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.     

Transcontinental tidal transect: European Atlantic coast-Southern Siberia-Russian Pacific coast

The paper presents results of measurements with digital tidal LaCoste-Romberg gravimeters on the European Atlantic coast-Southern Siberia-Russian Pacific coast transect in 1995–2005. The transect includes four West European (Chizé, Ménesplet, Mordelles, and Wikle), two South Siberian (Klyuchi and Talaya), and two Far Eastern (Zabakalskoe and Yuzhno-Sakhalinsk) stations. Gravimetric measurements at the Talaya station (SW Baikal rift zone) are supplemented by long-term laser extensometer observations. The position of the stations within the rectangle (45°–55°N, 0.4°–142°E) allows one to assess existing tidal strain models (WD93 and DDW99) and various ocean tide models (SCW80, CSR3, FES95, ORI96, CSR4, FES02, GOT00, NAO99, and TPX06). Data of intracontinental stations (with a small ocean effect at distances of 2000–3000 km) agree well with the DDW99 tidal strain model (with regard to the mantle viscosity). The uncertainty of digital tidal gravity measurements is 0.25%. Results of laser extensometer measurements are at the same accuracy level. Then, the Love and Shida numbers calculated at midlatitudes of the intracontinental zone of Eurasia from combined data are h = 0.6077 ± 0.0008, k = 0.3014 ± 0.0001, and l = 0.0839 ± 0.0001. The analysis of results of Pacific and Atlantic stations located at distances of 30–300 km from the ocean showed that the FES02, CSR4, GOT00, NAO99, and TPX06 ocean tide models are preferable.     

Time changes of the potential Love tidal parameters k2 and k3

The planet Earth is continuously changing in time, so there are phenomena that require continuous observation, including tidal parameters. The main goal of this study is to analyze time changes of the Love potential tidal parameters. This paper concerns an analysis of the estimated Love numbers k for the second and the third degree tides (numbers k₂ and k₃), associated with the tide variations of the satellite motion. The measured data used for determining the parameters k₂, k₃ were conducted within the period of January 1, 2014 until July 1, 2016 by LAGEOS-1 and LAGEOS-2 satellites. The results were compared with our previous determination of these parameters from LAGEOS data during the period from January 1, 2005 until July 1, 2007 to examine whether any systematic differences and time evolution occur. The adjusted values for k₂ equalling 0.29842 ± 0.00008 and k₃ equalling 0.0901 ± 0.0034 are discussed and compared with the nominal values given in International Earth Rotation and Reference Systems Service standards. The differences between the k₂ and k₃ values obtained for the time interval 2005.0–2007.5 and the results for 2014.0–2016.5 interval are –0.00288 for k₂ and 0.0042 for k₃. The obtained differences in the k₂ and k₃ values may indicate their evolution in time.     

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).     

Modeling studies of tidal dynamics and the associated responses to coastline changes in the Bohai Sea,China

Over the past 30 years, reclamation projects and related changes have impacted the hydrodynamics and sediment transport in the Bohai Sea. Three-dimensional tidal current models of the Bohai Sea and the Yellow Sea were constructed using the MIKE 3 model. We used a refined grid to simulate and analyze the effects of changes in coastline, depth, topography, reclamation, the Yellow River estuary, and coastal erosion on tidal systems, tide levels, tidal currents, residual currents, and tidal fluxes. The simulation results show that the relative change in the amplitude of the half-day tide is greater than that of the full-day tide. The changes in the tidal amplitudes of M₂, S₂, K₁, and O₁ caused by coastline changes accounted for 27.76–99.07% of the overall change in amplitude from 1987 to 2016, and water depth changes accounted for 0.93–72.24% of the overall change. The dominant factor driving coastline changes is reclamation, accounting for 99.55–99.91% of the amplitude changes in tidal waves, followed by coastal erosion, accounting for 0.05–0.40% of the tidal wave amplitude changes. The contribution of changes in the Yellow River estuary to tidal wave amplitude changes is small, accounting for 0.01–0.12% of the amplitude change factor. The change in the highest tide level (HTL) is mainly related to the amplitude change, and the correlation with the phase change is small. The dominant factor responsible for the change in the HTL is the tide amplitude change in M2, followed by S2, whereas the influence of the K1 and O1 tides on the change in the HTL is small. Reclamation resulted in a decrease in the vertical average maximum flow velocity (V_VAM) in the Bohai Sea. Shallower water depths have led to an increase in the V_VAM; deeper water depths have led to a decrease in the maximum flow velocity. The absolute value of the maximum flow velocity gradually decreases from the surface to the bottom, but the relative change value is basically constant. The changes in the tidal dynamics of the Bohai Sea are proportional to the degree of change in the coastline. The maximum and minimum changes in the tidal flux appear in Laizhou Bay (P-LZB) and Liaodong Bay (P-LDB), respectively. The changes in the tidal flux are related to the change in the area of the bay. Due to the reduced tidal flux, the water exchange capacity of the Bohai Sea has decreased, impacting the ecological environment of the Bohai Sea. Strictly controlling the scale of reclamation are important measures for reducing the decline in the water exchange capacity of the Bohai Sea and the deterioration of its ecological environment.     

Effect of tidal stress on fault nucleation and failure of the 2007 Ms6.4 Ning’er earthquake

Based on calculations of the tidal Coulomb failure stress and investigations of the correlation between the Earth tide and the Ning’er earthquake sequence, the processes of fault nucleation and failure were simulated. In these simulations we consider the influence of tidal stresses using the rate- and state-dependent friction laws. Furthermore, the effects on tidal triggering due to the stress amplitude and periodic oscillation properties were investigated, and the triggering effects between the tidal normal and tidal shear stresses were compared. The results showed that the Ning’er earthquake sequence was a physical consequence of tidal effects. A transition period T₀ exists between the nucleation and failure processes of a seismic fault. When the period T of stress is equal to or becomes larger than T₀, the fault response becomes dependent on the periodic features of the loading stress; however, for T < T₀, the response of the fault is nearly independent of the period. Both the tidal normal and tidal shear stresses have similar effect in the nucleation and failure processes; the clock changes generally increase with the maximum amplitudes of the tidal stresses. Tidal normal and tidal shear stresses with positive amplitudes mainly induce earthquake triggering; however, the triggering effects induced by negative tidal stresses are smaller and faults are not sensitive to negative tidal stresses. Our results primarily reveal the physical mechanisms of tidal stress triggering.     

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.     

Near-source attenuation of high-frequency body waves beneath the New Madrid Seismic Zone

Attenuation characteristics in the New Madrid Seismic Zone (NMSZ) are estimated from 157 local seismograph recordings out of 46 earthquakes of 2.6?≤?M?≤?4.1 with hypocentral distances up to 60 km and focal depths down to 25 km. Digital waveform seismograms were obtained from local earthquakes in the NMSZ recorded by the Center for Earthquake Research and Information (CERI) at the University of Memphis. Using the coda normalization method, we tried to determine Q values and geometrical spreading exponents at 13 center frequencies. The scatter of the data and trade-off between the geometrical spreading and the quality factor did not allow us to simultaneously derive both these parameters from inversion. Assuming 1/R ^1.0 as the geometrical spreading function in the NMSZ, the Q _P and Q _S estimates increase with increasing frequency from 354 and 426 at 4 Hz to 729 and 1091 at 24 Hz, respectively. Fitting a power law equation to the Q estimates, we found the attenuation models for the P waves and S waves in the frequency range of 4 to 24 Hz as Q _P?=?(115.80?±?1.36) f ^{(0.495?±?0.129)} and Q _S?=?(161.34?±?1.73) f ^{(0.613?±?0.067)}, respectively. We did not consider Q estimates from the coda normalization method for frequencies less than 4 Hz in the regression analysis since the decay of coda amplitude was not observed at most bandpass filtered seismograms for these frequencies. Q _S/Q _P?>?1, for 4?≤?f?≤?24 Hz as well as strong intrinsic attenuation, suggest that the crust beneath the NMSZ is partially fluid-saturated. Further, high scattering attenuation indicates the presence of a high level of small-scale heterogeneities inside the crust in this region.     

