A note on the interpretation of seismic surface waves over three - dimensional structures

AbstractThe underground city beneath the Nevşehir Castle located in the middle of Cappadocia region in Turkey with approximately cone shape is investigated by jointly utilizing the modern geophysical techniques of seismic surface waves and electrical resistivity. The systematic void structure under the Nevşehir Castle of Cappadocia, which is known to have widespread underground cities, is studied by the use of 33 separate two-dimensional profiles ~4-km long where electrical resistivities and seismic surface waves are concurrently measured. Seismic surface wave measurements are inverted to establish the shear-wave velocity distribution while resistivity measurements are inverted to resolve the resistivity distribution. Several high-resistivity anomalies with a depth range 8-20 m point to a systematic void structure beneath the Nevşehir Castle. We were able to effectively isolate the void structure from the embedding structure since the currently employed resistivity instrument has provided us high resolution quality measurements. Associated with the high resistivity anomalies there exist low-velocity depth zones acquired from the surface wave inversions also pointing to a systematic void structure where three-dimensional visualization techniques are used to show the extension of the void structure under the studied area.

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TRANSVERSE ISOTROPIC CRUST STRUCTURE BENEATH THE NORTHWEST AND CENTRAL NORTH ANATOLIA REVEALED BY SEISMIC SURFACE WAVES PROPAGATION

Malaysian Journal of Geosciences ◽

10.26480/mjg.02.2021.41.50 ◽

2020 ◽

Vol 5 (2) ◽

pp. 41-50

Author(s):

Özcan Çakır

Keyword(s):

Surface Waves ◽

Lower Crust ◽

Transverse Isotropy ◽

Three Dimensional ◽

Phase Speed ◽

Upper Crust ◽

One Dimensional ◽

Dimensional Group ◽

Single Station ◽

Seismic Surface Waves

The Anatolian crust, which is abnormally hot, is widely deformed by subduction related volcanism. Suture zones, transform faults, thrusts and folds and metamorphic core complexes add to the geological complexity. Volcanic provinces such as Western, Central and Eastern Anatolia and Galatea are recognized as distinct features in the region. The middle-to-lower crust depths appear to be intruded by horizontal sills and the upper crust by vertical dykes. Both horizontal sills and vertical dykes leave anisotropic signs detected as Vertical Transverse Isotropy (VTI) that is explored by Love and Rayleigh surface wave inversions, i.e., Love-Rayleigh wave discrepancy which arises because the dykes and sills act differently against the Love and Rayleigh surface waves. The current study gives emphasis to the Northwest and Central North Anatolia utilizing both single-station and two-station tomography techniques to recover the two-dimensional group and phase speed charts from which one-dimensional dispersion inversions are implemented. The one-dimensional inversions are joined to construct the three-dimensional crust of the studied region. The shear-wave anisotropy is used to locate the anisotropy in the crust. The vertical dykes in the upper crust fit into negative VTI around -10% while the horizontal sills in the middle-to-lower crust yield positive VTI around 12%. The vertical magma flows within the vertical dykes and the horizontal magma flows within the horizontal sills contribute constructively to the anisotropy created by the special shape orientations of sills and dykes. The earthquakes hypocenter distribution and high and low speeds alongside the VTI provide significant clues to differentiate between diverse geological districts.

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Development and Validation of Quasi-Eulerian Mean Three-Dimensional Equations of Motion Using the Generalized Lagrangian Mean Method

Journal of Marine Science and Engineering ◽

10.3390/jmse9010076 ◽

2021 ◽

Vol 9 (1) ◽

pp. 76

Author(s):

Duoc Nguyen ◽

Niels Jacobsen ◽

Dano Roelvink

Keyword(s):

Surface Waves ◽

Deep Water ◽

Surf Zone ◽

Equations Of Motion ◽

Three Dimensional ◽

Breaking Waves ◽

Successful Implementation ◽

Random Waves ◽

Mean Motion ◽

Generalized Lagrangian

This study aims at developing a new set of equations of mean motion in the presence of surface waves, which is practically applicable from deep water to the coastal zone, estuaries, and outflow areas. The generalized Lagrangian mean (GLM) method is employed to derive a set of quasi-Eulerian mean three-dimensional equations of motion, where effects of the waves are included through source terms. The obtained equations are expressed to the second-order of wave amplitude. Whereas the classical Eulerian-mean equations of motion are only applicable below the wave trough, the new equations are valid until the mean water surface even in the presence of finite-amplitude surface waves. A two-dimensional numerical model (2DV model) is developed to validate the new set of equations of motion. The 2DV model passes the test of steady monochromatic waves propagating over a slope without dissipation (adiabatic condition). This is a primary test for equations of mean motion with a known analytical solution. In addition to this, experimental data for the interaction between random waves and a mean current in both non-breaking and breaking waves are employed to validate the 2DV model. As shown by this successful implementation and validation, the implementation of these equations in any 3D model code is straightforward and may be expected to provide consistent results from deep water to the surf zone, under both weak and strong ambient currents.

