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The elementary system which can emit light is a dipole. Theoretical method of light propagation from point like dipole source is presented in this paper. The propagation is considered through two media divided by 3D arbitrary surface. Orientation of new formed dipole on surface segment is determined according to the refraction of incident wave-front electric field strength on boundary surface. Generalized formulation of Fresnel-Kirchhoff integral is derived for elementary dipole as a source and arbitrary surface dividing two media with arbitrary refraction indexes. This model shows that distribution of light depends on orientation of primary point like dipole source and curvature of 3D boundary surface. The model presented here can be used for extended surface or volume source of light, where each point of the source is point like dipole. In this way, the propagation of light wavefront could be modeled.

This study aims to fully investigate the volumetric radiative properties of irregular open-cell foams made from semitransparent absorbing-scattering media such as ceramics. A Monte Carlo ray-tracing model was established in the limit of geometric optics to extract volumetric radiative properties of foams generated by a Voronoi tessellation technique. Three shape parameters for struts were proposed to mimic real struts. It was found that for extinction coefficient, the most influent parameters are porosity, mean cell diameter, and cross-sectional shape. For scattering albedo, it no longer depends on the surface reflectivity of solid struts but on the component radiative properties and strut shape parameters. Similarly, the scattering phase function no longer depends on the local reflection type but on an integrated contribution of the surface reflection, interface refraction, and volumetric radiation propagation inside the struts. The asymmetry factor is found closely related to the transparency of struts. Using the component radiative properties and structural parameters as input parameters, three analytical relations were established to respectively predict the extinction coefficients, scattering albedos, and asymmetry factors, which can be useful for the design and application of open-cell foams made from semitransparent media.

Urban sound propagation is influenced by meteorological conditions, causing refraction and scattering of sound waves. An experimental study on the effect of meteorology on urban sound propagation has not been addressed yet on long-term and long-range scales. For the first time, this paper presents an approach to measure the wind effect on urban sound propagation from an uncontrolled sound source. The approach is applied to a location in Eindhoven (the Netherlands), with church bells as the source of sound. Sound is continuously measured, downwind from the sound source according to the prevailing wind direction up to 527 m from the source, and during a period of 5 months. Results of this measurement campaign show an increase of the sound pressure level of 0.4 dB, 0.8 dB, and 1.9 dB across three measurement positions per 1 m/s increase of the wind velocity over 1/3rd octave bands. Effects are stronger for lower frequencies and increases for further microphone positions. Possible future improvements of the experimental approach are discussed.

Tunable transmission characteristics of electromagnetic waves in periodically layered metamaterials (PLMMs), constructed by alternating dielectric layer and gyromagnetic layer such as yttrium-iron-garnet (YIG), are investigated through an external magnetic field. Based on transfer matrix method (TMM) and effective medium theory (EMT), we compare the dispersion curves of TE waves propagating in the PLMMs, and obtain the effective permeability and permittivity tensors of the homogenized gyromagnetic PLMMs by expanding the exact dispersion relation in long-wavelength limit. Then, we calculate some propagating parameters when TE waves incident on the PLMMs by EMT in detail. Numerical results show that the refraction state of TE waves in the PLMMs can be dynamically changed between positive refraction state and cutoff state by controlling the external magnetic field. These exotic properties of gyromagnetic PLMMs may have wide potential applications in many fields such as sub-wavelength all-optical switches and wave cutoff devices.

Digital processing of seismic data, which are registered on Transbaikalian part of reference geophysical profile 1-SB, is executed. These data are registered on CDP source-receiver configuration. Time sections images and wavefields of P- and S- head waves are result from technique of head waves dynamic conversion. These time sections are image a structure of refraction boundaries on the upper Earth crust on some areas of Argunskaya fold area, Mongol-Okhotsky fold belt, West-Stanovaya and Selengino-Yablonevaya fold areas. Seismic sections of depth interval of 0-2 km are constructed. Boundaries of intrusive body are detected on upper crust of Argunskaya fold area. This body is underlying lens shaped sedimentary layers on depth interval of 0.5÷1.0 km. Top of crystalline basement is established on the depth interval of 1.6-2.0 km on the northern part of Mongol-Okhotsky fold belt.

