Comparative study of temporal variations in the earth’s gravity field using GRACE gravity models in the regions of three recent giant earthquakes

Comparative analysis of coseismic and postseismic variations of the Earth’s gravity field is carried for the regions of three giant earthquakes (Andaman-Sumatra, December 26, 2004, magnitude M _w = 9.1; Maule-Chile, February 27, 2010, M _w = 8.8, and Tohoku-Oki, March 11, 2011, M _w = 9.0) with the use of GRACE satellite data. Within the resolution of GRACE models, the coseismic changes of gravity caused by these seismic events manifest themselves by large negative anomalies located in the rear of the subduction zone. The real data are compared with the synthetic anomalies calculated from the rupture surface models based on different kinds of ground measurements. It is shown that the difference between the gravity anomalies corresponding to different rupture surface models exceeds the uncertainties of the GRACE data. There-fore, the coseismic gravity anomalies are at least suitable for rejecting part of the models that are equivalent in the ground data. Within the first few months after the Andaman-Sumatra earthquake, a positive gravity anomaly started to grow above the deep trench. This anomaly rapidly captured the area of the back-arc basin and largely compensated the negative coseismic anomaly. The processes of viscoelastic stress relaxation do not fully allow for these rapid changes of gravity. According to the calculations, even with a sufficiently low viscosity of the upper mantle, relaxation only covers about a half of the observed change of the field. In order to explain the remaining temporal variations, we suggested the process of downdip propagation of the coseismic rupture surface. The feasibility of such a process was supported by numerical simulations. The sum of the gravity anomalies caused by this process and the anomaly generated by the processes of viscoelastic relaxation accounts well for the observed changes of the gravity field in the region of the earthquake. The similar postseismic changes of gravity were also detected for the region of the Tohoku-Oki earthquake. Just as in the case discussed above, this earthquake was also followed by a rapid growth of a positive postseismic anomaly, which partially counterbalanced the negative coseismic anomaly. The time variations of the gravity field in the region of the Maule-Chile earthquake differ from the pattern of changes observed in the island arcs described above. The postseismic gravity variations are in this case concentrated in a narrower band above the deep trench and shelf, and they do not spread over the continental territory, where the negative coseismic anomaly is located. These discrepancies reflect the difference in the geodynamical settings of the studied earthquakes.     

Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients are applied to a spectral representation of Newton’s integral. In this study we utilise Molodensky’s truncation coefficients in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms of Molodensky’s truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data.     

Green’s function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green’s function,an essential representation of water-saturated ground under moving excitation,to simulate ground borne vibration from trains.First,general solutions to the governing equations of poroelastic medium are derived by means of integral transform.Secondly,the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground,which results in the matrix of the Green’s function.Then the Green’s function is combined into a train-track-ground model,and is verified by typical examples and a field test.Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area.The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure.The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil.When the train speed is equal to the velocity of the Rayleigh wave,the Mach cone appears in the simulated wave field.The proposed Green’s function is an appropriate representation for a layered ground with shallow ground water table,and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.     

Convection in anelastic models of the Earth’s liquid core

The effects of adiabatic cooling on the convection in the anelastic model of the liquid core of the Earth are considered. It is shown that even minor adiabatic cooling causes significant changes in the pattern of the convection, shifting the peak in the convection intensity to the inner part of the core. Just as in the Boussinesq model, both direct and inverse kinetic energy cascades are simultaneously present, and the direct cascade of entropy is observed.     

Reflectionless acoustic gravity waves in the Earth’s atmosphere

The vertical wave propagation in an inhomogeneous compressible atmosphere is studied in the framework of a linear theory. Under specific conditions imposed on atmospheric parameters, solutions can be found in the form of travelling waves with variable amplitudes and wave numbers that do not reflect in the atmosphere in spite of its strong inhomogeneity. Model representations for the sound speed have been found, for which waves can propagate in the atmosphere without reflection. A wave energy flux retains these reflectionless profiles, which confirms that energy can be transferred to high altitudes. The number of these model representations is fairly large, which makes it possible to approximate real vertical distributions of the sound speed in the Earth??s atmosphere using piecewise reflectionless profiles. The Earth??s standard atmosphere is shown to be well approximated by four reflectionless profiles with weak jumps in the sound speed gradient. It has been established that the Earth??s standard atmosphere is almost completely transparent for the considered vertical acoustic waves in a wide range of frequencies, which is confirmed by observational data and conclusions derived using numerical solutions of original equations.     

Transformation and absorption of MHD oscillations in plane-stratified models of the Earth’s magnetosphere

Geomagnetism and Aeronomy - The process of resonant transformation of fast magnetosonic (FMS) waves originating from the solar wind in Alfvén and slow magnetosonic (SMS) oscillations in the...     

Determination of the Earth’s free core nutation parameters by using tidal gravity data

The Earth’s free core nutation (FCN) is a retrograde eigenmode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth.     

The effect of wind on the gravity wave propagation in the Earth’s ionosphere

The effect of ionospheric wind on the gravity wave propagation is studied. These waves arise in the ionosphere due to intensification of their sources near the Earth’s surface during enhanced seismic activity. The influence of the wind on these waves is connected with the Ampere’s force that produces the ion-drag force acting on the atmosphere. This results in the occurrence of the discrete wave spectrum the maximum of which increases in proportion to the numbers of the natural scale. Furthermore, these waves are amplified during propagation from the source region in the direction perpendicular to the wind direction. These peculiarities of the gravity waves can be used for monitoring of seismic activity based on the ionosphere sounding.     

Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.     

