On the solution stability in the problem of determining the time variations of the tidal responses of a medium in the vicinity of the sources of severe earthquakes

In (Molodenskii M.S. et al., 2016), the data from horizontal pendulums recording the tilts in the closest vicinity of the Great Tohoku earthquake of March 11, 2011 in Japan were analyzed. A significantly improved method for statistical analysis of the observational data enabled the authors to reveal a slow growth in tidal tilts during a period of six years before the earthquake, which was superseded by an instantaneous drop in the amplitudes at the time of the earthquake. After this, during the subsequent four years, the tidal amplitudes have remained at a significantly lower level than their average values before the earthquake. These changes in tidal amplitudes testify to the nonlinear character of the tidal response of the medium in the presence of large tectonic stresses: as is well known, the linear relationship between stresses and strains in a real medium is only the case for stresses that are far below the yield stress. When the stresses approach the failure limit, two counteracting effects come into play: (1) the shear moduli in some areas decrease as a result of the avalanche growth of the crack formation processes, and (2) the moduli increase due to the compression in the other areas. Irrespective of which particular effect of these two is predominant, in either case the linearity of the relationship between the stresses and strains should be violated. This violation cannot but affect the amplitudes of the tidal tilts and strains characterizing this relationship in the presence of fairly low additional tidal stresses (i.e., the derivative of the off-diagonal stress tensor components with respect to the same components of the strain tensor). Since there is presently a sufficiently dense network of the horizontal pendulums recording the tilts (the global IRIS network and the particularly dense F-NET network in Japan), monitoring the changes in the amplitudes of tidal tilts can be considered as a key instrument for capturing the signs of the approach of tectonic stresses to their critical values. The increase in tidal amplitudes before the Tohoku earthquake and their drop at the moment of the earthquake, which were revealed by us, as well as the constancy of the amplitudes during four years after the event, unambiguously indicate that the accumulation of tectonic stresses caused the growth in tidal amplitudes, whereas the stress release by the earthquake caused their diminution. This does not however mean that stress accumulation is accompanied by a decrease in the elastic moduli and that the release of stresses is accompanied by the growth of elastic moduli all over the source area. As was shown in (Molodenskii M.S. et al., 2012), even in the simplest model of spatially homogeneous variations of elastic modules, the variations in tidal tilts are an odd function of the distance from the epicenter. Therefore, irrespective of whether the elastic moduli decrease or increase, the amplitudes of tidal tilts should decrease in some areas and increase in other areas. Hence, the very fact of the growth of tidal tilt amplitudes with time cannot be considered as a sign of the growth of tectonic stresses. To be positive about the latter, one should make sure that the consistent (unidirectional) changes have been observed during a sufficiently long time interval and that their magnitudes were significantly larger than the measurement errors. Hence, it is important to reliably estimate the errors of the observational data.     

Tectonic stress accumulation in the region of the Kuril–Kamchatka Island Arc system

The time variations in the tidal response of the medium in 2011–2015 according to the measurements at the global seismographic network (GSN) in Kamchatka are considered. Based on the data from the horizontal pendulums recording the eastward tilts at the station, it is established that there was a linear growth in the tidal tilt amplitudes up to May 24, 2013 due to the changes in the elastic moduli caused by tectonic stress accumulation. The growth phase was followed by the decline in the tidal tilt amplitudes induced by the release of stresses after the Sea-of-Okhotsk earthquake.     

Time variations of the stresses in the source region of the Tohoku earthquake of March 11, 2011 (<Emphasis Type="Italic">M</Emphasis> = 9) from tidal response data

The idea of forecasting the earthquakes by continuous monitoring the time variations of tidal responses was suggested by E. Nishimura in 1950. However, the implementation of this idea has only become possible with the deployment of the GSN and F-net global seismic networks. Below, we present the new method for identifying the time variations of tidal response of the medium in seismically active regions using the data from these networks. We show that our approach significantly increases the sensitivity and time resolution of the standard methods of moving spectral analysis. The analysis of the data from the horizontal pendulums which record the northward tilts demonstrates the slow growth of the tidal tilts during six years before the earthquake, which is followed by the instantaneous drop of the amplitudes at the moment of the earthquake. During four years after this drop, the tidal amplitudes remained at a noticeably lower level than their average preearthquake values. These changes in the tidal amplitudes indicate the nonlinear response of the medium in the presence of large tectonic     