The history of refraction is extensive and quite complex, it can be dated back to Ptolemy and Ibn Sahl, and the law of refraction itself is usually called Snell’s law. We do not wish however, to gi...

Using exact and explicit analytical solutions and MODFLOW simulations we show that downstream of an unconformity (transition from an aquifuge layer to a homogeneous aquitard) groundwater seeps at varying angles with respect to the layering. As a generalization of the Anderson (2003) two-layered composite, a steady, 2-D Darcian flow in a three-layered aquifer is studied. This flow is generated by different inlet piezometric heads in thick upper and lower strata and a cross-flow through an aquitard sandwiched between them. Analytically, a line vortex combined with a dipole at infinity describes commingling between the strata with refraction (continuity of head and normal flux component) along the upper and lower boundaries of the aquitard. The Fourier method by Riesenkampf (1940) gives explicit expressions for the specific discharge vector fields in the three media. MODFLOW models finite lengths composites of rectangular and octagonal shapes. The Dupuit–Forchheimer approximation is illustrated to oversimplify the flow topology.

The main objective of the present study is the combination of short- with long-term wave statistics in deep waters in order to achieve a more accurate description of the long-term wave climate in shallower waters. Such a description would provide vital information for many engineering applications in deep and intermediate waters, including design of coastal structures. This task can be accomplished by accumulating the statistics for all short-term sea conditions, considering the frequency of occurrence of each sea state during a certain period of years. A modification of an existing relationship has been developed aiming at achieving this purpose. More specifically, by using the relative frequencies of occurrence of the significant wave height (Hs) and mean zero-crossing wave period (Tm), measured at a specific location, as well as the short-term joint distributions of wave height (H) and period (T) associated with each sea state, the long-term joint distribution of H and T can be produced at that location in deep waters. Then, the long-term joint probability density function of Hs and Tm and the long-term joint probability function of H and T can be estimated at any intermediate water depth by considering wave directionality in deep waters and wave transformation of each individual wave, as waves propagate from the open sea towards shallower waters. Wave measurements obtained at three different locations in the Aegean (Greece) have been examined and compared. The results showed that, as waves propagate from deep to shallower waters, wave statistics differ from those in deeper waters, especially when waves become significantly depth limited. It is noted that this individual wave analysis refers to short-crested waves, thus wave directionality and refraction have been considered. However, in this approach, the nonlinear wave – wave interactions have not been taken into account.

Possible deviations of a laser beam from a detector in the case of slant propagation paths are calculated based on air temperature profiles measured in the atmospheric boundary layer. The possible seasonal and diurnal dynamics of the deviations under regular refraction is considered. The cases of simultaneous strong (regular) refraction and significant broadening of a laser beam due to the turbulence effect are revealed and analyzed.

When stellar refraction occurs, the refraction apparent rays contain two kinds of refraction information, stellar refraction angle and stellar refraction direction. The refraction apparent height and the stellar refraction angle are two typical measurements used in stellar refraction navigation, which essentially only uses stellar refraction angle, and does not use stellar refraction direction. In fact, the stellar refraction direction is a function of the satellite position vector, which is useful in determining the satellite position. In this paper, a new stellar refraction navigation method using the star pixel coordinates as a measurement is proposed to improve navigation accuracy by using two kinds of refraction information at the same time. The corresponding measurement model for the star pixel coordinates is established. Simulations show that the proposed method's navigation performance is better than that of refraction apparent height and stellar refraction angle.