Comparison of Earth’s magnetospheric magnetic field models in the context of cosmic ray physics

Over the last two decades, models of the Earth’s magnetospheric magnetic field have been continuously improved to describe more precisely the different magnetospheric current systems (magnetopause current, symmetric and partial ring currents, tail currents and field aligned currents). In this paper we compare the different Tsyganenko models and the Alexeev and Feldstein model in the context of cosmic ray physics. We compare the vertical cutoff rigidity and asymptotic direction of vertical incidence obtained with these models for the January 20, 2005, ground level enhancement and for the big magnetic storm of April 6, 2000. For the event of January 20, 2005, we study the impact of the differences in asymptotic direction obtained with the models on the radiation dose computation at aircraft altitude. For the magnetic storm of April 6, 2000, we discuss the importance of the different magnetospheric current systems in causing cutoff rigidity variations. Finally we summarise the advantages and drawbacks of the different models in the context of space weather.     

Probabilistic ecological risk assessment of heavy metals in sediments from China’s major aquatic bodies

An overall and comparative ecological risk assessment of heavy metals (including Cd, Cr, Cu, Pb, Zn, Hg and As) in surface sediments from China’s eight major aquatic bodies was conducted to better understand their potential risks on a national scale. By applying the joint approach of Hakanson risk index (RI) and Monte Carlo simulation, ecological risk in this work is expressed as probability distribution of RI values instead of single point calculations to reflect the uncertainties in risk assessment process. The results show that the highest ecological risks posed by heavy metals existed in Xiangjiang River and Dianchi Lake. Although only a slim margin of high risk (651.88/600 = 1.08 and 700.61/600 = 1.17) was identified based on average RI values, the probabilities of high risk level derived from Monte Carlo simulation reached as high as 56.7 and 52.9 % in these two aquatic bodies, respectively. And the probability of low risk level was less than 1.6 %. Furthermore, the risk was mainly contributed by Hg and Cd, discharged through local intensive mining and industrial activities. The findings indicate that rigid control and effective management measures to prevent heavy metal pollution are urgently needed in China, especially for the high-risk aquatic bodies. This study shows that the joint approach can be used to identify the high risk water bodies and the major metal pollutants. It may avoid overestimating or underestimating the ecological risk and provide more decision-making support for risk alleviation in the polluted aquatic bodies.     

Impedances for induction soundings of the Earth’s mantle

Determination of impedances is necessary in order to eliminate some shortcoming of our knowledge about structures of the exciting source fields and their fickleness. The experimental impedances for induction soundings result from the impedance boundary conditions or heuristic models. The simplified models give just a rough idea of their domain of applicability. Impedances can depend on many factors, including the exciting field structures of several source types which are present in the period range of the mantle soundings (10⁴−4×10⁸ s). The problem in the mantle investigations arises if impedances measured by different methods have to be jointly inverted in order to essentially prolongate the analyzed period range and hence to increase the reliability and depth of induction soundings on land. The subject of our work is an analysis of the known magnetotelluric and magnetovariation impedances to suggest a physically substantiated approach for their joint inversions.     

On the gradient of curvature of the plumblines of the Earth’s normal gravity field and its isocurvature lines

This paper presents an approach to determine the gradient of curvature of the normal plumblines at a point P above the ellipsoid and introduces a new geometrical object which is the isocurvature line. The assumed facts are the coordinates of the point P and the formula for the normal gravity potential U. For the determination of the gradient of the normal plumbline curvature k at the point P we define a small circle on the meridian plane of P whose center is at the point P. The circle has the radius of one meter and interior D. In this circle we construct a curvature replacement function to approximate the curvature function k. This replacement function is a quotient of polynomials hence it is easy to find its partial derivatives at the point P. For the construction of replacement function we make the assumption that in the interior of the circle D the first order partial derivatives of U behave linearly and the second order partial derivatives have constant values which equal their value at the point P. Then we set the gradient of the curvature function to be equal with the gradient of the aforementioned replacement function at P. An isocurvature line of the normal gravity field passing through a point P is a curve such that the value of the function of the plumblines’ curvature k is constant and equals k(P). We give a formula to find the direction of the isocurvature line on the meridian plane and we prove that there are infinitely many isocurvature lines passing through the point P and they all lie on a special surface, the isocurvature surface.     

An approach to refined mapping of the anomalous gravity field in the Earth’s polar caps

This work describes the different sets of instruments and methodic approaches for testing the models of gravity anomalies by repeated airborne gravimetric surveys in the polar cap regions of the Earth. The survey design including the specifications for flying the survey profiles and the arrangement of the base stations in polar areas is described, and the necessary modifications of the airborne gravity metering complexes for high-latitude measurements are suggested.     

Adaptation of P-wave moment magnitude of Turkey’s earthquakes for early warning purpose

Journal of Seismology - The determination of an earthquake’s magnitude correctly is vital to understand the situation and prevent loss of lives and planning first organization for the rescue...     

Ellipsoidal area mean gravity anomalies — precise computation of gravity anomaly reference fields for remove-compute-restore geoid determination

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation (‘ellipsoidal area means’) by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values.     

Accurate determination of calibration factor for tidal gravity observation of a GWR-superconducting gravimeter

Introduction The superconducting gravimeters (SGs) are widely used to observe the change in temporal and spatial gravity field by many countries along the world, considering their characteristics as of the high-precision, good continuity and stability. By using the temporal variation of the tidal grav-ity obtained from the global network of SGs, the Global Geophysics Project (GGP) aims at some hot problems in geophysics and geodynamics (SUN, HSU, 1997). The original observations of the c…     

Reproducing kernel and Galerkin��s matrix for the exterior of an ellipsoid: Application in gravity field studies

In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary-value problems are mentioned. Subsequently a weak formulation of Neumann??s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin??s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach), based on an approximation version of Legendre??s ordinary differential equation, resulting from the method of separation of variables in solving Laplace??s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations.