Testing the reference Moon model in respect of the thermal regime and chemical composition of the mantle: Thermodynamics versus seismology

The VPREMOON seismic reference Moon model (Garcia et al., 2011) has been tested with respect to the thermal regime and chemical composition of the mantle. Based on a self-consistent thermodynamic approach and petrological models of the lunar mantle covering a wide range of concentrations of CaO, Al₂O₃, and FeO, we convert the P- and S-wave velocity profiles to the temperature–depth profiles. The solution procedure relies on the method of the Gibbs free energy minimization and the equations of state for the mantle material which take into account the effects of phase transformations, anharmonicity, and anelasticity. We find that regardless of the chemical composition, the positive P- and S-wave velocity gradient in the lunar mantle leads to a negative temperature gradient, which has no physical basis. For adequate mantle temperatures, the P- and S-wave velocities should remain almost constant or slightly decrease with depth (especially V_S) as a result of the effects of the temperature, which grows faster than pressure. These findings underscore the importance of the relationship of the thermodynamics and physics of minerals with seismology.     

On the possible correlation between the Gutenberg-Richter parameters of the frequency-magnitude relationship

The study of the Gutenberg-Richter (GR) parameters a and b has been very important to describe and characterize the seismicity over the different seismic provinces around the world. As far as we know, the possible correlation between the GR parameters a and b has not received enough attention. Bayrak et al. reported the a and b values for 27 active seismic regions around the boundaries of the main tectonic plates of the world. From these data, we found that there exists a positive correlation between the a and b parameters (R =?0.85, R² =?0.72). On the other hand, we made around 150 computer runs of a spring-block model proposed by Olami et al. (Phys Rev Lett 68(8):1244–1247, 1992). This model roughly emulates the interaction between two fault planes and it reaches a self-organized critical state. With these simulations, we also found that the a and b parameters are positively correlated. Motivated by these results, we propose an analytical demonstration that indeed a and b are positively correlated. In addition, we discuss on other possible applications of the spring-block model to actual seismicity and to frictional experiments made with sandpapers.     

Hydrodynamic Equilibrium for Sediment Transport and Bed Response to Wave Motion

An experimental and theoretical identification of hydrodynamic equilibrium for sediment transport and bed response to wave motion are considered. The comparison between calculations and the results of laboratory experiments indicates the linear relation between sediment transport rate and the thickness zm of bed layer in which sediments are in apparent rectilinear motion. This linear relationship allows to use the first order “upwind” numerical scheme of FDM ensuring an accurate solution of equation for changes in bed morphology. However, it is necessary to carry out a decomposition of the sediment transport into transport in onshore direction during wave crest and offshore direction during wave trough. Further, the shape of bed erosion in response to sediment transport coincides with the trapezoid envelope or with part of it, when some sediments still remain within it. Bed erosion area is equal to the one of a rectangle with thickness znm.     

Long-Term Trends in the Critical Frequency of the E-layer

A search for trends k(foE) in the critical frequency of the ionospheric E layer at Juliusruh and Slough stations is performed by the method often used by the authors to analyze trends in the F2-layer parameters. It is found that k(foE) could differ in both magnitude and even sign within different time intervals. However, the k(foE) trends have been stably negative over the last two decades for both stations and all months of the year. The k(foE) values averaged over a year are ?0.012 and ?0.005 MHz per year for Juliusruh and Slough stations, respectively. The method used in the recent paper by La?tovi?ka et al. (2016) to determine foE trends is analyzed, and it is shown that the difference in linear approximation of the dependence of the observed foE values on F10.7 within different time intervals could be interpreted not as the presence of a different foE dependence on the F10.7 index within these intervals but as the presence within them of foE trends that change the slope of the linear approximation.     

