• Coupled systems mechanics
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• v.12 no.4
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• pp.337-364
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• 2023

The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.335-354
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• 2023

In this study, analysis of wave propagation characteristics for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates is performed using first-order shear deformation theory (FSDT) and nonlocal strain gradient theory. Uniform distribution (UD) and three types of functionally graded distributions of carbon nanotubes (CNTs) are assumed. The effective mechanical properties of the FG-CNTRC nanoplate are assumed to vary continuously in the thickness direction and are approximated based on the rule of mixture. Also, the governing equations of motion are derived via the extended Hamilton's principle. In numerical examples, the effects of nonlocal parameter, wavenumber, angle of wave propagation, volume fractions, and carbon nanotube distributions on the wave propagation characteristics of the FG-CNTRC nanoplate are studied. As represented in the results, it is clear that the internal length-scale parameter has a remarkable effect on the wave propagation characteristics resulting in significant changes in phase velocity and natural frequency. Furthermore, it is observed that the strain gradient theory yields a higher phase velocity and frequency compared to those obtained by the nonlocal strain gradient theory and classic theory.

• Economic and Environmental Geology
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• v.34 no.4
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• pp.375-383
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• 2001

We extracted sea surface heights(SSH) from the TopexJPoseidon(T/P) radar altimeter data to compare with fhe SSH estimated from in-situ lide gauges(T/G) at Ulleungdo, Pohang, and SockcholMucko sites. Selection criteria such as wet/dry troposphere, ionosphere, and ocean tide were used to estimate accurate SSH. For time series analysis, the one-hour interval tide gauge SSHs were resampled al lO-day interval of the satellite SSHs. The ocean tide model applied in the altimeter data processing showed periodic aliasings of 175.5 day, 87.8 day, 62J day, 58.5 day, 49.5 day and 46.0 day, and, hence, the ZOO-day filtering was applied to reduce these spectral noises. Wavenumber correlation analysis was also applied to extract common components between the two SSHs, resulting in enhancing the correlation coefficient(CC) dramatically. The original CCs between the satenite and tide gauge SSHs are 0.46. 0.26, and 0.]5, respectively. Ulleungdo shows the largest cc bec;luase the site is far from the coast resulting in the minimun error in the satellite observations. The CCs were then increased to 0.59, 030, and 0.30, respectively, after 200.day filtering, and to 0.69, 0.63. and 0.59 after removing inversely correlative components using wavenumber correlation analysis. The CCs were greatly increased by 87, 227, and 460% when the wavenumber correlation analysis was followed by 2oo-day filtering, resulting in the final CCs of 0.86, 0.85, 0.84, respectively. It was found that the best SSHs were estimated when the two methods were applied to the original data. The low-pass filtered TIP SSHs were found to be well correlated with the TIG SSHs from tide gauges, and the best correlation results were found when we applied both low-pass filtering and spectral correlation analysis to the original SSHs.

• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.132-142
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• 2009

The Tamar rift valley runs through the City of Launceston, Tasmania. Damage has occurred to city buildings due to earthquake activity in Bass Strait. The presence of the ancient valley, the Tamar valley, in-filled with soft sediments that vary rapidly in thickness from 0 to 250mover a few hundreds metres, is thought to induce a 2D resonance pattern, amplifying the surface motions over the valley and in Launceston. Spatially averaged coherency (SPAC), frequency-wavenumber (FK) and horizontal to vertical spectrum ratio (HVSR) microtremor survey methods are combined to identify and characterise site effects over the Tamar valley. Passive seismic array measurements acquired at seven selected sites were analysed with SPAC to estimate shear wave velocity (slowness) depth profiles. SPAC was then combined with HVSR to improve the resolution of these profiles in the sediments to an approximate depth of 125 m. Results show that sediments thicknesses vary significantly throughout Launceston. The top layer is composed of as much as 20m of very soft Quaternary alluvial sediments with a velocity from 50 m/s to 125 m/s. Shear-wave velocities in the deeper Tertiary sediment fill of the Tamar valley, with thicknesses from 0 to 250m vary from 400 m/s to 750 m/s. Results obtained using SPAC are presented at two selected sites (GUN and KPK) that agree well with dispersion curves interpreted with FK analysis. FK interpretation is, however, limited to a narrower range of frequencies than SPAC and seems to overestimate the shear wave velocity at lower frequencies. Observed HVSR are also compared with the results obtained by SPAC, assuming a layered earth model, and provide additional constraints on the shear wave slowness profiles at these sites. The combined SPAC and HVSR analysis confirms the hypothesis of a layered geology at the GUN site and indicates the presence of a 2D resonance pattern across the Tamar valley at the KPK site.

• Journal of the Korean earth science society
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• v.28 no.7
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• pp.936-946
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• 2007

Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to the equator) of the Rossby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation background flow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. The inversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions based on the Poisson's equation. In the second step, the forcing terms in the from of Legendre function were readily inverted due to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms were solved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to be expressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. In association with asymmetricity, the advantageous point of the balanced field as a validation method for the numerical model was addressed. In special cases where the strength of the background flow is a half of or exactly the same as the rotation rate of the Earth it was revealed that one of the zonal wavenumber components vanishes. The analytical balanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model. It was found that the normalized difference lied in the order of machine rounding, indicating the reliability of the analytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field was discussed, comparing with the flrst antisymmetric mode.

• Geophysics and Geophysical Exploration
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• v.2 no.2
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• pp.86-95
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• 1999

This paper presents an efficient three-dimensional (3-D) modeling algorithm using the extended approximation to an electric field integral equation. Numerical evaluations of Green's tensor integral are performed in the spatial wavenumber domain. This approach makes it possible to reduce computing time, to handle smoothly varying conductivity model and to remove singularity problems encountered in the integration of Green's tensor at a source point. The responses obtained by 3-D modeling algorithm developed in this study are compared with those by the full integral equation for a thin-sheet EM scattering. The extensive analyses on the performance of modeling algorithm are made with the conductivity contrasts and source frequencies. These results show that the modeling algorithm are accurate up to the conductivity contrast of 1:16 and the frequency range of 100 Hz-100 kHz. The extended Born approximation, however, may produce inaccurate results for some source and model configurations in which the electric field is discontinuous across the conductivity boundary. We performed the modeling of a composite model of which conductivity varies continuously and this shows the modeling algorithm developed in this study is efficient for 3-D EM modeling. For a cross-hole source-receiver configuration a composite model of which conductivity varies continuously can be successfully simulated using this algorithm.

• Geophysics and Geophysical Exploration
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• v.9 no.1
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• pp.73-85
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• 2006

Array observations of the vertical component of microtremors are frequently conducted to estimate a subsurface layered-earth structure on the assumption that microtremors consist predominantly of the fundamental mode Rayleigh waves. As a useful tool in the data collection, processing and analysis, the spatial autocorrelation (SPAC) method is widely used, which in practice requires a circle array consisting of M circumferential stations and one centre station (called "M-station circle array", where M is the number of stations). The present paper considers the minimum number of stations required for a circle array for efficient data collection in terms of analytical efficacy and field effort. This study first rearranges the theoretical background of the SPAC algorithm, in which the SPAC coefficient for a circle array with M infinite is solely expressed as the Bessel function, $J_0(rk)$ (r is the radius and k the wavenumber). Secondly, the SPAC coefficient including error terms independent of the microtremor energy field for an M-station circle array is analytically derived within a constraint for the wave direction across the array, and is numerically evaluated in respect of these error terms. The main results of the evaluation are: 1) that the 3-station circle array when compared with other 4-, 5-, and 9-station arrays is the most efficient and favourable for observation of microtremors if the SPAC coefficients are used up to a frequency at which the coefficient takes the first minimum value, and 2) that the Nyquist wavenumber is the most influential factor that determines the upper limit of the frequency range up to which the valid SPAC coefficient can be estimated.

