<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.     

The instability of the <Emphasis Type="Italic">M</Emphasis><Subscript>W</Subscript> and <Emphasis Type="Italic">M</Emphasis><Subscript>L</Subscript> comparison for earthquakes in Greece for the period 1969 to 2007

We use 576 earthquakes of magnitude, M _w, 3.3 to 6.8 that occurred within the region 33° N–42.5° N, 19° E–30° E in the time period 1969 to 2007 to investigate the stability of the relation between moment magnitude, M _w, and local magnitude, M _L, for earthquakes in Greece and the surrounding regions. We compare M _w to M _L as reported in the monthly bulletins of the National Observatory of Athens (NOA) and to M _L as reported in the bulletins of the Seismological Station of the Aristotle University of Thessaloniki. All earthquakes have been analyzed through regional or teleseismic waveform inversion, to obtain M _w, and have measured maximum trace amplitudes on the Wood–Anderson seismograph in Athens, which has been in operation since 1964. We show that the Athens Wood–Anderson seismograph performance has changed through time, affecting the computed by NOA M _L by at least 0.1 magnitude units. Specifically, since the beginning of 1996, its east–west component has been recording systematically much larger amplitudes compared to the north–south component. From the comparison between M _w and M _L reported by Thessaloniki, we also show that the performance of the sensors has changed several times through time, affecting the calculated M _L’s. We propose scaling relations to convert the M _L values reported from the two centers to M _w. The procedures followed here can be applied to other regions as well to examine the stability of magnitude calculations through time.     

GPS time-series and its response to <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=8.1 Kunlunshan earthquake

In this paper, observation data in 25 GPS reference stations of China have been analyzed by calculating GPS position coordinate time-series with GIPSY. Result shows there is an obvious trend variation in such time-series. The trend variations of time series along the longitude and latitude coordinate reflect the motion of each position in the global-plate, in which the trend variation in the vertical direction reveals some large-scale construction information or reflects the local movement around the positions. The analysis also shows that such time-series have a variation cycle of nearly 1.02 a, but the reason still remains to be further studied. At the end of this paper, response of the time-series of M _S=8.1 Kunlunshan earthquake was analyzed, and the seismogenic process of M _S=8.1 Kunlunshan earthquake, according to the time proceeding and the feature of anomaly, was divided into 3 phases—changes in blocks with forces, strain accumulation, quick accumulation and slow release of energy. At the initial stage of seismogenic process of M _S=8.1 earthquake and at the imminent earthquake, coseismic process as well as during the post earthquake recovery, anomaly in vertical direction is always in a majority. The anomalous movement in vertical direction at the initial stage resulted in a blocking between faults, while at the middle stage of seismogenic process, the differential movement between blocks are in a majority, which is the major reason causing energy accumulating at the blocking stage of faults.     

The 20-second regional magnitude <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript>(20R) for the Russian Far East

A new modified magnitude scale M _S (20R) is elaborated. It permits us to extend the teleseismic magnitude scale M _S (20) to the regional epicenter distances. The data set used in this study contains digital records at 12 seismic stations of 392 earthquakes that occured in the northwest Pacific Ocean in the period of 1993–2008. The new scale is based on amplitudes of surface waves of a narrow range of the periods (16–25 s) close to the period of 20 s, for distances of 80–3000 km. The digital Butterworth filter is used for processing. On the basis of the found regional features concerning distance dependence for seismic wave attenuation, all the stations of the region have been subdivided into two groups, namely, “continental” and “island-arc.” For each group of stations, its own calibration function is proposed. Individual station corrections are used to compensate for the local features.     

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.     

Magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> in metropolitan France

The recent seismicity catalogue of metropolitan France Sismicité Instrumentale de l’Hexagone (SI-Hex) covers the period 1962–2009. It is the outcome of a multipartner project conducted between 2010 and 2013. In this catalogue, moment magnitudes (M _w) are mainly determined from short-period velocimetric records, the same records as those used by the Laboratoire de Détection Géophysique (LDG) for issuing local magnitudes (M _L) since 1962. Two distinct procedures are used, whether M _L-LDG is larger or smaller than 4. For M _L-LDG >4, M _w is computed by fitting the coda-wave amplitude on the raw records. Station corrections and regional properties of coda-wave attenuation are taken into account in the computations. For M _L-LDG ≤4, M _w is converted from M _L-LDG through linear regression rules. In the smallest magnitude range M _L-LDG <3.1, special attention is paid to the non-unity slope of the relation between the local magnitudes and M _w. All M _w determined during the SI-Hex project is calibrated according to reference M _w of recent events. As for some small events, no M _L-LDG has been determined; local magnitudes issued by other French networks or LDG duration magnitude (M _D) are first converted into M _L-LDG before applying the conversion rules. This paper shows how the different sources of information and the different magnitude ranges are combined in order to determine an unbiased set of M _w for the whole 38,027 events of the catalogue.     

Gravity variation before Kunlun mountain pass western <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=8.1 earthquake

The relation between the gravity variation features and M _S=8.1 earthquake in Qinghai-Xizang monitoring area is analyzed preliminarily, by using spatial dynamic variation results of regional gravity field from absolute gravity and relative gravity observation in 1998 and 2000. The results show that: 1) M _S=8.1 earthquake in Kulun mountain pass western occurred in the gravity variation high gradient near gravity’s high negative variation; 2) The main tectonic deformation and energy accumulation before M _S=8.1 earthquake are distributed at south side of the epicenter; 3) The range of gravity’s high negative variation at east of the M _S=8.1 earthquake epicenter relatively coincides with that rupture region according to field geology investigation; 4) Gravity variation distribution in high negative value region is just consistent with the second shear strain’s high value region of strain field obtained from GPS observation.     

A new <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> estimation parameter for use in earthquake early warning systems

We propose a method that employs the squared displacement integral (ID2) to estimate earthquake magnitudes in real time for use in earthquake early warning (EEW) systems. Moreover, using τ _c and P _d for comparison, we establish formulas for estimating the moment magnitudes of these three parameters based on the selected aftershocks (4.0 ≤ M _s  ≤ 6.5) of the 2008 Wenchuan earthquake. In this comparison, the proposed ID2 method displays the highest accuracy. Furthermore, we investigate the applicability of the initial parameters to large earthquakes by estimating the magnitude of the Wenchuan M _s 8.0 mainshock using a 3-s time window. Although these three parameters all display problems with saturation, the proposed ID2 parameter is relatively accurate. The evolutionary estimation of ID2 as a function of the time window shows that the estimation equation established with ID2 ^Ref determined from the first 8-s of P wave data can be directly applicable to predicate the magnitudes of 8.0. Therefore, the proposed ID2 parameter provides a robust estimator of earthquake moment magnitudes and can be used for EEW purposes.     

Sampling uncertainties and source <Emphasis Type="Italic">b</Emphasis> likelihood for the Gutenberg-Richter <Emphasis Type="Italic">b</Emphasis> value from the Aki-Utsu method

The Aki-Utsu method of Gutenberg-Richter (G-R) b value estimation is often misapplied so that estimations not using the G-R histogram are often meaningless because they are not based on adequate samples. We propose a method to estimate the likelihood Pr(b?b _m , N, M ₁, M ₂) that an observed b _m estimate, based on a sample of N magnitudes within an [M ₁????≤?ΔM/2,?M ₂?+?ΔM/2) range, where ΔM?=?0.1 is the usual rounding applied to magnitudes, is due to a “true” source b value, b, and use these likelihoods to estimate source b ranges corresponding to various confidence levels. As an example of application of the method, we estimate the b values before and after the occurrence of a 7.4-magnitude earthquake in the Mexican subduction zone, and find a difference of 0.82 between them with 100% confidence that the b values are different.     