Quantitative Analysis of Seismicity Before Large Taiwanese Earthquakes Using the G-R Law

Seismicity has been identified as an example of a natural, nonlinear system for which the distribution of frequency and event size follow a power law called the “Gutenberg–Richter (G-R) law.” The parameters of the G-R law, namely b- and a-values, have been widely used in many studies about seismic hazards, earthquake forecasting models, and other related topics. However, the plausibility of the power law model and applicability of parameters were mainly verified by statistical error σ of the b-value, the effectiveness of which is still doubtful. In this research, we used a newly defined p value developed by Clausetet al. (Power-Law Distributions in Empirical Data, SIAM Rev. 51, 661–703, 2009) instead of the statistical error σ of the b-value and verified its effectiveness as a plausibility index of the power-law model. Furthermore, we also verified the effectiveness of K–S statistics as a goodness-of-fit test in estimating the crucial parameter \(M_{\text{c}}\) of the power-law model.     

An experimental study on variation of <Emphasis Type="Italic">b</Emphasis> value during deformation of rock samples with different structural models

A preliminary study of b value of rocks with two kinds of structural models has been made on the base of a new acoustic emission recording system. It shows that b value of the sample decreases obviously when the sample with compressive en echelon faults changes into a tensile one after interchange occurs between stress axis σ ₁ and σ ₂. A similar experiment is observed when the sample with tensile en echelon faults changes into that with a bend fault after two segments of the en echelon fault linking up. These facts indicate that the variation of b value may contain the information of the regional dominant structural model. Therefore, b-value analyses could be a new method for studying regional dominant structural models.     

Investigation of isolated substorms: Generation conditions and characteristics of different phases

Characteristics of isolated substorms selected by variations in the 1-min values of the AL index are analyzed. The substorms were divided into several types with respect to the behavior of the Bz component of the interplanetary magnetic field (IMF) during the expansion phase. The probability of observations of substorms associated with the northward turn of the Bz component of IMF was ~19%, while the substorms taking place at Bz < 0 were observed in 53% of cases. A substantial number of events in which no substorm magnetic activity was observed in the auroral zone after a long (>30 min) period of the southward IMF and a following sharp turn of the Bz component of IMF before the north was detected. The data suggest that a northward IMF turn is neither a necessary nor sufficient condition for generating substorms. It has been shown for substorms of the both types that the average duration of the southward IMF to moment T ₀ and the average intensity of the magnetic perturbation in the maximum are approximately the same and amount to ~80 min and–650 nT, respectively. However, for substorms at Bz < 0, their mean duration, including the expansive and recovery phases, is on average 30 min longer than that at a northward turn of IMF. Correlations between the loading–unloading processes in the magnetosphere in the periods of magnetospheric substorms were investigated with different functions that determine the efficiency of the energy transfer from the solar wind to the magnetosphere. It has been shown that the highest correlation coefficient (r = 0.84) is observed when the function suggested by Newell et al. (2007) is used. It has been detected that a simple function VB _S yields a high correlation coefficient (r = 0.75).     

The seismic wave absorption in the crust and upper mantle in the vicinity of the Kislovodsk seismic station

The Q-factor estimates of the Earth’s crust and upper mantle as the functions of frequency (Q(f)) are obtained for the seismic S-waves at frequencies up to ~35 Hz. The estimates are based on the data for ~40 earthquakes recorded by the Kislovodsk seismic station since 2000. The magnitudes of these events are M_W > 3.8, the sources are located in the depth interval from 1 to 165 km, and the epicentral distances range from ~100 to 300 km. The Q-factor estimates are obtained by the methods developed by Aki and Rautian et al., which employ the suppression of the effects of the source radiation spectrum and local site responses in the S-wave spectra by the coda waves measured at a fixed lapse time (time from the first arrival). The radiation pattern effects are cancelled by averaging over many events whose sources are distributed in a wide azimuthal sector centered at the receiving site. The geometrical spreading was specified in the form of a piecewise-continuous function of distance which behaves as 1/R at the distances from 1 to 50 km from the source, has a plateau at 1/50 in the interval from 50–70 km to 130–150 km, and decays as \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sqrt R }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sqrt R }$}}\) beyond 130–150 km. For this geometrical spreading model and some of its modifications, the following Q-factor estimates are obtained: Q(f) ~ 85f^0.9 at the frequencies ranging from ~1 to 20 Hz and Q(f) ~ 75f^1.0 at the frequencies ranging from ~1 to 35 Hz.     

Stochastic models of severe weather watches and warnings: transition probabilities

To alert the public to the possibility of tornado (T), hail (H), or convective wind (C), the National Weather Service (NWS) issues watches (V) and warnings (W). There are severe thunderstorm watches (SV), tornado watches (TV), and particularly dangerous situation watches (PV); and there are severe thunderstorm warnings (SW), and tornado warnings (TW). Two stochastic models are formulated that quantify uncertainty in severe weather alarms for the purpose of making decisions: a one-stage model for deciders who respond to warnings, and a two-stage model for deciders who respond to watches and warnings. The models identify all possible sequences of watches, warnings, and events, and characterize the associated uncertainties in terms of transition probabilities. The modeling approach is demonstrated on data from the NWS Norman, Oklahoma, warning area, years 2000–2007. The major findings are these. (i) Irrespective of its official designation, every warning type {SW, TW} predicts with a significant probability every event type {T, H, C}. (ii) An ordered intersection of SW and TW, defined as reinforced warning (RW), provides additional predictive information and outperforms SW and TW. (iii) A watch rarely leads directly to an event, and most frequently is false. But a watch that precedes a warning does matter. The watch type \(\{SV\), TV, \(PV\}\) is a predictor of the warning type \(\{SW\), RW, \(TW\}\) and of the warning performance: It sharpens the false alarm rate of the warning and the predictive probability of an event, and it increases the average lead time of the warning.     

Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”

In this short note, I comment on the research of Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014) regarding the extreme value theory and statistics in the case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic model for the block maxima of a random variable and the generalized Pareto distribution (GPD) as a model for the peaks over threshold (POT) of the same random variable is presented more clearly. Inappropriately, Pisarenkoet al. (Pure Appl. Geophys 171:1599–1624, 2014) have neglected to note that the approximations by GEVD and GPD work only asymptotically in most cases. This is particularly the case with truncated exponential distribution (TED), a popular distribution model for earthquake magnitudes. I explain why the classical models and methods of the extreme value theory and statistics do not work well for truncated exponential distributions. Consequently, these classical methods should be used for the estimation of the upper bound magnitude and corresponding parameters. Furthermore, I comment on various issues of statistical inference in Pisarenkoet al. and propose alternatives. I argue why GPD and GEVD would work for various types of stochastic earthquake processes in time, and not only for the homogeneous (stationary) Poisson process as assumed by Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014). The crucial point of earthquake magnitudes is the poor convergence of their tail distribution to the GPD, and not the earthquake process over time.     

Spherical cap harmonic analysis of regional magnetic anomalies based on CHAMP satellite data

We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over mainland China. We assumed satellite points on the same surface (307.69 km) and constructed a spherical cap harmonic model of the satellite magnetic anomalies for elements X, Y, Z, and F over Chinese mainland for 2010.0 (SCH2010) based on selected 498 points. We removed the external field by using the CM4 model. The pole of the spherical cap is 36N° and 104°E, and its half-angle is 30°. After checking and comparing the root mean square (RMS) error of ΔX, ΔY, and ΔZ and X, Y, and Z, we established the truncation level at K ^max = 9. The results suggest that the created China Geomagnetic Referenced Field at the satellite level (CGRF2010) is consistent with the CM4 model. We compared the SCH2010 with other models and found that the intensities and distributions are consistent. In view of the variation of F at different altitudes, the SCH2010 model results obey the basics of the geomagnetic field. Moreover, the change rate of X, Y, and Z for SCH2010 and CM4 are consistent. The proposed model can successfully reproduce the geomagnetic data, as other data-fitting models, but the inherent sources of error have to be considered as well.     

Estimation of maximum mass velocities in the focal zones of strong earthquakes based on measured displacements of rock blocks: A case study of Kyrgyzstan

An important task in seismic hazard assessment is estimation of the intensity and frequency of extremely strong earthquake effects, in particular, peak ground velocities (PGV). Earlier, a method was proposed to evaluate PGV values based on the magnitude of displacements of rock blocks (Rodkin et al., 2012). In this study, this method is used to analyze field data on the source zones of the August 19, 1992, M_S = 7.3 Susamyr earthquake and the January 3, 1911, M_w = 7.9 Kemin earthquake, and estimate maximum ground shaking at the upper construction site of the Upper Naryn series of hydropower plants, Kyrgyz Republic. It is shown that the resulting estimates are consistent with data obtained through other techniques. Therefore, the new approach can be recommended to estimate earthquake effects.     