Integrated geophysical data provides a powerful tool for subsurface imaging with reasonable accuracy. The 2-D electric resistivity tomography and seismic refraction tomography profiling are carried out at four sites in Thuwal-Rabigh area, west-central Saudi Arabia. These profiles oriented perpendicular to the proposed strike of the Qadimah fault to detect the Qadimah fault. The results indicate the presence of the Qadimah fault underneath the northern two profiles at shallow depths, while not recorded through the southern two profiles indicating the absence of fault or changing in its strike southward. These results confirmed the passing of Qadimah fault through the King Abdullah Economic City. The study displayed the extension of the fault through King Abdullah Economic City worming serious hazards in the future in case of reactivating the movement along the fault plane, especially the area has a noticeable seismic activity. Continuous monitoring of earthquake activities and displacement along the fault plane through installation local earthquake monitoring network equipped by global positioning system are highly recommended.

To solve the problem that the traditional cable fault location method is limited by the traveling wave velocity, a new cable fault location method is proposed. Firstly, based on the traveling wave model of fault cable, the traveling wave is divided into four types according to the traveling wave propagation position and the number of refraction and reflection. Secondly, the cable line is divided into three sections according to the time when the refraction and reflection waves at the fault point and the reflection waves at the opposite end reach the detection bus and the polarity combination of each traveling wave head, and the corresponding location algorithm of removing wave velocity limitation for each section is derived. The fault distance is calculated by using the new algorithm on the Matlab/Simulink. Compared with the existing methods, the results show that the method has high accuracy and strong stability. Meanwhile, a cable fault location system is designed based on the new algorithm, and the cable fault location experiment is carried out. The experimental results show that the error of the positioning system is less than 1 % when different faults occur in the cable, which can effectively realize the cable fault location.

The ocean wave climate has a variety of applications in Naval defence. However, a long-term and reliable wave climate for the Indian Seas (The Arabian Sea and The Bay of Bengal) over a desired grid resolution could not be established so far due to several constraints. In this study, an attempt was made for the simulation of wave climate for the Indian Seas using the third-generation wave model (3g-WAM) developed by WAMDI group. The 3g-WAM as such was implemented at NPOL for research applications. The specific importance of this investigation was that, the model utilized a “mean climatic year of winds” estimated using historical wind measurements following statistical and probabilistic approaches as the winds which were considered for this purpose were widely scattered in space and time. Model computations were carried out only for the deep waters with current refraction. The gridded outputs of various wave parameters were stored at each grid point and the spectral outputs were stored at selected locations. Monthly, seasonal and annual distributions of significant wave parameters were obtained by post-processing some of the model outputs. A qualitative validation of simulated wave height and period parameters were also carried out by comparing with the observed data. The study revealed that the results of the wave climate simulation were quite promising and they can be utilized for various operational and ocean engineering applications.Therefore, this study will be a useful reference/demonstration for conducting such experiments in the areas where wind as well as wave measurements are insufficient.

The uncertainty behavior of an enhanced three-dimensional (3D) localization scheme for pulsed sources based on relative travel times at a large-aperture three-hydrophone array is studied. The localization scheme is an extension of a two-hydrophone localization approach based on time differences between direct and surface-reflected arrivals, an approach with significant advantages, but also drawbacks, such as left-right ambiguity, high range/depth uncertainties for broadside sources, and high bearing uncertainties for endfire sources. These drawbacks can be removed by adding a third hydrophone. The 3D localization problem is separated into two, a range/depth estimation problem, for which only the hydrophone depths are needed, and a bearing estimation problem, if the hydrophone geometry in the horizontal is known as well. The refraction of acoustic paths is taken into account using ray theory. The condition for existence of surface-reflected arrivals can be relaxed by considering arrivals with an upper turning point, allowing for localization at longer ranges. A Bayesian framework is adopted, allowing for the estimation of localization uncertainties. Uncertainty estimates are obtained through analytic predictions and simulations and they are compared against two-hydrophone localization uncertainties as well as against two-dimensional localization that is based on direct arrivals.

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2021-04-26, PA2220013000

Electromagnetic (EM) wave propagation inside and along the surface of the human body is the subject of active research in the field of biomedical applications of microwaves. This research area is the basis for wireless monitoring of biological object parameters and characteristics. Solutions to the following problems are crucial for achieving the stated goals in the area of wireless monitoring: EM wave propagation inside and on-body surface. The biological object monitoring is based on a consideration of the following problems: (i) dielectric properties of a biological issue; (ii) EM wave propagation in biological medium; (iii) propagation of EM waves across the boundary of two media (biological medium–air): wave reflection and refraction; (iv) EM wave propagation in a multilayer biological medium; (v) EM wave propagation along the plane or curved surface of biological objects.

