<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.     

<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.     

Multi-scale Tomography for Crustal <Emphasis Type="Italic">P</Emphasis> and <Emphasis Type="Italic">S</Emphasis> Velocities in Southern California

Seismic tomography is a viable tool in building depth-velocity models in the presence of strong lateral velocity variations. In this study 3-D P- and S-velocity models for the crust of southern California are constrained using more than 1,000,000 P-wave first arrivals and 130,000 S-wave arrivals from local earthquakes. To cope with the uneven distribution of raypaths, a multi-scale tomography is applied with overlapping model cells of different sizes. Within the 300 × 480 × 39 km³ model volume, the smallest cell size is 10 × 10 × 3 km³. During the iterations of velocity updating, earthquake hypocenters are determined using both P and S arrivals, and full 3-D ray tracing is implemented. Except near the edges and in the lower crust, the resultant models are robust according to various tests on the effects of reference models, resolution and signal-to-noise ratio. The tomographic velocities at shallow depths correlate very well with the regional geology of southern California. In the upper crust the P-wave and S-wave models exhibit slow velocities in major sedimentary basins and fast velocities in areas of crystalline rocks. Mid-crustal low velocity zones are present under the Coso Range, San Gabriel Mountains, and a large portion of the Mojave Desert. P- and S-velocity patterns maintain their similarity in the lower crust though the models are less reliable there.     

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.     

Combined Method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-Approximations of Increased Dimensionality in Solving the Problems of Geophysics and Geomorphology

The interrelation between different variants of the method of linear integral representations in the spaces of an arbitrary dimension is considered. The combined approximations of the topography and geopotential fields allows the selection of the optimal parameters of the method in solving a wide range of inverse problems in geophysics and geomorphology, as well as a most thorough use of the a priori information about the elevations and elements of anomalous fields. A method for numerically solving an inverse problem on finding the equivalent, in terms of the external field, mass distributions in the ordinary three-dimensional (3D) space and in the four-dimensional (4D) space is described.     

Application of Fisher method to discriminating earthquakes and explosions using criterion <Emphasis Type="Italic">m</Emphasis><Subscript>b</Subscript>/<Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>

We try to give a quantitative and global discrimination function by studying m _b/M _S data using Fisher method that is a kind of pattern recognition methods. The reliability of the function is also analyzed. The results show that this criterion works well and has a global feature, which can be used as first-level filtering criterions in event identification. The quantitative and linear discrimination function makes it possible to identify events automatically and achieve the goal to react the events quickly and effectively.     

Combined method of <Emphasis Type="Italic">F</Emphasis>-, <Emphasis Type="Italic">S</Emphasis>-, and <Emphasis Type="Italic">R</Emphasis>-approximations in solving the problems of geophysics and geomorphology

The interrelation between different modifications of the method of linear integral representation is studied. Combined approximations of the topography and geopotential fields enable more refined tuning of the method in solving inverse problems of geophysics and geomorphology and provide a more complete allowance for the a priori information about the surface elevation data and elements of anomalous fields. A technique for finding the numerical solution for the inverse problem for determining the mass distributions equivalent in terms of the external field is presented. The results of the mathematical experiment are discussed.     

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.     

On the <Emphasis Type="Italic">P</Emphasis> and <Emphasis Type="Italic">S</Emphasis> Receiver Functions Used for Inverting the One-Dimensional Upper Mantle Shear-Wave Velocities

The teleseismic P receiver functions are customarily inverted to attain the seismic velocities beneath a seismic station. Surface wave dispersion data are often added to reduce the effect of the non-uniqueness. The combination of P receiver function and surface wave works well in resolving the structures in the crust and uppermost mantle, but is less effective in characterizing greater (lithosphere and asthenosphere) depths due to the interference from crustal multiples. A solution to this problem is jointly to model teleseismic S receiver functions with surface wave and P receiver functions. This study adopts a fast, one-dimensional (1-D) inversion scheme. To avoid the effect of multidimensional structures away from the seismic station, we eliminate multiples that reverberate between the surface and interfaces below a restriction depth (RD), as well as S-to-P conversions below an inversion depth (ID). P-to-S conversions off the interfaces above the half-space and S-to-P conversions above the ID and multiples above the RD are properly modelled. This approach favours ray paths travelling close to stations and is, therefore, more suitable for 1-D inversions. We perform numerical experiments with and without noise and highlight the advantages of a joint receiver function and surface wave analysis.     

Studying the spread <Emphasis Type="Italic">F</Emphasis> effect before earthquakes

The observations of spread F during the nighttime hours (0000–0500 LT) have been statistically analyzed based on data of Tokyo, Akita, Wakkanai, and Yamagawa Japan vertical ionospheric sounding stations for the time intervals a month before and a month after an earthquake. The disturbances in the probability of spread F appearance before an earthquake are revealed against a background of the variations depending on season, solar activity cycle, geomagnetic and solar disturbances. The days with increased solar (Wolf number W > 100) and geomagnetic (ΣK > 30) activity are excluded from the analysis. The spread F effects are considered for more than a hundred earthquakes with magnitude M > 5 and epicenter depth h < 80 km at distances of R < 1000 km from epicenters to the vertical sounding station. An average decrease in the spread F occurrence probability one-two weeks before an earthquake has been revealed using the superposed epoch method (the probability was minimal approximately ten days before the event and then increased until the earthquake onset). Similar results are obtained for all four stations. The reliability of the effect has been estimated. The dependence of the detected effect on the magnitude and distance has been studied.     

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.     

Behavior of <Emphasis Type="Italic">foF</Emphasis>2 and <Emphasis Type="Italic">hmF</Emphasis>2 after sunset

The time behavior of the foF2 and hmF2 values at the time moment T(ss + 2 h) 2 h after sunset is considered. It is assumed that at this moment, the horizontal winds in the thermosphere in the strongest way influence hmF2 and, therefore, foF2. It is found that a fairly well pronounced and statistically significant change (trend) is observed for the foF2(ss + 2)/foF2(14) ratio, the sign of the change being different for different stations and even different seasons at the same station. A similar picture is obtained for the value of hmF2(ss + 2). It is shown that a positive correlation between the trends of these two values is observed. This confirms the initial concept of the paper that the foF2 and hmF2 trends are caused by long-term trends in the thermospheric dynamics.     

Stochastic finite-fault simulation of ground motion from the August 11, 2012, <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> 6.4 Ahar earthquake,northwestern Iran

In this study, the 11 August 2012 M _w 6.4 Ahar earthquake is investigated using the ground motion simulation based on the stochastic finite-fault model. The earthquake occurred in northwestern Iran and causing extensive damage in the city of Ahar and surrounding areas. A network consisting of 58 acceleration stations recorded the earthquake within 8–217 km of the epicenter. Strong ground motion records from six significant well-recorded stations close to the epicenter have been simulated. These stations are installed in areas which experienced significant structural damage and humanity loss during the earthquake. The simulation is carried out using the dynamic corner frequency model of rupture propagation by extended fault simulation program (EXSIM). For this purpose, the propagation features of shear-wave including \( {Q}_s \) value, kappa value \( {k}_0 \), and soil amplification coefficients at each site are required. The kappa values are obtained from the slope of smoothed amplitude of Fourier spectra of acceleration at higher frequencies. The determined kappa values for vertical and horizontal components are 0.02 and 0.05 s, respectively. Furthermore, an anelastic attenuation parameter is derived from energy decay of a seismic wave by using continuous wavelet transform (CWT) for each station. The average frequency-dependent relation estimated for the region is \( Q=\left(122\pm 38\right){f}^{\left(1.40\pm 0.16\right)}. \) Moreover, the horizontal to vertical spectral ratio \( H/V \) is applied to estimate the site effects at stations. Spectral analysis of the data indicates that the best match between the observed and simulated spectra occurs for an average stress drop of 70 bars. Finally, the simulated and observed results are compared with pseudo acceleration spectra and peak ground motions. The comparison of time series spectra shows good agreement between the observed and the simulated waveforms at frequencies of engineering interest.     

Long-term changes in the relation between <Emphasis Type="Italic">foF</Emphasis>2 and <Emphasis Type="Italic">hmF</Emphasis>2

The change in the dependence of the F2-layer critical frequency on its height hmF2 is considered based on two sources of initial data used earlier by the authors. It is found that the slope k of the foF2 dependence on hmF2 systematically decreases from the earlier (“etalon”) period, 1958–1980, to the later periods of 1988–2010, 1998–2010, and 1998–2014. Since the foF2 value depends on the atomic oxygen concentration in the F region much more strongly than hmF2, the found decrease in k confirms the concept of a decrease in the atomic oxygen concentration in the thermosphere with time previously formulated by the authors.     

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.     

Mechanisms of stratification of the <Emphasis Type="Italic">F</Emphasis>2 layer and formation of the <Emphasis Type="Italic">F</Emphasis>3 and <Emphasis Type="Italic">G</Emphasis> layers in the equatorial ionosphere

The paper is dedicated to the studies of formation mechanisms of additional layers in the equatorial ionosphere carried out using numerical simulations with use of the Global Self-Consistent Model of the Thermosphere, Ionosphere, and Protonosphere (GSM TIP) modified in the part of the solution of the electric field equation in the Earth’s ionosphere. Calculations were preformed for quiet geomagnetic conditions using the MSIS-90 model for the calculation of thermospheric parameters. The obtained spatio-temporal pattern of thermospheric circulation and the variations in the dynamo electric field obtained on its basis make it possible to reproduce the stratification effect of the F2 layer and the appearance of the F3 layer in the equatorial ionosphere due to the action of the nonuniform in height zonal electric field at the geomagnetic equator. On the basis of the earlier presented results of calculations using the modified GSM TIP model, the appearance of a maximum in the vertical profile of the electron density at a height of ∼1000 km formed by H+ ions, which we called the G layer, has been predicted. Numerical simulations showed that this layer is formed by the meridional component of the thermospheric wind and is related to the formation of the nighttime midlatitude maximum at heights of the ionospheric F region.     

<Emphasis Type="Italic">S</Emphasis>-wave velocity model for several regions of the Kamchatka Peninsula from the cross correlations of ambient seismic noise

The data from the seismic networks of the Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences are used for calculating the cross correlations of seismic noise for the stationary digital stations over 2013 and for radio telemetric stations (RTS) in the region of the Klyuchevskoy volcano over the period from January 1, 2009 to May 31, 2013. Four hundred and two correlations overall are calculated. The fundamental-mode group velocities of the Rayleigh waves are calculated in the periods ranging from 5 to 50 s. The calculations for the region of the Klyuchevskaya group of volcanoes are based on the RTS data and cover the periods from 2 to 8 s. The two-dimensional (2D) maps of group velocity distributions in different periods are constructed with the use of the algorithm of surface wave tomography (Barmin, 2001). The velocity sections for the selected Kamchatka regions are reconstructed by the dispersion curve inversion technique (Mordret, 2014). For each region, the structure of the Earth’s crust and upper mantle down to a depth of 50 km was obtained.     

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.     

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.     

A real <Emphasis Type="Italic">P</Emphasis>-wave and its dependence on the presence of gas

Attenuation of seismic compression waves leads to the real existence of a fast P₁ wave in rocks which are fully saturated with dropping fluid and a slow P₂ wave in the rocks containing gas in their pores. This accounts for the seismic blanking zones below the gas horizons for the P₁ waves. Oscillations of gaseous inclusions ensure the energy transfer to the dominant frequencies which are different for the cases of passive seismic (few Hz) and active source seismic (10–20 Hz). The intervals of dominant frequencies are determined from the negative attenuation of these low-frequency waves. According to the observations and the suggested equation, random noise amplifies the signal at these frequencies. Thus, the P₂ waves at the dominant frequency of the active source seismics are applicable for elaborating on the details of the saturation of the production layer by hydrocarbons. The relation to the AVO method (Amplitude Variation with Offset) and dilatancy effect during the preparation of an earthquake is noted.