Inclination shallowing in the Permian/Triassic boundary sedimentary sections of the Middle Volga region in light of the new paleomagnetic data

One of the key challenges which are traditionally encountered in studying the paleomagnetism of terrigenous sedimentary strata is the necessity to allow for the effect of shallowing of paleomagnetic inclinations which takes place under the compaction of the sediment at the early stages of diagenesis and most clearly manifests itself in the case of midlatitude sedimentation. Traditionally, estimating the coefficient of inclination flattening (f) implies routine re-deposition experiments and studying their magnetic anisotropy (Kodama, 2012), which is not possible in every standard paleomagnetic laboratory. The Elongation–Inclination (E–I) statistical method for estimating the coefficient of inclination shallowing, which was recently suggested in (Tauxe and Kent, 2004), does not require the investigation of the rock material in a specially equipped laboratory but toughens the requirements on the paleomagnetic data and, primarily, regarding the volume of the data, which significantly restricts the possibilities of the post factum estimation and correction for inclination shallowing. In this work, we present the results of the paleomagnetic reinvestigation of the Puchezh and Zhukov ravine (ravine) reference sections of the Upper Permian and Lower Triassic rocks in the Middle Volga region. The obtained paleomagnetic data allowed us to estimate the coefficient of inclination shallowing f by the E–I method: for both sections, it is f = 0.9. This method was also used by us for the paleomagnetic data that were previously obtained for the Permian–Triassic rocks of the Monastyrskii ravine (Monastirskoje) section (Gialanella et al., 1997), where the inclination shallowing coefficient was estimated at f = 0.6.     

Estimation of storm-time level of day-side wave geomagnetic activity using a new <Emphasis Type="Italic">ULF</Emphasis> index

The level of wave geomagnetic activity in the morning and daytime sectors of auroral latitudes during strong magnetic storms with Dst _min varying from ?100 to ?150 nT in 1995–2002 have been studied using a new ULF index of wave activity proposed in [Kozyreva et al., 2007]. It has been detected that daytime Pc5 pulsations (2–6 mHz) are most intense during the main phase of a magnetic storm rather than during the recovery phase as was considered previously. It has been indicated that morning geomagnetic pulsations during the substorm recovery phase mainly contribute to daytime wave activity. The appearance of individual intervals with the southward IMF B _z component during the magnetic storm recovery phase results in increases in the ULF index values.     

Precursor times of abnormal <Emphasis Type="Italic">b</Emphasis>-values prior to mainshocks

Seismic observations exhibit the presence of abnormal b-values prior to numerous earthquakes. The time interval from the appearance of abnormal b-values to the occurrence of mainshock is called the precursor time. There are two kinds of precursor times in use: the first one denoted by T is the time interval from the moment when the b-value starts to increase from the normal one to the abnormal one to the occurrence time of the forthcoming mainshock, and the second one denoted by T _p is the time interval from the moment when the abnormal b-value reaches the peak one to the occurrence time of the forthcoming mainshock. Let T* be the waiting time from the moment when the abnormal b-value returned to the normal one to the occurrence time of the forthcoming mainshock. The precursor time, T (usually in days), has been found to be related to the magnitude, M, of the mainshock expected in a linear form as log(T)?=?q?+?rM where q and r are the coefficient and slope, respectively. In this study, the values of T, T _p , and T* of 45 earthquakes with 3?≤?M?≤?9 occurred in various tectonic regions are compiled from or measured from the temporal variations in b-values given in numerous source materials. The relationships of T and T _p , respectively, versus M are inferred from compiled data. The difference between the values of T and T _p decreases with increasing M. In addition, the plots of T*/T versus M, T* versus T, and T* versus T-T* will be made and related equations between two quantities will be inferred from given data.     