Fractured reservoir delineation using multicomponent seismic data

The characteristic seismic response to an aligned-fracture system is shear-wave splitting, where the polarizations, time-delays and amplitudes of the split shear waves are related to the orientation and intensity of the fracture system. This offers the possibility of delineating fractured reservoirs and optimizing the development of the reservoirs using shear-wave data. However, such applications require carefully controlled amplitude processing to recover properly and preserve the reflections from the target zone. Here, an approach to this problem is suggested and is illustrated with field data. The proposed amplitude processing sequence contains a combination of conventional and specific shear-wave processing procedures. Assuming a four-component recording (two orthogonal horizontal sources recorded by two orthogonal horizontal receivers), the split shear waves can be simulated by an effective eigensystem, and a linear-transform technique (LTT) can be used to separate the recorded vector wavefield into two principal scalar wavefields representing the fast and slow split shear waves. Conventional scalar processing methods, designed for processing P-waves, including noise reduction and stacking procedures may be adapted to process the separated scalar wavefields. An overburden operator is then derived from and applied to the post-stacked scalar wavefields. A four-component seismic survey with three horizontal wells drilled nearby was selected to illustrate the processing sequence. The field data show that vector wavefield decomposition and overburden correction are essential for recovering the reflection amplitude information in the target zone. The variations in oil production in the three horizontal wells can be correlated with the variations in shear-wave time-delays and amplitudes, and with the variations in the azimuth angle between the horizontal well and the shear-wave polarization. Dim spots in amplitude variations can be correlated with local fracture swarms encountered by the horizontal wells. This reveals the potential of shear waves for fractured reservoir delineation.     

Variations of the lunar geomagnetic tide in the Indian region

The seasonal variations of the lunar geomagnetic tide are analysed at a group of stations around the longitude of India. The position of the focus of the lunar ionospheric current system is found to move with season and to disappear in northern winter. A year-to-year variability of the phases is also demonstrated. The phase relationships indicate the presence of antisymmetric atmospheric tidal modes of various strengths in different seasons. The different lunar Hough mode amplitudes, derived earlier, may also explain the observed September maximum in the lunar horizontal magnetic component at the equator.     

Meteor wind radar observations of tidal amplitudes over a low-latitude station Trivandrum (8.5°N, 77°E): Interannual variability and the effect of background wind on diurnal tidal amplitudes

Based on the horizontal winds measured using SKiYMET meteor wind radar during the period of June 2004–May 2007, the seasonal and interannual variability of the diurnal and semidiurnal amplitudes and phases in the mesospheric and lower thermospheric (MLT) region over a low-latitude station Trivandrum (8.5°N) are investigated. The monthly values of amplitudes and phases are calculated using a composite day analysis. The zonal and meridional diurnal tidal amplitudes exhibit both annual and semiannual oscillations. The zonal and meridional components of semidiurnal tide show a significant annual oscillation. The phase values of both diurnal and semidiurnal tides exhibit annual oscillation above 90 km. The effect of background wind in the lower atmosphere on the strength of diurnal tidal amplitudes in the MLT region is studied. The effect of diurnal tides on the background wind in the lower thermosphere is also discussed.     

Temporal variations in the tidal response of the medium in the vicinities of the sources of catastrophic earthquakes

The idea of predicting earthquakes by continuously monitoring temporal variations in the tidal response of the medium was suggested by Beaumont and Berger in 1974. However, it became possible to implement the idea only recently. This possibility has arisen due to the deployment of Global Seismic Network (GSN), which collects the data on tidal tilts and gravity in the epicenters of strong earthquakes before and after the strongest events. In this paper, we present the results of model analytical and numerical calculations of the elastic displacements of the Earth’s surface caused by the earthquakes and their preparatory processes. The analytical calculations are limited to the model of a uniform elastic halfspace; the numerical calculations, in addition to this model, also cover the models with radially heterogeneous distributions of elastic moduli in the crust and in the upper mantle, which are determined by the PREM model. We describe the results of modeling temporal variations in the tidal response of the medium in the vicinity of the source of a catastrophic earthquake. The model of seismic source is specified by the length and the orientations of the fault plane and by the value of the discontinuity in the tangential component of the displacement vector on the opposite sides of the fault. The model is based on the GPS data on the horizontal and vertical displacements of the Earth’s surface. We suggest the method for determining temporal changes in the tidal response of the medium in the seismically active regions. This method improves the sensitivity and time resolution of the standard techniques of sliding-window analysis by more than an order of magnitude. The comparative analysis of temporal variations in the tidal response of the medium in the zones of the magnitude 9 earthquake in Japan (March 9, 2011) illustrates the described approach.

     

Temporal variations in the tidal response of the medium in the vicinities of the sources of catastrophic earthquakes

The idea of predicting earthquakes by continuously monitoring temporal variations in the tidal response of the medium was suggested by Beaumont and Berger in 1974. However, it became possible to implement the idea only recently. This possibility has arisen due to the deployment of Global Seismic Network (GSN), which collects the data on tidal tilts and gravity in the epicenters of strong earthquakes before and after the strongest events. In this paper, we present the results of model analytical and numerical calculations of the elastic displacements of the Earth??s surface caused by the earthquakes and their preparatory processes. The analytical calculations are limited to the model of a uniform elastic halfspace; the numerical calculations, in addition to this model, also cover the models with radially heterogeneous distributions of elastic moduli in the crust and in the upper mantle, which are determined by the PREM model. We describe the results of modeling temporal variations in the tidal response of the medium in the vicinity of the source of a catastrophic earthquake. The model of seismic source is specified by the length and the orientations of the fault plane and by the value of the discontinuity in the tangential component of the displacement vector on the opposite sides of the fault. The model is based on the GPS data on the horizontal and vertical displacements of the Earth??s surface. We suggest the method for determining temporal changes in the tidal response of the medium in the seismically active regions. This method improves the sensitivity and time resolution of the standard techniques of sliding-window analysis by more than an order of magnitude. The comparative analysis of temporal variations in the tidal response of the medium in the zones of the magnitude 9 earthquake in Japan (March 9, 2011) illustrates the described approach.     

Analysis of 19-year tidal data

19-year tidal data of the 3 stations, Huludao, Qinhuangdao and Kanmen, have totally been analysed, and the amplitudes and phases of 472 tidal constituents have been calculated with a resolution of Δσ⩾ 0.002 2°/h. Based on the draconitic tide, the anornalistic tide and pole tide obtained, the ultra-long-period variations of the mean sea level have been predicted. The annual tidal analysis of 19-year data at the above-mentioned stations and at Tanggu, Longkou has been carried out. The stability of the annual tidal analysis has been investigated with regard to the astronomical factors, the nonlinear effects and the variations of sea-bottom topography.     

中国大陆井水温度潮汐动态的统计与调和分析

用收集到的全国356个井水温度测点的数据, 分析了水温对地球固体潮汐的响应, 统计出 35个存在水温潮汐现象的测点。 利用Baytap-G调和分析方法, 计算了水温潮汐分波的振幅、 振幅比和相位差。 结果表明: 水温潮汐现象是一类较普遍的地球物理现象, 其机制与水位潮汐相关, 可用水动力学模式解释; 水温潮汐变化特征还受太阳辐射热、 含水层和地温的影响, 自流井水温记录潮汐现象的能力高于非自流井、 东部地区水温测点记录潮汐现象的能力高于西部, 与太阳辐射热的影响有关, 在含水层附近的水温测点, 其潮汐动态比其他井段显著, 在受地温影响较大的井段, 水温的潮汐变化幅度与水温梯度成正比; 水温的应力-应变灵敏度量级为0.01～10℃/10^-6m·s^-2。     

Climatology of the semidiurnal tide at 52–56°N from ground-based radar wind measurements 1985–1995

Long-term wind measurements carried out at 6 northern midlatitude sites (Saskatoon, Sheffield, Juliusruh, Collm, Obninsk, Kazan) are investigated to establish a climatology of the semidiurnal tide in the mesopause region for the narrow latitudinal range between 52°N and 56°N. Comparison of zonal and meridional components shows that in general the horizontal components are circularly polarized. Intercomparison of amplitudes and phases generally shows good agreement between the results from the different measuring systems. The results are compared with an empirical model of the semidiurnal tide. The longitudinal variation of the semidiurnal tide is small in summer, but the tidal amplitudes in winter are larger at Saskatoon and Kazan, compared with the results from the other sites. The possible influence of wave–tidal interaction in the stratosphere on the interannual variability of this difference is discussed.     