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Guided Surface Waves on an Elastic Half Space

Journal of Applied Mechanics ◽

10.1115/1.3408973 ◽

1971 ◽

Vol 38 (4) ◽

pp. 899-905 ◽

Cited By ~ 5

Author(s):

L. B. Freund

Keyword(s):

Wave Propagation ◽

Surface Wave ◽

Surface Waves ◽

Half Space ◽

Body Wave ◽

Three Dimensional ◽

Elastic Half Space ◽

Normal Displacement ◽

Rigid Barrier ◽

Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

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Internal-inertia waves in a fluid of variable depth

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100047617 ◽

1973 ◽

Vol 73 (1) ◽

pp. 205-213 ◽

Cited By ~ 10

Author(s):

W. D. McKee

Keyword(s):

Exact Solutions ◽

Surface Waves ◽

Internal Waves ◽

Vertical Velocity ◽

General Problem ◽

Three Dimensional ◽

Variable Depth ◽

Internal Inertia ◽

Perturbation Pressure ◽

Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

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A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

10.1115/imece2001/htd-24112 ◽

2001 ◽

Author(s):

Patrick H. Oosthuizen ◽

Matt Garrett

Keyword(s):

Heat Transfer ◽

Prandtl Number ◽

Surface Waves ◽

Heat Transfer Rate ◽

Transfer Rate ◽

Three Dimensional ◽

Wavy Surface ◽

Surface Waviness ◽

Dimensionless Amplitude ◽

The Mean

Abstract Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

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What Is Tsunami Earthquake?

10.1115/omae2021-63104 ◽

2021 ◽

Author(s):

Toshikazu Ebisuzaki

Keyword(s):

Surface Waves ◽

Seismic Waves ◽

Submarine Landslides ◽

Lower Efficiency ◽

Tsunami Waves ◽

Tsunami Earthquakes ◽

Seismic Surface Waves ◽

Tsunami Earthquake ◽

Volcanic Islands ◽

2004 Tsunami

Abstract A tsunami earthquake is defined as an earthquake which induces abnormally strong tsunami waves compared with its seismic magnitude (Kanamori 1972; Kanamori and Anderson 1975; Tanioka and Seno 2001). We investigate the possibility that the surface waves (Rayleigh, Love, and tsunami waves) in tsunami earthquakes are amplified by secondly submarine landslides, induced by the liquefaction of the sea floor due to the strong vibrations of the earthquakes. As pointed by Kanamori (2004), tsunami earthquakes are significantly stronger in longer waves than 100 s and low in radiation efficiencies of seismic waves by one or two order of magnitudes. These natures are in favor of a significant contribution of landslides. The landslides can generate seismic waves with longer period with lower efficiency than the tectonic fault motions (Kanamori et al 1980; Eissler and Kanamori 1987; Hasegawa and Kanamori 1987). We further investigate the distribution of the tsunami earthquakes and found that most of their epicenters are located at the steep slopes in the landward side of the trenches or around volcanic islands, where the soft sediments layers from the landmass are nearly critical against slope failures. This distribution suggests that the secondly landslides may contribute to the tsunami earthquakes. In the present paper, we will investigate the rapture processes determined by the inversion analysis of seismic surface waves of tsunami earthquakes can be explained by massive landslides, simultaneously triggered by earthquakes in the tsunami earthquakes which took place near the trenches.

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Evidence of metamaterial physics at the geophysics scale: the METAFORET experiment

Geophysical Journal International ◽

10.1093/gji/ggz528 ◽

2019 ◽

Cited By ~ 1

Author(s):

Martin Lott ◽

Philippe Roux ◽

Stéphane Garambois ◽

Philippe Guéguen ◽

Andrea Colombi

Keyword(s):

Surface Waves ◽

Attenuation Length ◽

Dense Forest ◽

Complex Wave ◽

Seismic Surface Waves ◽

Source Excitation ◽

Ground Penetrating ◽

Dense Seismic Array ◽

Seismic Wavefield ◽

Large Frequency

Abstract The METAFORET experiment was designed to demonstrate that complex wave physics phenomena classically observed at the meso- and micro-scales in acoustics and in optics also apply at the geophysics scale. In particular, the experiment shows that a dense forest of trees can behave as a locally resonant metamaterial for seismic surface waves. The dense arrangement of trees anchored into the ground creates anomalous dispersion curves for surface waves, which highlight a large frequency band-gap around one resonant frequency of the trees, at ∼45 Hz. This demonstration is carried out through the deployment of a dense seismic array of ∼1000 autonomous geophones providing seismic recordings under vibrating source excitation at the transition between an open field and a forest. Additional geophysical equipment was deployed (e.g. ground-penetrating radar, velocimeters on trees) to provide essential complementary measurements. Insights and interpretations on the observed seismic wavefield, including the attenuation length, the intensity ratio between the field and the forest and the surface wave polarization, are validated with 2D numerical simulations of trees over a layered halfspace.

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