Asymptotic behavior of an n-species stochastic Gilpin–Ayala cooperative model

An n-species stochastic Gilpin–Ayala cooperative model was investigated in this study. The Lyapunov function and the M-matrix method were applied to study the stability of the solutions. Sufficient conditions for the existence of a global positive solution of the Gilpin–Ayala cooperative model were established. Certain asymptotically stable results of a global positive solution of the cooperative model and its domain of attraction were estimated. That main objective of this study is to provide corrections for errors in some theorems given in the work of Lian et al. (2007). The errors of Theorems 2, 3, 5, and 6 from the published work appeared in the parameters θ _i and p _ii .     

The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models

An alternative model for the nonlinear interaction term S_nl in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863–884, 2003; Annenkov and Shrira J Fluid Mech 561:181–207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280–303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of S_nl which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481–500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of S_nl, and to compare it to the existing models for S_nl in WAVEWATCH; the DIA and WRT. Some differences between the different models for S_nl are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of S_nl (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Alcohol compounds in <Emphasis Type="Italic">Azolla imbricata</Emphasis> and potential source implication for marine sediments

This study investigated the composition of long-chain alkyl diols, triols, sec-alcohols, hydroxyl acids, and other hydroxylated compounds in Azolla imbricata and compared the organic alcohol components of Azolla filiculoides, Azolla microphylla, and South China Sea (SCS) sediments in order to investigate the possible indication of Azolla being the biological source of diols and triols in SCS sediment. Large amounts of diols, monohydroxy acids, and sec-alcohols with internal hydroxy groups at ω20 were detected in the three types of Azolla. Among these, 1,ω20-diol and ω20-hydroxy acid exhibited strong even-odd predominance distribution, whereas ω20-sec-alcohol exhibited strong odd-even predominance distribution. In addition, small amounts of diols, triols, and dihydroxy acids with internal hydroxy groups at 9, 10 or ω9, ω10 were detected, among which the chain length of C₂₉ was predominate. Compounds having similar structures as those in Azolla reflected a similar biosynthetic pathway: ω20-hydroxy acid exhibiting even-odd predominance distribution is decarboxylated to ω20-sec-alcohol exhibiting odd-even predominance distribution and converted to 1, ω20-diol with even-odd predominance distribution by acyl reduction; ω9, ω10-hydroxy acid is converted to 1,20,21(1, ω9, ω10)-triol by acyl reduction, and then converted to 9,10-diol by hydrogenation and dehydration. The alcohol components in A. imbricata were clearly not the biological source of 1,13/1,14/1,15-C_{28, 30, 32} diols and 1,3,4-C_27-29 triols in the SCS sediment. Certain marine diatoms might be the source of 1,14-C_{28, 30} diol in inshore sediment, but the biological source of diols and triols in the SCS sediment requires further investigation.     

Long-period irregular pulsations under the conditions of a quiet magnetosphere

Simultaneous observations of high-latitude long-period irregular pulsations at frequencies of 2.0–6.0 mHz (ipcl) and magnetic field disturbances in the solar wind plasma at low geomagnetic activity (Kp ~ 0) have been studied. The 1-s data on the magnetic field registration at Godhavn (GDH) high-latitude observatory and the 1-min data on the solar wind plasma and IMF parameters for 2011–2013 were used in an analysis. Ipcl (irregular pulsations continuous, long), which were observed against a background of the IMF Bz reorientation from northward to southward, have been analyzed. In this case other solar wind plasma and IMF parameters, such as velocity V, density n, solar wind dynamic pressure P = ρV² (ρ is plasma density), and strength magnitude B, were relatively stable. The effect of the IMF Bz variation rate on the ipcl spectral composition and intensity has been studied. It was established that the ipcl spectral density reaches its maximum (~10–20 min) after IMF Bz sign reversal in a predominant number of cases. It was detected that the ipcl average frequency (f) is linearly related to the IMF Bz variation rate (ΔBz/Δt). It was shown that the dependence of f on ΔBz/Δt is controlled by the α = arctan(By/Bx) angle value responsible for the MHD discontinuity type at the front boundary of magnetosphere. The results made it possible to assume that the formation of the observed ipcl spectrum, which is related to the IMF Bz reorientation, is caused by solar wind plasma turbulence, which promotes the development of current sheet instability and surface wave amplification at the magnetopause.