Observations of crustal tide strains in the Elbrus area

Results of observations of tidal strains of the crust in the tectonically active Elbrus area of the Northern Caucasus carried out with the use of the Baksan SSAI laser interferometer strainmeter over the period from 2003 through 2006 are presented. Harmonic analysis is performed with the help of the ETERNA software package. Statistically significant time variations in the amplitudes of the main tidal waves M ₂ and O ₁ are revealed. The influence of the topography on tidal strains in the Baksan gorge is estimated at 22% (an increase in the measured strain values). The reduced amplitude factors of the main diurnal (O ₁) and semidiurnal (M ₂) waves are underestimated. Numerical modeling of tidal anomalies produced by regional heterogeneous inclusions is performed in a 2-D approximation. The observed anomaly of the M ₂ wave (12%) is shown to be due to the influence of the main magma-controlling fault associated with the deep magma source of the Elbrus dormant volcano.     

Impacts of climate changes on ocean surface gravity waves over the eastern Canadian shelf

A numerical study is conducted to investigate the impact of climate changes on ocean surface gravity waves over the eastern Canadian shelf (ECS). The “business-as-usual” climate scenario known as Representative Concentration Pathway RCP8.5 is considered in this study. Changes in the ocean surface gravity waves over the study region for the period 1979–2100 are examined based on 3 hourly ocean waves simulated by the third-generation ocean wave model known as WAVEWATCHIII. The wave model is driven by surface winds and ice conditions produced by the Canadian Regional Climate Model (CanRCM4). The whole study period is divided into the present (1979–2008), near future (2021–2050) and far future (2071–2100) periods to quantify possible future changes of ocean waves over the ECS. In comparison with the present ocean wave conditions, the time-mean significant wave heights (H _s ) are expected to increase over most of the ECS in the near future and decrease over this region in the far future period. The time-means of the annual 5% largest H _s are projected to increase over the ECS in both near and far future periods due mainly to the changes in surface winds. The future changes in the time-means of the annual 5% largest H _s and 10-m wind speeds are projected to be twice as strong as the changes in annual means. An analysis of inverse wave ages suggests that the occurrence of wind seas is projected to increase over the southern Labrador and central Newfoundland Shelves in the near future period, and occurrence of swells is projected to increase over other areas of the ECS in both the near and far future periods.     

Verifying the body tide at the Canary Islands using tidal gravimetry observations

Gravity tide records from El Hierro, Tenerife and Lanzarote Islands (Canarian Archipelago) have been analyzed and compared to the theoretical body tide model (DDW) of Dehant el al. (1999). The use of more stringent criterion of tidal analysis using VAV program allowed us to reduce the error bars by a factor of two of the gravimetric factors at Tenerife and Lanzarote compared with previous published values. Also, the calibration values have been revisited at those sites. Precise ocean tide loading (OTL) corrections based on up-to-date global ocean models and improved regional ocean model have been obtained for the main tidal harmonics O₁, K₁, M₂, S₂. We also point out the importance of using the most accurate coastline definition for OTL calculations in the Canaries. The remaining observational errors depend on the accuracy of the calibration of the gravimeters and/or on the length of the observed data series. Finally, the comparison of the tidal observations with the theoretical body tide models has been done with an accuracy level of 0.1% at El Hierro, 0.4% at Tenerife and 0.5% at Lanzarote.     

Creepex of Kamchatka shallow earthquakes

Results of investigation of the lithosphere in the Kamchatka seismic focal zone from dynamic characteristics of earthquake records obtained at regional stations are presented. It is assumed that the specificity of the source zone can be estimated by the relation Cr = K _P ? bK _S ? c characterizing relative energies (energy classes, according to [Fedotov, 1972]) of short period transverse and longitudinal waves in the source. Azimuthal, spatial, and temporal variations in Cr and their relation to focal mechanisms are examined. Spatiotemporal variations in this parameter are shown to be caused by the influence of variations in the conditions in the source zone (its substance or process) on the radiation of P and S waves.     

