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1

Determination of the seismic structure of the Earth based on joint analysis of gravimetric and seismometric data – a case study

Karkowska Kamila, Wilde-Piórko Monika, Dykowski Przemysław, Sękowski Marcin, Polkowski Marcin

Geology, Geophysics and Environment

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2024

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Vol. 50, no. 1

5--22

EN

The evolution of the Earth’s surface is driven by external and internal forces, the latter of which can only be studied indirectly. Knowledge about the structure of the Earth’s interior is very important for modeling and predicting the processes occurring at the surface. This study presents a new concept of joint analysis of the gravimetric and seismometric recordings of earthquakes for determining the seismic structure of the Earth down to the depth of 1250 km. The proposed method allows the use of gravimetric data without the known full transfer function of the instrument. Group velocity dispersion curves of the fundamental mode of Rayleigh waves up to the period of 550 s are measured based on the joint analysis of the recordings of superconducting gravimeter and broadband seismometers operating at the same location in five testing sites in Europe, allowing for the exploration of a broader response for incoming seismic waves. Averaged dispersion curves for earthquakes around the world for each site are inverted by the weighted linear inversion and Monte Carlo methods to estimate the distribution of shear-wave seismic velocity in the Earth’s mantle. A comparison of the deterministic and probabilistic inversion methods can excellently demonstrate surface waves’ ability to determine the Earth’s mantle structure. The inversion results are compared with the global ak135 seismic model (Kennett et al. 1995) to verify the proposed method.

2

Formulas for the H/V ratio of Rayleigh waves in incompressible pre-stressed half-spaces

Chi Vinh P. C., Tuan T. T., Hue L. T.

Archives of Mechanics

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2018

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Vol. 70, nr 2

131--150

EN

In this paper, the propagation of a Rayleigh wave in an incompressible pre-stressed elastic half-space is considered. The main aim is to derive exact formulas for the H/V ratio, the ratio of the amplitude of the horizontal displacement to the amplitude of the vertical displacement of the Rayleigh wave. First, the H/V ratio equations are obtained using the secular equation and the relation between the H/V ratio and the Rayleigh wave velocity. Then, the exact formulas for the H/V ratio have been derived for a general strain-energy function by analytically solving the H/V ratio equations. These formulas are then specified to several particular strain-energy functions. Since the obtained formulas are exact and totally explicit, they will be a good tool for nondestructively evaluating pre-stresses of structures before and during loading.

3

Dispersion of Rayleigh Waves in a Microstructural Couple Stress Substrate Loaded with Liquid Layer Under the Effects of Gravity

Sharma V., Kumar S.

Archives of Acoustics

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2018

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Vol. 43, No. 1

11--20

EN

Bone loss is one of the serious health issues in bedridden patients or young generation due to lack of physical activities. Mechanical forces are exerted on the bones through ground reaction forces, liquid loadings and by other contraction activities of the muscles. We are assuming an isotropic half-space with mechanical properties equivalent to that of bone exhibiting microstructures. Consistent couple stress theory introduces an additional material parameter called characteristic length which accounts for inner microstructure of the material. Dispersion relations for leaky Rayleigh waves are derived by considering a model consisting of couple stress half space under the effects of gravity and loaded with inviscid liquid layer of finite thickness or a liquid half space. Impact of the gravity, liquid loadings and microstructures of the material are investigated on propagation of leaky Rayleigh type waves. Phase velocity of leaky Rayleigh waves is studied for five different values of characteristic length parameter which are of the order of internal cell size of the considered material. Variations in phase velocity of leaky Rayleigh waves are also studied under the effect of gravity parameter and thickness of liquid loadings.

4

Characterization of Site Conditions for Selected Seismic Stations in Eastern Part of Romania

Grecu B., Zaharia B., Diaconescu M., Bala A., Nastase E., Constantinescu E., Tataru D.

Acta Geophysica

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2018

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Vol. 66, no. 2

153--165

EN

Strong motion data are essential for seismic hazard assessment. To correctly understand and use this kind of data is necessary to have a good knowledge of local site conditions. Romania has one of the largest strong motion networks in Europe with 134 real-time stations. In this work, we aim to do a comprehensive site characterization for eight of these stations located in the eastern part of Romania. We make use of a various seismological dataset and we perform ambient noise and earthquake-based investigations to estimate the background noise level, the resonance frequencies and amplification of each site. We also derive the Vs30 parameter from the surface shear-wave velocity profiles obtained through the inversion of the Rayleigh waves recorded in active seismic measurements. Our analyses indicate similar results for seven stations: high noise levels for frequencies larger than 1 Hz, well defined fundamental resonance at low frequencies (0.15-0.29 Hz), moderate amplification levels (up to 4 units) for frequencies between 0.15 and 5-7 Hz and same soil class (type C) according to the estimated Vs30 and Eurocode 8. In contrast, the eighth station for which the soil class is evaluated of type B exhibits a very good noise level for a wide range of frequencies (0.0120 Hz), a broader fundamental resonance at high frequencies (~ 8 Hz) and a flat amplification curve between 0.1 and 3-4 Hz.