Linear transformations of anomalous potential fields using <Emphasis Type="Italic">S</Emphasis> and <Emphasis Type="Italic">R</Emphasis> approximations

Methods for linear transformations of anomalous physical fields based on R and S approximations of the elements of the initial field are described. The results of the numerical experiment and analytical extension of the gravity field measured in a detailed gravity survey in two regions of Russia are presented.     

Application of Fisher method to discriminating earthquakes and explosions using criterion m_b/M_S

Introduction Earthquake magnitude is a measurement of earthquake intensity, which is one of the basic seismic parameters. The body-wave magnitude mb and surface-wave magnitude MS are based re- spectively on different wave spectrum amplitudes, therefore, the magnitude used as a criterion has its sound physical basis, which is in fact to distinguish the frequency components of seismic waves excited by explosion and earthquake. The magnitude criterion has a very clear physical meaning. Proposed …     

Seasonal variation of the <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript> tide

The seasonal cycle of the main lunar tidal constituent M ₂ is studied globally by an analysis of a high-resolution ocean circulation and tide model (STORMTIDE) simulation, of 19 years of satellite altimeter data, and of multiyear tide-gauge records. The barotropic seasonal tidal variability is dominant in coastal and polar regions with relative changes of the tidal amplitude of 5–10 %. A comparison with the observations shows that the ocean circulation and tide model captures the seasonal pattern of the M ₂ tide reasonably well. There are two main processes leading to the seasonal variability in the barotropic tide: First, seasonal changes in stratification on the continental shelf affect the vertical profile of eddy viscosity and, in turn, the vertical current profile. Second, the frictional effect between sea-ice and the surface ocean layer leads to seasonally varying tidal transport. We estimate from the model simulation that the M ₂ tidal energy dissipation at the sea surface varies seasonally in the Arctic (ocean regions north of 60°N) between 2 and 34 GW, whereas in the Southern Ocean, it varies between 0.5 and 2 GW. The M ₂ internal tide is mainly affected by stratification, and the induced modified phase speed of the internal waves leads to amplitude differences in the surface tide signal of 0.005–0.0150 m. The seasonal signals of the M ₂ surface tide are large compared to the accuracy demands of satellite altimetry and gravity observations and emphasize the importance to consider seasonal tidal variability in the correction processes of satellite data.     

<Emphasis Type="Italic">R/S</Emphasis> analysis of the <Emphasis Type="Italic">Dst</Emphasis> index

The paper addresses estimation of the Hurst exponent for time series of the hourly values of the Dst index for the period from 1957 to 2011. It is found that the Hurst exponent is 0.79–0.94 for yearly intervals and 0.8–1.0 for monthly intervals. Based on R/S graphs, the Dst cycles are identified; they range from 3–4 months to 2.2 years and from 8.5 to 22 years in length. It is shown that a Dst time series can be quite satisfactorily described by an α-stable Levy process.     

Region-specific <Emphasis Type="Italic">S</Emphasis>-wave attenuation for earthquakes in northwestern Iran

In this study, continuous wavelet transform is applied to estimate the frequency-dependent quality factor of shear waves, Q _S , in northwestern Iran. The dataset used in this study includes velocigrams of more than 50 events with magnitudes between 4.0 and 6.5, which have occurred in the study area. The CWT-based method shows a high-resolution technique for the estimation of S-wave frequency-dependent attenuation. The quality factor values are determined in the form of a power law as Q _S (f)?=?(147?±?16)f ^0.71?±?0.02 and (126?±?12)f ^0.73?±?0.02 for vertical and horizontal components, respectively, where f is between 0.9 and 12 Hz. Furthermore, in order to verify the reliability of the suggested Q _S estimator method, an additional test is performed by using accelerograms of Ahar-Varzaghan dual earthquakes on August 11, 2012, of moment magnitudes 6.4 and 6.3 and their aftershocks. Results indicate that the estimated Q _S values from CWT-based method are not very sensitive to the numbers and types of waveforms used (velocity or acceleration).     

Dispersion Measurements of <Emphasis Type="Italic">P</Emphasis> Waves and their Implications for Mantle <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We analyze the anelasticity of the earth using group delays of P-body waves of deep (>200 km) events in the period range 4–32 s for epicentral distances of 5–85 degrees. We show that Time Frequency Analysis (TFA), which is usually applied to very dispersive surface waves, can be applied to the much less dispersive P-body waves to measure frequency-dependent group delays with respect to arrival times predicted from the CMT centroid location and PREM reference model. We find that the measured dispersion is due to: (1) anelasticity (described by the P-wave quality factor Q _p ), (2) ambient noise, which results in randomly distributed noise in the dispersion measurements, (3) interference with other phases (triplications, crustal reverberations, conversions at deep mantle boundaries), for which the total dispersion depends on the amplitude and time separation between the different phases, and (4) the source time function, which is dispersive when the wavelet is asymmetrical or contains subevents. These mechanisms yield dispersion ranging in the order of one to 10 seconds with anelasticity responsible for the more modest dispersion. We select 150 seismograms which all have small coda amplitudes extending to ten percent of the main arrival, minimizing the effect of interference. The main P waves have short durations, minimizing effects of the source. We construct a two-layer model of Q _p with an interface at 660 km depth and take Q _p constant with period. Our data set is too small to solve for a possible frequency dependence of Q _p . The upper mantle Q ₁ is 476 [299–1176] and the lower mantle Q ₂ is 794 [633–1064] (the bracketed numbers indicate the 68 percent confidence range of Q _p ^–1). These values are in-between the AK135 model (Kennett et al., 1995) and the PREM model (Dziewonski and Anderson, 1981) for the lower mantle and confirm results of Warren and Shearer (2000) that the upper mantle is less attenuating than PREM and AK135.     

The seismotectonic and macroseismic features of the Wenchuan (Sichuan) earthquake (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> = 8.0) of May 12, 2008

A disastrous earthquake with a magnitude M _S = 8.0 (M _W = 7.9), in China called “the 5.12 Wenchuan earthquake,” occurred on May 12, 2008, in Sichuan province on the border between the Sino-Tibetan Mountains and the Sichuan depression. The instrumental epicenter was registered in the southeastern part of Wenchuan county, and the hypocenter depth was 14 km. As the strongest and most destructive earthquake within mainland China, it caused numerous human losses and destruction of buildings and infrastructure. The seismic effect from the main shock and aftershocks was felt in many counties, towns, and villages, though Sichuan province suffered the most. The maximum intensity of the shocks was estimated at 11 degrees, according to the Chinese macroseismic scale. In the process of source opening, from the southern part of Wenchuan county to the vicinities of Quingchuan, a seismic fault system with a total length up to 240 km out-cropped on the earth’s surface, confined to the Longmenshan fault belt. The seismic fault system disturbed the original ground, resulting in the collapse or damage to various constructions, such as buildings, homes, bridges, roads, etc. Fault offsets had a dextral strike-slip and thrust kinematic combination. The earthquake generated several tens of thousands of landslides, rockfalls, and debris flows. Many dammed ponds appeared in the epicentral zone due to the activation of landslides. Thus, the geological effects turned out to be the most destructive factor in this case. At the same time, the seismic intensity of surface shaking was abnormally low even in direct proximity to the seismic fault system. Usually it was no more than 7–8 degrees. This macroseismic phenomenon may turn out to be rather typical for many major earthquakes.     

Structural damage patterns in the villages of Korf and Tilichiki due to the <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> 7.7 April 20(21), 2006 Olyutorskii earthquake

The area of the Koryak Autonomous Okrug was hit by an M _S 7.7 earthquake on April 20(21), 2006, the largest to have occurred in the area during the period of historical and instrumental observation. This event is now referred to as the Olyutorskii earthquake. We present results from a study of the associated macroseismic effects as observed in the villages of Korf and Tilichiki. The intensity was IX at Korf and VIII at Tilichiki on the MSK-64 scale.     

