The moment magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> and the energy magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>e</Subscript>: common roots and differences

Starting from the classical empirical magnitude-energy relationships, in this article, the derivation of the modern scales for moment magnitude M _w and energy magnitude M _e is outlined and critically discussed. The formulas for M _w and M _e calculation are presented in a way that reveals, besides the contributions of the physically defined measurement parameters seismic moment M ₀ and radiated seismic energy E _S, the role of the constants in the classical Gutenberg–Richter magnitude–energy relationship. Further, it is shown that M _w and M _e are linked via the parameter Θ = log(E _S/M ₀), and the formula for M _e can be written as M _e = M _w + (Θ + 4.7)/1.5. This relationship directly links M _e with M _w via their common scaling to classical magnitudes and, at the same time, highlights the reason why M _w and M _e can significantly differ. In fact, Θ is assumed to be constant when calculating M _w. However, variations over three to four orders of magnitude in stress drop Δσ (as well as related variations in rupture velocity V _R and seismic wave radiation efficiency η _R) are responsible for the large variability of actual Θ values of earthquakes. As a result, for the same earthquake, M _e may sometimes differ by more than one magnitude unit from M _w. Such a difference is highly relevant when assessing the actual damage potential associated with a given earthquake, because it expresses rather different static and dynamic source properties. While M _w is most appropriate for estimating the earthquake size (i.e., the product of rupture area times average displacement) and thus the potential tsunami hazard posed by strong and great earthquakes in marine environs, M _e is more suitable than M _w for assessing the potential hazard of damage due to strong ground shaking, i.e., the earthquake strength. Therefore, whenever possible, these two magnitudes should be both independently determined and jointly considered. Usually, only M _w is taken as a unified magnitude in many seismological applications (ShakeMap, seismic hazard studies, etc.) since procedures to calculate it are well developed and accepted to be stable with small uncertainty. For many reasons, procedures for E _S and M _e calculation are affected by a larger uncertainty and are currently not yet available for all global earthquakes. Thus, despite the physical importance of E _S in characterizing the seismic source, the use of M _e has been limited so far to the detriment of quicker and more complete rough estimates of both earthquake size and strength and their causal relationships. Further studies are needed to improve E _S estimations in order to allow M _e to be extensively used as an important complement to M _w in common seismological practice and its applications.     

Soil H<Subscript>2</Subscript> and CO<Subscript>2</Subscript> Surveys at Several Active Faults in Japan

Soil H₂ and CO₂ surveys were carried out along seven active faults and around the aftershock region of the 2000 Tottori-ken Seibu earthquake in Japan. Diffuse CO₂ effluxes were also measured along one fault and around the 2000 aftershock region. The results show highly variable H₂ concentration in space and time and it seems that the maximum H₂ concentration at each active fault correlates with fault activity as exemplified by the time of the latest big earthquakes. Even though observed H₂ concentrations in four faults were markedly lower than those collected previously in the latter half of the 1970s, it is evident that the higher H₂ concentrations in this study are due to the addition of the fault gases. Comparing the chemical composition of trapped gases (H₂: 5–20% and CO₂/H₂: 0.5–12) in fractured rocks of drill cores bored at the Nojima fault, a soil gas sample with the highest H₂ concentration showed large amounts of the trapped fault gas, diluted with atmospheric component. The profile experiment across a fracture zone at the Yamasaki fault showed higher H₂ concentrations and lower CO₂/H₂ ratios as was observed in soil gas from the fracture zone. A few days after the 2000 Tottori-kei Seibu earthquake, no CO₂ effluxes related to the occurrence of earthquakes were observed at the aftershock region. However, only above the epicenter zone, relatively high H₂ concentrations in soil gases were observed.     