Elastic moduli of dry rocks containing spheroidal pores based on differential effective medium theory

Differential effective medium (DEM) theory is applied to determine the elastic properties of dry rock with spheroidal pores. These pores are assumed to be randomly oriented. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, we derive analytical solutions of the bulk and shear moduli for dry rock from the differential equations by applying an analytical approximation for dry-rock modulus ratio, in order to decouple these equations. Then, the validity of this analytical approximation is tested by integrating the full DEM equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores (i.e., the pore aspect ratio is equal to 1) are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyze the relationship between the elastic moduli and porosity or pore shapes, and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formula for the sandstone experimental data show that the analytical formulae can accurately predict the variations of elastic moduli with porosity for dry sandstones. The effective elastic moduli of these sandstones can be reasonably well characterized by spheroidal pores, whose pore aspect ratio was determined by minimizing the error between theoretical predictions and experimental measurements. For sandstones the pore aspect ratio increases as porosity increases if the porosity is less than 0.15, whereas the pore aspect ratio remains relatively stable (about 0.14) if the porosity is more than 0.15.     

Simulation of full-waveform log in saturated cracked formations using Hudson's approach

We study the propagation of elastic waves that are generated in a fluid‐filled borehole surrounded by a cracked transversely isotropic medium. In the model studied the anisotropy and borehole axes coincide. To obtain the effective elastic moduli of a cracked medium we have applied Hudson's theory that enables the determination of the overall properties as a function of the crack orientation in relation to the symmetry axis of the anisotropic medium. This theory takes into account the hydrodynamic mechanism of the elastic‐wave attenuation caused by fluid filtration from the cracks into a porous matrix. We have simulated the full waveforms generated by an impulse source of finite length placed on the borehole axis. The kinematic and dynamic parameters of the compressional, shear and Stoneley waves as functions of the matrix permeability, crack orientation and porosity were studied. The modelling results demonstrated the influence of the crack‐system parameters (orientation and porosity) on the velocities and amplitudes of all wave types. The horizontally orientated cracks result in maximal decrease of the elastic‐wave parameters (velocities and amplitudes). Based on the fact that the shear‐ and Stoneley‐wave velocities in a transversely isotropic medium are determined by different shear moduli, we demonstrate the feasibility of the acoustic log to identify formations with close to horizontal crack orientations.     

Estimation of coseismic deformation, poroelasticity, and fracturing of rocks from the data on water level in a borehole

Variations in the water level in boreholes emerge in response to tidal, baric, and tectonic forcing. We analyze the data on atmospheric pressure and water level recorded in the boreholes located in the mid-latitude Eurasia (45°?C55°N) from Western Europe (Belgium, Uccle), Siberia (coastal area of Lake Baikal, Talaya River) to Far Eastern Russia (the Bychikha borehole near Khabarovsk and the boreholes on the Kamchatka Peninsula and Kurils). The response of the water level in a borehole to periodic tidal and baric impacts is investigated. In this case, water level variations reflect areal (lateral) and vertical deformations, which allows estimating the elastic moduli and porosity of the confined aquifer in a static model. Measurements in the boreholes drilled in the fractured solid rock enable determining the geometric parameters of the fractures. The possibility to apply the method for evaluating tectonic deformations is discussed. Application of tidal coefficients of boreholes for determining the coseismic deformation is demonstrated by the example of the Kultuk earthquake (Lake Baikal, August 27, 2008, M = 6.3).     