Valley pseudospins, as quantum states of energy extrema in momentum space, have been introduced from condensed-matter systems into classical sound systems, and several valley sonic crystals (VSCs) have been realized experimentally. However, in the existing VSCs, topological kink states generally appear in a single band gap, which apparently has become an obstacle for multiband topological sound devices. To overcome this challenge, we here experimentally demonstrate dual-band VSCs, in which robust valley kink states exist in two separated bulk band gaps. More interestingly, two opposite valleys separately located in two band gaps are locked to a single propagation direction, which arises from the fact that the bands below two band gaps show opposite valley Chern numbers at the K/K′ valley. This double valley-locking phenomenon has been demonstrated via measuring the topological refraction of the kink states into the ambient space at a zigzag termination. We observe positive refraction at the lower band gap, whereas the coexistence of positive and negative refraction at the higher band gap. Additionally, we observe the robust valley transport through the sharp corners at two band gaps. The designed VSCs with the dual-band topological refraction and robust valley transport could find potential applications in multiband and multidirectional devices. Ministry of Education (MOE) Published version This work was supported by the National Natural Science Foundation of China (Grants No. 11774137, No. 51779107, and No. 11834008), the National Key R&D Program of China (Grants No. 2020YFC1512400 and No. 2020YFC1512403), the Singapore Ministry of Education [Grants No. MOE2018-T2-1-022 (S), No. MOE2016-T3-1-006, and Tier 1 RG174/16 (S)], State Key Laboratory of Acoustics, Chinese Academy of Science (Grant No. SKLA202016), and the China Postdoctoral Science Foundation (Grant No. 2020M671351).

International audience; A model of E×B staircases is proposed, based on a wave kinetic equation coupled to a poloidal momentum equation. A staircase pattern is idealised as a periodic radial structure of zonal shear layers that bound regions of propagating wave packets, viewed as avalanches. Wave packets are trapped in shear flow layers due to refraction. In this model an E × B staircase motif emerges due to the interaction between propagating wave packets (avalanches) and trapped waves in presence of an instability drive. Amplitude, shape, and spatial period of the staircase E × B flow are predicted as functions of the background fluctuation spectrum and the growth rate of drift waves. The zonal flow velocity radial profile is found to peak near its maxima and to flatten near its minima. The optimum configuration for staircase formation is a growth rate that is maximum at zero radial wave number. A mean shear flow is responsible for a preferential propagation speed of avalanches. It is not a mandatory condition for the existence of staircase solutions, but has an impact on their spatial period.

We formulate and confirm experimentally a new law of refraction for wave packets endowed with judicious spatio-temporal correlations, which reveals an anomalous-refraction regime: the pulse speeds up when traveling from low-index to high-index non-dispersive media.

In this work we present a method to dynamically control the propagation of spin-wave packets. By altering an external magnetic field the refraction of the spin wave at a temporal inhomogeneity is enabled. Since the inhomogeneity is spatially invariant, the spin-wave impulse remains conserved while the frequency is shifted. We demonstrate the stopping and rebound of a traveling Backward-Volume type spin-wave packet.