5

Effective boundary condition method and Rayleigh waves in orthotropic half-spaces coated by a thin layer with sliding contact

Vinh P. C., Anh V. T.

Archives of Mechanics

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2015

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Vol. 67, nr 6

477--498

EN

This paper studies the propagation of Rayleigh waves in an orthotropic elastic half-space coated by a thin orthotropic elastic layer. The half-space and the layer are assumed to be either compressible or incompressible and they are in sliding contact with each other. The main aim of the paper is to establish approximate secular equations of the wave for all (four) possibilities of a compressible or incompressible half-space covered with a compressible or incompressible thin layer, except the case of a compressible half-space coated by a compressible layer that has been considered [19]. In order to do that, the effective boundary condition method is employed and the approximate third-order secular equations regarding the dimensionless thickness of the layer are derived. It is shown that these approximate secular equations have a high accuracy. Based on the obtained secular equations, the effect of incompressibility on the Raleigh wave propagation is considered through some numerical examples. It is shown that incompressibility strongly affects the Raleigh wave velocity and the effect becomes stronger when the coating is incompressible.

6

Surface wave characteristics in a micropolar transversely isotropic halfspace underlying an inviscid liquid layer

Gupta R. R., Gupta R. R.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 1

49--60

EN

The present investigation deals with the propagation of waves in a micropolar transversely isotropic half space with an overlying inviscid fluid layer. Effects of fluid loading and anisotropy on the phase velocity, attenuation coefficient, specific loss and relative frequency shift. Finally, a numerical solution was carried out for aluminium epoxy material and the computer simulated results for the phase velocity, attenuation coefficient, specific loss and relative frequency shift are presented graphically. A particular case for the propagation of Rayleigh waves in a micropolar transversely isotropic half-space is deduced and dispersion curves are plotted for the same as functions of the wave number. An amplitude of displacements and microrotation together with the path of surface particles are also calculated for the propagation of Rayleigh waves in the latter case.

7

Rayleigh waves in an incompressible orthotropic half-space coated by a thin elastic layer

Vinh P. C., Linh N. T., Anh V. T.

Archives of Mechanics

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2014

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Vol. 66, nr 3

173--184

EN

The present paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The halfspace and the layer are both incompressible and they are in welded contact to each other. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method an approximate secular equation of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From it an approximate formula of third-order for the velocity of Rayleigh waves is obtained and it is a good approximation. The obtained approximate secular equation and formula for the velocity will be useful in practical applications.

8

Surface waves in fibre-reinforced anisotropic solid elastic media under the influence of gravity

Sethi M., Gupta K. C., Gupta D., Manisha

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

177--188

EN

The aim of the present paper is to investigate surface waves in an anisotropic, elastic solid medium under the influence of gravity. First, a theory of generalised surface waves was developed and then it was employed to investigate particular cases of waves, viz., Stoneley and Rayleigh, Love type. The wave velocity equations were obtained for different cases and they are in well agreement with the corresponding classical result, when the effect of gravity, viscosity as well as parameters for fibre-reinforcement of the material medium are ignored.

9

Propagation of waves in generalized thermoelastic continua with two temperature

Kaushal S., Sharma N., Kumar R.

International Journal of Applied Mechanics and Engineering

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2010

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Vol. 15, no 4

1111-1127

EN

The present investigation is concerned with the following two problems. (i) Reflection and transmission of thermoelastic waves between two thermoelastic/ thermoelastic solids with two temperatures at an imperfect interface. The amplitude ratios of different reflected and transmitted waves are obtained and deduced for normal force stiffness, transverse force stiffness, thermal contact conductance and perfect bonding. The variations of amplitude ratios with angle of incidence are shown graphically for the longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. (ii) Propagation of Rayleigh waves in a thermoelastic half-space with two temperature at the free surface. The phase velocity and attenuation coefficient are obtained and presented graphically to depict the effect of two temperatures. Some special cases of interest are deduced from the present investigation.