Focal depths for moderate-sized aftershocks of the Wenchuan <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>8.0 earthquake and their implications

Sliding-window cross-correlation method is firstly adopted to identify sPn phase, and to constrain focal depth from regional seismograms, by measuring the time separation between sPn and Pn phases. We present the focal depths of the 17 moderate-sized aftershocks (M _S⩾5.0) of the Wenchuan M _S8.0 earthquake, using the data recorded by the regional seismic broadband networks of Shaanxi, Qinghai, Gansu, Yunnan and Sichuan. Our results show focal depths of aftershocks range from 8 to 20 km, and tend to cluster at two average depths, separate at 32.5°N, i.e., 11 km to the south and 17 km to the north, indicating that these aftershocks are origin of upper-to-middle crust. Combined with other results, we suggest that the Longmenshan fault is not a through-going crustal fault and the Pingwu-Qingchuan fault may be not the northward extension of the Longmenshan thrust fault. Supported by the National Natural Science Foundation of China (Grant Nos. 40604009 and 40574040) and Special Project for the Fundamental R & D of Institute of Geophysics, China Earthquake Administration (Grant No.DQJB08B20)     

The instability of the <Emphasis Type="Italic">M</Emphasis><Subscript>max</Subscript> parameter and an alternative to its using

The work presents statistical methods for estimating the distribution parameters of rare, strong earthquakes. Using the two main theorems of extreme value theory (EVT), the distribution of T-maximum (the maximum magnitude over the time period T). Two methods for estimating the parameters of this distribution are proposed using the Generalized Pareto Distribution (GPD) and the General Extreme Value Distribution (GEV). In addition, the that allow the determination of the distribution of the T-maximum for an arbitrary value of T are proposed. The approach being used clarifies the nature of the instability of the widely accepted M max parameter. In the work, instead of unstable values of the M max parameter, the robust parameter Q _T (q), the q level quantile for the distribution of the T-maximum, is proposed to be used. The described method has been applied to the Harvard Catalogue of Seismic Moments of 1977–2006 and to the Magnitude Catalogue for Fennoscandia in 1900–2005. Moreover, the estimates of parameters of the corresponding GPD and GEV distributions, in particular, the most interesting shape parameter and the values of the M _max and Q _T (q) parameters are given.     

Source process of the 14 November 2001 western Kunlun Mountain <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=8.1 earthquake

Based on digital teleseismic P-wave seismograms recorded by 28 long-period seismograph stations of the global seismic network, source process of the November 14, 2001 western Kunlun Mountain M _S=8.1 (M _W=7.8) earthquake is estimated by a new inversion method. The result shows that the earthquake is a very complex rupture event. The source rupture initiated at the hypocenter (35.95°N, 90.54°E, focal depth 10 km, by USGS NEIC), and propagated to the west at first. Then, in several minutes to a hundred minutes and over a large spatial range, several rupture growth points emerged in succession at the eastern end and in the central part of the finite fault. And then the source rupture propagated from these rupture growth points successively and, finally, stopped in the area within 50 km to the east of the centroid position (35.80°N, 92.91°E, focal depth 15 km, by Harvard CMT). The entire rupture lasted for 142 s, and the source process could be roughly separated into three stages: The first stage started at the 0 s and ended at the 52 s, lasting for 52 s and releasing approximately 24.4% of the total moment; The second stage started at the 55 s and ended at the 113 s, lasting for 58 s and releasing approximately 56.5% of the total moment; The third stage started at the 122 s and ended at the 142 s, lasting for 20 s and releasing approximately 19.1% of the total moment. The length of the ruptured fault plane is about 490 km. The maximum width of the ruptured fault plane is about 45 km. The rupture mainly occurred within 30 km in depth under the surface of the Earth. The average static slip in the underground rocky crust is about 1.2 m with the maximum static slip 3.6 m. The average static stress drop is about 5 MPa with the maximum static stress drop 18 MPa. The maximum static slip and the maximum stress drop occurred in an area within 50 km to the east of the centroid position.