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.     

Characterisation of ground motion recording stations in the Groningen gas field

The seismic hazard and risk analysis for the onshore Groningen gas field requires information about local soil properties, in particular shear-wave velocity (V_S). A fieldwork campaign was conducted at 18 surface accelerograph stations of the monitoring network. The subsurface in the region consists of unconsolidated sediments and is heterogeneous in composition and properties. A range of different methods was applied to acquire in situ V_S values to a target depth of at least 30 m. The techniques include seismic cone penetration tests (SCPT) with varying source offsets, multichannel analysis of surface waves (MASW) on Rayleigh waves with different processing approaches, microtremor array, cross-hole tomography and suspension P-S logging. The offset SCPT, cross-hole tomography and common midpoint cross-correlation (CMPcc) processing of MASW data all revealed lateral variations on length scales of several to tens of metres in this geological setting. SCPTs resulted in very detailed V_S profiles with depth, but represent point measurements in a heterogeneous environment. The MASW results represent V_S information on a larger spatial scale and smooth some of the heterogeneity encountered at the sites. The combination of MASW and SCPT proved to be a powerful and cost-effective approach in determining representative V_S profiles at the accelerograph station sites. The measured V_S profiles correspond well with the modelled profiles and they significantly enhance the ground motion model derivation. The similarity between the theoretical transfer function from the V_S profile and the observed amplification from vertical array stations is also excellent.     

Limits of transversely isotropic elastic parameters for the existence of classical Rayleigh waves

Solutions of P-SV equations of motion in a homogeneous transversely isotropic elastic layer contain a factor exp(±ν _j z), where z is the vertical coordinate and j?=?1, 2. For computing Rayleigh wave dispersion in a multi-layered half space, ν _j is computed at each layer. For a given phase velocity (c), ν _j becomes complex depending on the transversely isotropic parameters. When ν _j is complex, classical Rayleigh waves do not exist and generalised Rayleigh waves propagate along a path inclined to the interface. We use transversely isotropic parameters as α _H , β _V , ξ, ? and η and find their limits beyond which ν _j becomes complex. It is seen that ν _j depends on ? and η, but does not depend on ξ. The complex ν _j occurs when ? is small and η is large. For a given c/β _V , the region of complex ν _j in a ? -η plane increases with the increase of α _H /β _V . Further, for a given α _H /β _V , the complex region of ν _j increases significantly with the decrease of c/β _V . This study is useful to compute dispersion parameters of Rayleigh waves in a layered medium.     

Body wave attenuation characteristics in the crust of Alborz region and North Central Iran

Attenuation of P and S waves has been investigated in Alborz and north central part of Iran using the data recorded by two permanent and one temporary networks during October 20, 2009, to December 22, 2010. The dataset consists of 14,000 waveforms from 380 local earthquakes (2 < M _L < 5.6). The extended coda normalization method (CNM) was used to estimate quality factor of P (Q _P) and S waves (Q _S) at seven frequency bands (0.375, 0.75, 1.5, 3, 6, 12, 24 Hz). The Q _P and Q _S values have been estimated at lapse times from 40 to 100 s. It has been observed that the estimated values of Q _P and Q _S are time independent; therefore, the mean values of Q _P and Q _S at different lapse times have been considered. The frequency dependence of quality factor was determined by using a power-law relationship. The frequency-dependent relationship for Q _P was estimated in the form of (62 ± 7)f ^{(1.03 ± 0.07)} and (48 ± 5)f ^{(0.95 ± 0.07)} in Alborz region and North Central Iran, respectively. These relations for Q _S for Alborz region and North Central Iran have estimated as (83 ± 8)f ^{(0.99 ± 0.07)} and (68 ± 5)f ^{(0.96 ± 0.05)}, respectively. The observed low Q values could be the results of thermoelastic effects and/or existing fracture. The estimated frequency-dependent relationships are comparable with tectonically active regions.     