10

Generalized Rayleigh waves in thermoelastic solids under viscous fluid loading

Sharma J. N., Sharma R., Sharma Y. D.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 1

217-238

EN

The paper is aimed to study the propagation of Rayleigh surface waves in a homogeneous isotropic, thermally condueting, and elastic solid halfspace underlying a viscous liquid semi space in the context of generalized theories of thermoelasticity. The investigation is based on modelling the viscous liquid as a hypothetical solid in addition to conduction-convection condition of heat transfer at the interface. After developing the mathematical model, boundary conditions and formal solutions, the secular equations for a thermoelastic solid in closed form and isolated mathematical conditions for generalized Rayleigh waves (Stoneley waves), in complete forms are derived. The amplitude ratios of solid and liquid displacements and temperature change on the surface (interface) are obtained analytically. The surface particle motion has also been discussed and found to be elliptical. The semi-major and semi-minor axes, eccentricity and inclination of major axes with the wave normal are computed analytically and analyzed numerically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum-epoxy composite material solid (half space) underlying water, in the case of both light and heavy semi spaces. The dispersion curves, attenuation coefficient profiles and amplitude ratios of surface displacements, temperature change in the solid half space for generalized Rayleigh waves are presented and illustrated graphically in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement. The present analysis is useful in electronics and navigation applications.

11

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

Acharya D.P., Maji Ch.

Acta Geophysica

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2007

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Vol. 55, no. 4

554-576

EN

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as ob-tained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.

12

Waves in thermoelastic materials with memory in generalized thermoelasticity

Baksi A., Bera R. K.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

771-785

EN

Many studies on classical thermoelastoicity have been denoted to materials with memory Nunziato, Chen and Gurtin, whereas few on generalized thermoelasticity address materials with memory. The present paper deals with the wave propagation in materials with memory in generalized thermoelasticity. Plane progressive waves and Rayleigh waves have been discussed in detail. The results show appreciable differences with those in the usual classical thermoelasticity theory.

13

Rayleigh waves speed in transversely isotropic material

Rehman A., Khan A., Ali A.

Engineering Transactions

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2006

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Vol. 54, iss. 4

323-328

EN

Rayleigh wave speed in transversely isotropic material is studied. A very simple technique is adopted to solve the secular equation. Speed in some transversely isotropic materials is calculated.

14

Formulas for the Rayleigh wave speed in orthotropic elastic solids

Vinh P. Chi, Ogden R. W.

Archives of Mechanics

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2004

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Vol. 56, nr 3

247-265

EN

Formulas for the speed of Rayleigh waves in orthotropic compressible elastic materials are obtained in explicit form by using the theory of cubic equations. Different formulas are obtained by using different forms of the (cubic) secular equation. Each formula is expressed as a continuous function of three dimensionless material parameters, which are the ratios of certain elastic constants. It is interesting to note that one of the formulas includes as a special case the formula obtained recently by Malischewsky for isotropic materials.

15

High frequency solution of elastodynamic stress intensity factors due to the diffraction of plane longitudinal wave by an edge crack in a semi-infinite medium

Pramanik R. K., Pal S. C., Ghosh M. L.

Journal of Technical Physics

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2002

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Vol. 43, no 2

113-132

EN

A harmonic in time, plane longitudinal wave is incident on a half-space containing a vertical edge crack. Both the incident field as well as the scattered field have been decomposed into symmetric and antisymmetric fields with respect to the plane of the crack, so that the problem is reduced to the boundary value problem for a 90° wedge. In both the symmetric and antisymmetric problem, incident body waves are at first diffracted by the edge of the crack. For a high frequency solution, the diffracted body wave rapidly decreasing after a few wave-lengths, the significant part of the diffracted wave is the Rayleigh wave which is reflected back from the corner of the wedge giving rise to a Rayleigh wave diffracted by the crack tip. This process of reflection of surface wave from the corner of the wedge and subsequent diffraction by the crack tip continues. Considering the contribution from the incident body waves and all the reflected Rayleigh waves, the stress intensity factors have been determined and their dependence on the frequency and on the angle of incidence has been depicted by means of graphs.

16

Propagation of Rayleigh waves over a thermo-viscoelastic half space with a slightly curved free space

Pal P. Ch., Kumar L.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 4

363-373

EN

Propagation of Rayleigh waves over a thermo-viscoelastic half space with a slightly curved (cylindrical) free space is considered. It is shown that, like in the case of curved elastic space, the surface displacement components and the temperature for the curved thermo-viscoelastic half space can be expressed in terms of the corresponding quantities in a plane-faced half space with a unit surface line source. Expressions for corrections to the Rayleigh wave displacements due to the curvature are obtained. Some special cases are also derived, and solution of frequency equation is considered. The roots of frequency equations are obtained approximately and numerical results are obtained.