Constraining potential earthquake sources from the geophysical data

The spatial models describing the physico-mechanical properties of the rocks within the seismically active segment of the Altai–Sayan region are constructed from the ground-based geophysical data. The comparative analysis of their probability density functions at the nodes of the spatial grid covering the studied domain and at the hypocenters of the previous earthquakes shows that the bulk and shear moduli are the most efficient markers of the weakened crustal zones, which are prone to earthquakes. The algorithm for constraining the potential earthquake sources based on the spatial distributions of the elastic moduli of the rocks is suggested. When applied to the Taellin segment of the Altai–Sayan region, this algorithm has localized four echelons of the potential source zones of earthquakes at different depths in the crust. The horizontal positions of two of these zones were delineated by the previous studies based on the ground observations of seismicity, whereas the other two zones have been identified by the suggested algorithm for the first time.     

Impact of tidal power dams upon tides and environmental conditions in the Sea of Okhotsk

The transformation of natural tidal sea-level and currents is studied resulting from large-scale tidal power plant (TPP) dams in bays of the Sea of Okhotsk (SO). Some effects due to this transformation are estimated based on predictive modelling and a number of expected changes in amplitudes and phases, and spectral composition of tidal oscillations are described. Changes of morphometric properties of basins change the character of tidal motions even on significant distance from a dam. That is why, it is impossible to estimate this impact as usual boundary-value problems. The problem is solved based on “impedance” conditions on the open boundary of the model area, allowing to take into account the radiation of the additional perturbations induced by both waves reflected from the dam and nonlinear effects inside the area. In general, the transformation effects are proportional to the dam size and depend essentially on the dam location, the creation of which can change dissipative and resonance properties of the bays. The changes in tidal energetics of SO due to the dam construction are also considered to show noticeable reconstruction of horizontal energy fluxes and changes in the energy dissipation. Possible environmental consequences are related mainly to the transformation of tidal currents.     

A semi-empirical velocity-porosity-clay model for petrophysical interpretation of P- and S-velocities

We design a velocity–porosity model for sand-shale environments with the emphasis on its application to petrophysical interpretation of compressional and shear velocities. In order to achieve this objective, we extend the velocity–porosity model proposed by Krief et al., to account for the effect of clay content in sandstones, using the published laboratory experiments on rocks and well log data in a wide range of porosities and clay contents. The model of Krief et al. works well for clean compacted rocks. It assumes that compressional and shear velocities in a porous fluid-saturated rock obey Gassmann formulae with the Biot compliance coefficient. In order to use this model for clay-rich rocks, we assume that the bulk and shear moduli of the grain material, and the dependence of the compliance on porosity, are functions of the clay content. Statistical analysis of published laboratory data shows that the moduli of the matrix grain material are best defined by low Hashin–Shtrikman bounds. The parameters of the model include the bulk and shear moduli of the sand and clay mineral components as well as coefficients which define the dependence of the bulk and shear compliance on porosity and clay content. The constants of the model are determined by a multivariate non-linear regression fit for P- and S-velocities as functions of porosity and clay content using the data acquired in the area of interest. In order to demonstrate the potential application of the proposed model to petrophysical interpretation, we design an inversion procedure, which allows us to estimate porosity, saturation and/or clay content from compressional and shear velocities. Testing of the model on laboratory data and a set of well logs from Carnarvon Basin, Australia, shows good agreement between predictions and measurements. This simple velocity-porosity-clay semi-empirical model could be used for more reliable petrophysical interpretation of compressional and shear velocities obtained from well logs or surface seismic data.     

Common-volume measurements of mesospheric winds using radar and optical instruments: 1. Comparison of observations

The Millstone Hill incoherent scatter radar (42.6°N, 71.5°W) and the nearby Durham meteor wind radar (43.1°N, 70.9°W) have been used to study the structure of the winds in the mesosphere and lower thermosphere and to investigate the propagation of tidal components from the mesosphere into the lower thermosphere. In general, good agreement is found between the tidal wind amplitudes and phases determined by the two radars, but occasionally, some discontinuities have been observed in the vertical structure of the tidal components in the 90–110 km region. In order to validate the accuracy of the two techniques and the methodologies used in determining neutral winds, two common-volume experiments were conducted in 1996 and 1997 in which the two radar beams were overlayed at an altitude of 100 km. The horizontal components of the measured radar line-of-sight velocities during day-time periods were then compared at the overlapping altitudes of 95–100 km. Night-time measurements were also made using a Fabry–Perot Interferometer co-located with the radar at Millstone Hill which observed the Doppler shift of the atomic oxygen green line emission in the mesosphere. Good overall agreement is found between the instruments within the statistical uncertainties of the measurement techniques, although some differences have been found that are explained by consideration of the data statistics, the exact overlap of common volume within the different beam sizes, and the presence of altitude gradients and small scale irregularities in the sampled volumes of the atmosphere.     