Spectral decomposition and de‐noising via time‐frequency and space‐wavenumber reassignment

The reassignment method remaps the energy of each point in a time‐frequency spectrum to a new coordinate that is closer to the actual time‐frequency location. Two applications of the reassignment method are developed in this paper. We first describe time‐frequency reassignment as a tool for spectral decomposition. The reassignment method helps to generate more clear frequency slices of layers and therefore, it facilitates the interpretation of thin layers. The second application is to seismic data de‐noising. Through thresholding in the reassigned domain rather than in the Gabor domain, random noise is more easily attenuated since seismic events are more compactly represented with a relatively larger energy than the noise. A reconstruction process that permits the recovery of seismic data from a reassigned time‐frequency spectrum is developed. Two approaches of the reassignment method are used in this paper, one of which is referred to as the trace by trace time reassignment that is mainly used for seismic spectral decomposition and another that is the spatial reassignment that is mainly used for seismic de‐noising. Synthetic examples and two field data examples are used to test the proposed method. For comparison, the Gabor transform method, inversion‐based method and common deconvolution method are also used in the examples.     

Kinematic characteristics and the influence of reference velocities of phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier migration methods

The phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier methods are wavefield‐continuation algorithms for seismic migration imaging. These two methods can be applied to regions with complex geological structures. Based on their unified separable formulas, we show that these two methods have the same kinematic characteristics by using the theory of pseudodifferential operators. Numerical tests on a Marmousi model demonstrate this conclusion. Another important aspect of these two methods is the selection of reference velocities and we explore the influence of the selection of reference velocities by comparing the geometric progression method and the statistical method. We show that the geometric progression method is simple but does not take into account the velocity distribution while the statistical approach is relatively complex but reflects the velocity distribution.     

<Emphasis Type="Italic">Q</Emphasis><Subscript>c</Subscript> and <Emphasis Type="Italic">Q</Emphasis><Subscript>S</Subscript> wave attenuation of South African earthquakes

Quality factor Q, which describes the attenuation of seismic waves with distance, was determined for South Africa using data recorded by the South African National Seismograph Network. Because of an objective paucity of seismicity in South Africa and modernisation of the seismograph network only in 2007, I carried out a coda wave decay analysis on only 13 tectonic earthquakes and 7 mine-related events for the magnitude range 3.6?≤?M _L ?≤?4.4. Up to five seismograph stations were utilised to determine Q _c for frequencies at 2, 4, 8 and 16 Hz resulting in 84 individual measurements. The constants Q ₀ and α were determined for the attenuation relation Q _c(f)?=?Q ₀ f ^α . The result was Q ₀?=?396?±?29 and α?=?0.72?±?0.04 for a lapse time of 1.9*(t _s???t ₀) (time from origin time t ₀ to the start of coda analysis window is 1.9 times the S-travel time, t _s) and a coda window length of 80 s. This lapse time and coda window length were found to fit the most individual frequencies for a signal-to-noise ratio of at least 3 and a minimum absolute correlation coefficient for the envelope of 0.5. For a positive correlation coefficient, the envelope amplitude increases with time and Q _c was not calculated. The derived Q _c was verified using the spectral ratio method on a smaller data set consisting of nine earthquakes and one mine-related event recorded by up to four seismograph stations. Since the spectral ratio method requires absolute amplitudes in its calculations, site response tests were performed to select four appropriate stations without soil amplification and/or signal distortion. The result obtained for Q _S was Q ₀?=?391?±?130 and α?=?0.60?±?0.16, which agrees well with the coda Q _c result.     

Ergodicity and the ‘scale effect’

Solute plume spreading in an aquifer exhibits a ‘scale effect’ if the second spatial concentration moment of a plume has a non-constant time-derivative. Stochastic approaches to modeling this scale effect often rely on the critical assumption that ensemble averages can be equated to spatial averages measured in a single field experiment. This ergodicity assumption should properly be evaluated in a strictly dynamical context, and this is done in the present paper. For the important case of trace plume convection by steady groundwater flow in an isotropic, heterogeneous aquifer, ergodicity does not obtain because of the existence of an invariant function on stream surfaces that is not uniform throughout the aquifer. The implications of this result for stochastic models of solute transport are discussed. © 1997 Elsevier Science Ltd. All rights reserved     

Vibrationally excited N<Subscript>2</Subscript> and O<Subscript>2</Subscript> in the upper atmosphere: A review

The present-day state of studies of vibrationally excited N₂ and O₂ in the upper atmosphere and the mechanisms by which these molecules affect the electron density and temperature in the ionosphere and neutral densities in the upper atmosphere are considered.     

Attenuative Dispersion of <Emphasis Type="Italic">P</Emphasis> Waves and Crustal <Emphasis Type="Italic">Q</Emphasis> in Turkey and Germany

We have measured group delays of the spectral components of high-frequency P-waves along two portions of the North Anatolian Fault Zone (NAFZ) in Turkey and in a region of southern Germany. Assuming that the observed dispersion is associated with attenuation in the crust and that it can be described by a continuous relaxation model, we obtained Q and the high-frequency relaxation times for those waves for each of the three regions. Individual P-wave Q values exhibit large scatter, but mean values in the NAFZ increase from about 25 to 60 over the distance range 5–90 km. Mean Q values are somewhat higher in the eastern portion of the NAFZ than in the western portion for measurements made at distances between 10 and 30 km. P-wave Q values in Germany range between about 50 and 300 over the hypocentral distance range 20–130 km. In that region we separated the effects of Q for basement rock (2–10 km depth) from that of the overlying sediment (0–2 km depth) using a least-squares method. Q varies between 100 and 500 in the upper 8–10 km of basement, with mean values for most of the distance range being about 250. Q in the overlying sediments ranges between 6 and 10. Because of large scatter in the Q determinations we investigated possible effects that variations of the source-time function of the earthquakes and truncation of the waveform may have on Q determinations. All of our studies indicate that measurement errors are relatively large and suggest that useful application of the method requires many observations, and that the method will be most useful in regions where the number of oscillations following the initial P pulse is minimized. Even though there is large scatter in our Q determinations, the mean values that we obtained in Turkey are consistent with those found in earlier studies. Our conclusions that Q is significantly higher in the basement rock of Germany than in the basement rock of Turkey and that Q is lower in western Turkey than in eastern Turkey are also consistent with results of Q studies using Lg coda.     

Microbial and molecular fossils from the Permian Zoophycos in South China

The trace fossil Zoophycos was enriched in the lower part of the Guadalupian Maokou Formation of Permian in Laibin, Guangxi of South China, and characterized by observable lamellae within its spreiten. Associated with these lamellae are the prolific coccus- and spirillum-shaped microbe fossils. These microbes morphologically identified are 0.4―3.0 μm in diameter or length. Molecular fossils, including normal alkanes (dominated by C18, without an odd-over-even predominance), acyclic isoprenoids (such as pristane (Pr) and phytane (Ph)), extended tricyclic terpanes, pentacyclic triterpanes, steranes, al-kylcyclohexanes, dibenzothiophenes, benzonaphthothiophenes, benzobisbenzothiophenes, were in-strumentally identified in the wackestone characterized by the occurrence of abundant Zoophycos (composite ichnofabric indices are 4) and crowded microbial fossils. The value of the Pr/Ph ratio is less than 1, indicative of a dysoxic condition. The identification of abundant sulfur compounds (the thio-phene series) related to the contribution of reductive sulfur favors the occurrence of sulphate-reducing bacteria. The association of abundant microbial colonies with microbial molecular fossils within the spreiten suggests that trace fossils Zoophycos would be a multifunctional garden carefully constructed by the Zoophycos-producer, where different microbial colonies were orderly and carefully planted and cultured in different minor lamellae within spreiten. Hence, it is proposed that the Zoophycos-producer symbiosed with microbial colonies on the mutual basis of food supply and the redox conditions.     

Distribution of<Emphasis Type="Italic">L</Emphasis><Subscript>g</Subscript> coda<Emphasis Type="Italic">Q</Emphasis> in the Chinese continent and its adjacent regions

785 traces of vertical components from shallow earthquakes recorded by 10 CDSN (Chinese Digital Seismographic Network) stations and 5 GSN (Global Seismographic Network) stations were collected to study the attenuation characteristics ofL _g coda in the Chinese continent and its adjacent regions. The records were processed first using the stack spectral ratio method to obtain the average values ofQ ₀ (Q at 1Hz) and η, the frequency dependence, ofL _g coda in the ellipses corresponding to the paths. The back-projection technique was then employed to obtain the tomographic maps ofQ ₀ and η values, and the distribution of their errors. Results indicate that in the studied areaQ ₀ varies between 200 and 500. The lowest value ofQ ₀ exists in the Yun-nan-Tibetan region, while the highest value ofQ ₀ occurs in the southern edge of Siberian platform. η varies between 0.3 and 0.8. For most part of the studied area η varies inversely withQ ₀.     

Tests and model calibration of high‐strength steel tubular beam‐to‐column and column‐base composite joints for moment‐resisting structures

Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.     

Rupture behavior and deformation localization of the Kunlunshan earthquake (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript>7.8) and their tectonic implications

Earthquake surface rupture is the result of transformation from crustal elastic strain accumulation to permanent tectonic deformation. The surface rupture zone produced by the 2001 Kunlunshan earthquake (M _w 7.8) on the Kusaihu segment of the Kunlun fault extends over 426 km. It consists of three relatively independent surface rupture sections: the western strike-slip section, the middle transtensional section and the eastern strike-slip section. Hence this implies that the Kunlunshan earthquake is composed of three earthquake rupturing events, i.e. the M _w =6.8, M _w =6.2 and M _w ⩽=7.8 events, respectively. The M _w =7.8 earthquake, along the eastern section, is the main shock of the Kunlunshan earthquake, further decomposed into four rupturing subevents. Field measurements indicate that the width of a single surface break on different sections ranges from several meters to 15 m, with a maximum value of less than 30 m. The width of the surface rupture zone that consists of en echelon breaks depends on its geometric structures, especially the stepover width of the secondary surface rupture zones in en echelon, displaying a basic feature of deformation localization. Consistency between the Quaternary geologic slip rate, the GPS-monitored strain rate and the localization of the surface ruptures of the 2001 Kunlunshan earthquake may indicate that the tectonic deformation between the Bayan Har block and Qilian-Qaidam block in the northern Tibetan Plateau is characterized by strike-slip faulting along the limited width of the Kunlun fault, while the blocks themselves on both sides of the Kunlun fault are characterized by block motion. The localization of earthquake surface rupture zone is of great significance to determine the width of the fault-surface-rupture hazard zone, along which direct destruction will be caused by co-seismic surface rupturing along a strike-slip fault, that should be considered before the major engineering project, residental buildings and life line construction. Supported by the National Natural Science Foundation of China (Grant No. 40474037) and the National Basic Research Program of China (Grant No. 2004CB418401)     

Physics and Seismic Modeling for Monitoring CO<Subscript>2</Subscript> Storage

We present a new petro-elastical and numerical-simulation methodology to compute synthetic seismograms for reservoirs subject to CO₂ sequestration. The petro-elastical equations model the seismic properties of reservoir rocks saturated with CO₂, methane, oil and brine. The gas properties are obtained from the van der Waals equation and we take into account the absorption of gas by oil and brine, as a function of the in situ pore pressure and temperature. The dry-rock bulk and shear moduli can be obtained either by calibration from real data or by using rock-physics models based on the Hertz-Mindlin and Hashin-Shtrikman theories. Mesoscopic attenuation due to fluids effects is quantified by using White's model of patchy saturation, and the wet-rock velocities are calculated with Gassmann equations by using an effective fluid modulus to describe the velocities predicted by White's model. The simulations are performed with a poro-viscoelastic modeling code based on Biot's theory, where viscoelasticity is described by generalizing the solid/fluid coupling modulus to a relaxation function. Using the pseudo-spectral method, which allows general material variability, a complete and accurate characterization of the reservoir can be obtained. A simulation, that considers the Utsira sand of the North Sea, illustrates the methodology.     