• Journal of the Mineralogical Society of Korea
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• v.29 no.4
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• pp.209-220
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• 2016

Clay minerals are a major player to determine geochemical cycles of trace metals and carbon in the critical zone which covers the atmosphere down to groundwater aquifers. Molecular dynamics (MD) simulations can examine the Earth materials at an atomic level and, therefore, provide detailed fundamental-level insights related to physicochemical properties of clay minerals. In the current study, we have applied classical MD simulations with clayFF force field to dioctahedral clay minerals (i.e., gibbsite, kaolinite, and pyrophyllite) to analyze and compare structural parameters (lattice parameter, atomic pair distance) with experiments. We further calculated vibrational power spectra for the hydroxyls of the minerals by using the MD simulations results. The MD simulations predicted lattice parameters and interatomic distances respectively deviated less than 0.1~3.7% and 5% from the experimental results. The stretching vibrational wavenumber of the hydroxyl groups were calculated $200-300cm^{-1}$ higher than experiment. However, the trends in the frequencies among different surface hydroxyl groups of each mineral was consistent with experimental results. The angle formed by the surface hydroxyl group with the (001) plane and hydrogen bond distances of the surface hydroxyls were consistent with experimental result trends. The inner hydroxyls, however, showed results somewhat deviated from reported data in the literature. These results indicate that molecular dynamics simulations with clayFF can be a useful method in elucidating the roles of surface hydroxyl groups in the adsorption of metal ions to clay minerals.

• Geophysics and Geophysical Exploration
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• v.5 no.2
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• pp.84-92
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• 2002

In this study, the new modeling scheme has been developed for recently designed and tested electromagnetic survey, which adapts horizontal magnetic dipole with $1\;kHz\~1\;MHz$ frequency range as a source. The 2.5-D secondary field formulation in wavenumber domain was constructed using finite element method and verified through comparing results with layered-earth solutions calculated by integral equations. 2-D conductive- and resistive-block models were constructed for calculating electric field, magnetic field and impedance - the ratio of electric and magnetic fields which are orthogonal each other. This study showed that electric field and impedance are superior in identifying 2-D isolated-body model to magnetic field. In particular, impedance gives more stable results than electric field with similar spatial resolving power, because electric field is divided by magnetic field in impedance. Thus the impedance analysis which uses electric and magnetic fields together would give better result in imaging the shallow anomalies than conventional EM method.

• Geophysics and Geophysical Exploration
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• v.13 no.4
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• pp.315-322
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• 2010

The phase-screen and the split-step Fourier migrations, which are implemented in both the frequency-wavenumber and frequency-space domains by using one-way scalar wave equation, allow imaging in laterally heterogeneous media with less computing time and efficiency. The generalized-screen migration employs the series expansion of the exponential, unlike the phase-screen and the split-step Fourier migrations which assume the vertical propagation in frequency-wavenumber domain. In addition, since the generalized-screen migration generalizes the series expansion of the vertical slowness, it can utilize higher-order terms of that series expansion. As a result, the generalized-screen migration has higher accuracy in computing the propagation with wide angles than the phase-screen and split-step Fourier migrations for media with large and rapid lateral velocity variations. In this study, we developed a 2D prestack generalized-screen migration module for imaging a complex subsurface efficiently, which includes various dips and large lateral variations. We compared the generalized-screen propagator with the phase-screen propagator for a constant perturbation model and the SEG/EAGE salt dome model. The generalized-screen propagator was more accurate than the phase-screen propagator in computing the propagation with wide angles. Furthermore, the more the higher-order terms were added for the generalized-screen propagator, the more the accuracy was increased. Finally, we compared the results of the generalizedscreen migration with those of the phase-screen migration for a model which included various dips and large lateral velocity variations and the synthetic data of the SEG/EAGE salt dome model. In the generalized-screen migration section, reflectors were positioned more accurately than in the phase-screen migration section.