Magnetic field variations in the umbra of single sunspots during their passage across the solar disk

Temporal variations of the maximum (B _max) and average (〈B〉) magnetic inductions, minimum (α _min) and average (〈α〉) inclination angles of the field lines to the radial direction from the center of the Sun, and areas of the sunspot umbra S in the umbra of single sunspots during their passage across the solar disk are investigated. The variation of the properties of single sunspots has been considered at different stages of their existence, i.e., during formation, the “quiet” period, and the disappearance stage. It has been found that, for the majority of the selected single sunspots, there is a positive correlation between B _max and S and between 〈B〉 and S defined at different times during the passage of sunspots across the solar disk. It is shown in this case that the nature of the dependence between the parameters α _min and B _max, α _min and S, as well as between 〈α〉 and 〈B〉, 〈α〉 and S, can vary from sunspot to sunspot, but for many sunspots the inclination angle of the field lines decreases on average with the growth of the sunspot umbra area and the field strength.     

Influence of the modified global ocean tide model with local tides of East and South China Seas on load gravity in China and its neighbor area

Introduction With the development of science and technology, the accuracy of gravity measurement is im-proved. The gravity observation with FG5 gravimeter has reached accuracy of μ magnitude. And the high accurate superconducting gravimeter can detect the tiny signal of 10?2 μ magnitude in frequency domain. With the high-accuracy gravity observation on Earth′s surface, the Earth′s tidal parameters can be determined precisely. And the observations can also be used to invert the struc-ture…     

Determination of source parameters of strong earthquakes of Kamchatka,the Kurile Islands,and Japan from aftershock sequences

Aftershock sequences of some strong earthquakes of Kamchatka, the Kurile Islands, and Japan are examined. Such source parameters as the length L, along-dip width W, motion on fault D, and stress drop Δσ are determined from the aftershock sequences considered. The values of these parameters were obtained by the formal estimation of linear source parameters (lower bound estimates) and visually (upper bound estimates). The correlation dependences of the obtained parameters on the surface wave (M _S ) and seismic moment (M _W ) magnitudes are calculated.     

The ratio between corner frequencies of source spectra of <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">S</Emphasis>-waves—a new discriminant between earthquakes and quarry blasts

This study analyzes and compares the P- and S-wave displacement spectra from local earthquakes and explosions of similar magnitudes. We propose a new approach to discrimination between low-magnitude shallow earthquakes and explosions by using ratios of P- to S-wave corner frequencies as a criterion. We have explored 2430 digital records of the Israeli Seismic Network (ISN) from 456 local events (226 earthquakes, 230 quarry blasts, and a few underwater explosions) of magnitudes Md?=?1.4–3.4, which occurred at distances up to 250 km during 2001–2013 years. P-wave and S-wave displacement spectra were computed for all events following Brune’s source model of earthquakes (1970, 1971) and applying the distance correction coefficients (Shapira and Hofstetter, Teconophysics 217:217–226, 1993; Ataeva G, Shapira A, Hofstetter A, J Seismol 19:389-401, 2015), The corner frequencies and moment magnitudes were determined using multiple stations for each event, and then the comparative analysis was performed.The analysis showed that both P-wave and especially S-wave displacement spectra of quarry blasts demonstrate the corner frequencies lower than those obtained from earthquakes of similar magnitudes. A clear separation between earthquake and explosion populations was obtained for ratios of P- to S-wave corner frequency f ₀(P)/f ₀(S). The ratios were computed for each event with corner frequencies f ₀ of P- and S-wave, which were obtained from the measured f ₀ ^I at individual stations, then corrected for distance and finally averaged. We obtained empirically the average estimation of f ₀(P)/f ₀(S)?=?1.23 for all used earthquakes, and 1.86 for all explosions. We found that the difference in the ratios can be an effective discrimination parameter which does not depend on estimated moment magnitude M _w .The new multi-station Corner Frequency Discriminant (CFD) for earthquakes and explosions in Israel was developed based on ratios P- to S-wave corner frequencies f ₀(P)/f ₀(S), with the empirical threshold value of the ratio for Israel as 1.48.