CORRELATION PATTERNS IN CHARACTERISTICS OF SPATIALLY VARIABLE SEISMIC GROUND MOTIONS

A methodology for the investigation of the spatial variation of seismic ground motions is presented; data recorded at the SMART-1 dense instrument array in Lotung, Taiwan, during Events 5 and 39 are used in the analysis. The seismic motions are modeled as superpositions of sinusoidal functions, described by their amplitude, frequency, wavenumber and phase. For each event and direction (horizontal or vertical) analysed, the approach identifies a coherent, common component in the seismic motions at all recording stations, and variabilities in amplitudes and phases around the common component sinusoidal characteristics, that are particular for each recording station. It is shown that the variations in both the amplitudes and the phases of the motions at the station locations around the common component characteristics contribute significantly to the spatially variable nature of the motions, and, furthermore, they are correlated: increase in the variability of the amplitudes of the motions recorded at individual stations around the common amplitude implies increase in the variability of the phases around the common phase. The dispersion range of the amplitude and phase variability around their corresponding common components appear also to be associated with physical parameters. The spatially variable arrival time delays of the waveforms at the stations due to their upward travelling through the site topography, in addition to the wave passage delays identified from signal processing techniques, constitute another important cause for the spatial variation of the motions; their consideration in the approach facilitates also the identification of the correlation patterns in the amplitudes and phases. © 1997 by John Wiley & Sons, Ltd.     

Semidiurnal tides from the extended Canadian Middle Atmosphere Model (CMAM) and comparisons with TIMED Doppler interferometer (TIDI) and meteor radar observations

The extended Canadian Middle Atmosphere Model (extended CMAM) is a general circulation model, which extends from the surface to about 210 km. Spatial complex spectral analysis is applied to horizontal winds simulated by the extended CMAM to obtain semidiurnal tidal amplitudes and phases (from e5 to w5) in the mesosphere and lower thermosphere (MLT) region. The dominant w2 migrating component and the presence of eight nonmigrating tides (w3, w4, w5, e1, e2, e3, e4 and e5) in the mid-latitudes are identified. Components w1 and s0, which tend to maximize at high latitudes, will be discussed separately in a later paper. The migrating semidiurnal tide (w2) has amplitudes reaching over 20 m s⁻¹ for both zonal and meridional winds in the mid-latitude region. Its form compares well to the published results. The amplitudes of nonmigrating semidiurnal tides are non-negligible compared with the migrating semidiurnal tides. The amplitudes for w3 and e2 exceed 12 and 8 m s⁻¹, respectively.Comparisons are made with four nonmigrating semidiurnal components (w3, w4, e1 and e2) derived from the TIMED Doppler interferometer (TIDI) wind measurements between 85 and 105 km altitude and between 45°S and 45°N latitude. Overall, the basic CMAM and TIDI latitudinal structures of the amplitudes agree well and the agreement between the annual mean amplitudes varies with component. Relative to the TIDI results, the CMAM seasonal variations of w4 are in good agreement, of e2 are in reasonable agreement, of w3 are in partial agreement and of e1 are in poor agreement.The 11 semidiurnal components from the model are superimposed to generate the total semidiurnal winds at Jakarta (6°S, 106°E) and Kototabang (0°, 100°E) and are compared with measurements from two equatorial meteor radar stations at these sites. The relative contributions of components to the reconstructed amplitude vary from month to month. The CMAM reconstructions are generally larger than the radar results by a factor varying between one and two. The phases in the radar data are typically stationary with respect to height, whereas they generally decrease with height in the CMAM reconstruction.