fraction of aftershocks that are indirectly triggered and is given by the average number of triggered events per earthquake. Previous observations that a significant fraction of earthquakes are triggered earthquakes therefore imply that most aftershocks are indirectly triggered by the mainshock.Comment: Latex document of 17 pages + 2 postscript figure

e^+ e^- --> {tilde t}_1 {tilde t}_1^* (H_1) in the MSSM with explicit CP violations

The author considers the effects of the CP-violating phases, e. g. arg(A_t) and arg(mu) on the e^+ e^- --> {tilde t}_1 {tilde t}_1^* (H_1) processes. The third generation squark trilinear terms give significant contributions to the Higgs potential at the one-loop level. This results in the changes of the stop masses and the lighter stop - the lighter anti-stop - the lightest Higgs coupling. The author shows the coupling and the loop effects on the processes. And the author will discuss the determination method of soft parameters.Comment: 18 pages, 7 figures. Detailed comments and minor changes added; To appear in Phys. Lett.

Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks

We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by a single mainshock decreases with the time from the mainshock according to the modified Omori law K/(t+c)^p with p=1+theta. A mainshock at time t=0 triggers aftershocks according to the local Omori law, that in turn trigger their own aftershocks and so on. The effective branching parameter n, defined as the mean aftershock number triggered per event, controls the transition between a sub-critical regime n<1 to a super-critical regime n>1. In the sub-critical regime, we recover and document the crossover from an Omori exponent 1-theta for t<t* to 1+theta for t<t* found previously in [Sornette and Sornette, 1999a] for a special case of the ETAS model. In the super-critical regime n>1 and theta>0, we find a novel transition from an Omori decay law with exponent 1-theta fot t<t* to an explosive exponential increase of the seismicity rate fot t>t*. The case theta<0 yields an infinite n-value. In this case, we find another characteristic time tau controlling the crossover from an Omori law with exponent 1-theta for t<tau, similar to the local law, to an exponential increase at large times. These results can rationalize many of the stylized facts reported for aftershock and foreshock sequences, such as (i) the suggestion that a small p-value may be a precursor of a large earthquake, (ii) the relative seismic quiescence sometimes observed before large aftershocks, (iii) the positive correlation between b and p-values, (iv) the observation that great earthquakes are sometimes preceded by a decrease of b-value and (v) the acceleration of the seismicity preceding great earthquakes.Comment: Latex document of 41 pages + 6 eps figures + 1 tabl

Quark Dipole Operators in Extended Technicolor Models

We study diagonal and transition quark dipole operators in a class of extended technicolor (ETC) models, taking account of the multiscale nature of the ETC gauge symmetry breaking and of the mixing among ETC interaction eigenstates. Because of this mixing, terms involving the lowest ETC scale can play an important role in dipole operators, and we focus on these terms. We derive from experiment new correlated constraints on the quark mixing angles and phases. Our bounds yield information on mixing angles individually in the up- and down-sectors, for both left- and right-handed quark fields and thus constrain even quark mixing parameters that do not enter in the CKM matrix. With phases of order unity, we conclude that these mixing angles are small, constraining future ETC model building, but plausibly in the range suggested by the size of the CKM elements. These values still allow substantial deviations from the standard model predictions, in particular for several CP violating quantities, including the asymmetries in $b \to s \gamma$ and $B_{d} \to \phi K_S$, $Re(\epsilon^\prime/\epsilon)$, and the electric dipole moments of the neutron and the ${}^{199}$Hg atom.Comment: 9 pages, late

Development and Validation of the Mukbang Addiction Scale

Recent literature has speculated that some individuals spend lots of time watching mukbang (i.e., combination of the South Korean words ‘eating’ [‘meokneun’] and ‘broadcast’ [‘bangsong’] that refers to eating broadcasts where a person eats a large portion of food on camera whilst interacting with viewers) and compensate different needs using this activity. However, compensating unattained offline needs using a specific online activity could lead to the addictive use of that activity. The present study investigated problematic mukbang watching by developing and validating the Mukbang Addiction Scale (MAS). An online survey was administered to 236 university students (Mage = 20.50 years; 62% female) who had watched mukbang at least once. Construct validity, criterion validity, and reliability analyses indicated that the MAS had good psychometric properties. Exploratory and confirmatory factor analyses confirmed the unidimensional structure of the scale. The Cronbach’s alpha (α = .95) and composite reliability (CR = .92) suggested that the MAS had excellent internal consistency. Latent class analyses (LCA) revealed two primary profiles, one with high endorsement and one with low endorsement of the items assessed. Item response theory (IRT) findings also indicated a good model fit. IRT findings provisionally supported a cut-off scale raw score of 22 (out of 30). Assessment and clinical-related implications of the findings are illustrated in accordance with other excessive behaviours