3D <Emphasis Type="Italic">v</Emphasis><Subscript>P</Subscript> and <Emphasis Type="Italic">v</Emphasis><Subscript>S</Subscript> models of southeastern margin of the Tibetan plateau from joint inversion of body-wave arrival times and surface-wave dispersion data

A new 3D velocity model of the crust and upper mantle in the southeastern (SE) margin of the Tibetan plateau was obtained by joint inversion of body- and surface-wave data. For the body-wave data, we used 7190 events recorded by 102 stations in the SE margin of the Tibetan plateau. The surface-wave data consist of Rayleigh wave phase velocity dispersion curves obtained from ambient noise cross-correlation analysis recorded by a dense array in the SE margin of the Tibetan plateau. The joint inversion clearly improves the v _S model because it is constrained by both data types. The results show that at around 10 km depth there are two low-velocity anomalies embedded within three high-velocity bodies along the Longmenshan fault system. These high-velocity bodies correspond well with the Precambrian massifs, and the two located to the northeast of 2013 M _S 7.0 Lushan earthquake are associated with high fault slip areas during the 2008 Wenchuan earthquake. The aftershock gap between 2013 Lushan earthquake and 2008 Wenchuan earthquake is associated with low-velocity anomalies, which also acts as a barrier zone for ruptures of two earthquakes. Generally large earthquakes (M ≥ 5) in the region occurring from 2008 to 2015 are located around the high-velocity zones, indicating that they may act as asperities for these large earthquakes. Joint inversion results also clearly show that there exist low-velocity or weak zones in the mid-lower crust, which are not evenly distributed beneath the SE margin of Tibetan plateau.     

Improved method to determine the molar volume and compositions of the NaCl-H<Subscript>2</Subscript>O-CO<Subscript>2</Subscript> system inclusion

On the basis of Parry’s method (1986), an improved method was established to determine the molar volume (Vm) and compositions (X) of the NaCl-H2O-CO2 (NHC) system inclusion. To use this method, the determination of Vm-X only requires three microthermometric data of a NHC inclusion: partial homog-enization temperature (Th ,CO2), salinity (S) and total homogenization temperature (Th). Theoretically, four associated equations are needed containing four unknown parameters: X CO2, XNaCl, Vm and F (volume fraction of CO2 phase in total inclusion when occurring partial homogenization). When they are released, the Vm-X are determined. The former three equations, only correlated with Th ,CO2, S and F, have simplified expressions:XCO2=f1(Th,CO2,S,F),XNaCl=f2(Th,CO2,S,F),Vm=f3(Th,CO2,S,F). The last one is the thermodynamic relationship of X CO2, XNaCl, Vm and Th:f4(XCO2,XNaCl,Vm,Th)=0.Since the above four associated equations are complicated, it is necessary to adopt iterative technique to release them. The technique can be described by:(i) Freely input a F value (0≤F≤1),with Th ,CO2 and S, into the former three equations. As a result,X CO 2,XNaCl and the molar volume value recorded as Vm1 are derived. (ii) Input the X CO2 and XNaCl gotten in the step above into the last equation, and another molar volume value recorded as Vm2 is determined. (iii) If Vm1 is unequal to Vm2, the calculation will be restarted from “(i)”. The iteration is completed until Vm1 is equal to Vm2, which means that the four associated equations are released. Compared to Parry’s (1986) solution method, the improved method is more convenient to use, as well as more accurate to determine X CO 2. It is available for a NHC inlusion whose partial homogenization temperature is higher than clatherate melting temperature and there are no solid salt crystals in the inclusion at parital homogenization.