We gratefully acknowledge the research funding (grant number: OSR-2-16-RPP-3268.02 from KAUST (King Abdullah University of Science and Technology). We also appreciate the computational resources related to the supercomputer Shaheen II and the assistance provided by KAUST Supercomputer Laboratory. A.B.V.B. was funded by the SWOT program with NASA grants NNX16AH67G and 80NSSC20K1136. We wish to thank Fabrice Ardhuin for discussing the simulation results and the setup of the numerical simulations

We propose a simple solid-fluid layered structure where narrow Gaussian acoustic beam propagates practically without spreading. It is demonstrated that the coefficient (so-called diffraction coefficient), which defines the rate of linear spreading, vanishes if a certain relation between frequency and direction of propagation is hold. Unlike nonspreading “light bullets” recently proposed in optics, acoustic monochromatic signal can propagate in diffraction-free regime without sophisticated modulation. In the experiment with steel-water layered structure we observe nonspreading propagation of a signal with frequency ~ 100 kHz at a distance ~ 1m. Such long-range collimation is accompanied by negative phase velocity refraction, anomalous dispersion, and very strong anisotropy of the effective mass density. Such long-range collimation is accompanied by negative phase velocity refraction, anomalous dispersion, and very strong anisotropy of the effective mass density.

Phononic crystals have the ability to manipulate the propagation of elastic waves in solids by generating unique dispersion characteristics. They can modify the conventional behavior of wave spreading in isotropic materials, known as attenuation, which negatively influences the ability of acoustic emission method to detect active defects in long-range, pipe-like structures. In this study, pipe geometry is reconfigured by adding gradient-index (GRIN) phononic crystal lens to improve the propagation distance of waves released by active defects such as crack growth and leak. The sensing element is designed to form a ring around the pipe circumference to capture the plane wave with the improved amplitude. The GRIN lens is designed by a special gradient-index profile with varying height stubs adhesively bonded to the pipe surface. The performance of GRIN lens for improving the amplitude of localized sources is demonstrated with finite element numerical model using multiphysics software. Experiments are conducted using pencil lead break simulating crack growth, as well as an orifice with pressured pipe simulating leak. The amplitude of the burst-type signal approximately doubles on average, validating the numerical findings. Hence, the axial distance between sensors can be increased proportionally in the passive sensing of defects in pipe-like geometries.

In this presented article, modified 1/G'-expansion and modified Kudryashov methods are applied to generate traveling wave solutions of perturbed Chen-Lee-Liu (CLL) equation. The similar and different aspects of the solutions produced by both analytic methods are discussed in the results and discussion section. By giving special values to the constants in the solutions obtained by analytical methods, 2D, 3D and contour graphics representing the shape of the standing wave at any time are presented. Additionally, the advantages and disadvantages of the two analytic methods are discussed and presented in the results and discussion section. Also, a solitary wave is produced by giving special values ​​to the parameters in the hyperbolic type complex traveling wave solution. Simulations are created for different values ​​of the frequency and velocity propagation parameters of the solitary wave. The values ​​of these parameters are calculated for the breakage event physically. A computer package program is used for operations such as solving complex operations, drawing graphics and systems of algebraic equations.

Ultrasonic guided wave inspection is considered to detect flaw effectively in rails for high-speed railway and simultaneously it can be used for SHM(structure health monitor). the propagation process of ultrasonic in the railway turnout is complex. In order to make the guided waves become visible and people can observe complicated Ultrasonic field directly, according to the Maxwell law of stress-optic refraction, polarized light interference method is employed for establishing the dynamic photoelastic imaging system, and the bottom of the switch rail and rail waist variable cross-section optical test block with K9 optical glass material are designed and produced. Choosing different probes, research of different probes to excite guided wave in the test block in the sound field is carried on. Using CCD shooting test block, guided wave sound field images through the computer software are taken for acquisition and analysis. The sound field visualization is implemented, which can be used to guide ultrasonic guided wave inspection in practice.

The Baltic Shield is located in the northern part of Europe, which formed by amalgamation of a series of terranes and microcontinents during the Archean to the Paleoproterozoic, followed by significant modification in Neoproterozoic to Paleozoic time. The Baltic Shield includes an up-to 2500 m high mountain range, the Scandes , along the western North Atlantic coast, despite being a stable craton located far from any active plate boundary.We study a crustal scale seismic profile experiment in northern Scandinavia between 63oN and 71oN. Our Silverroad seismic profile extends perpendicular to the coastline around Lofoten and extends ~300km in a northwest direction across the shelf into the Atlantic Ocean and ~300km in a southeastern direction across the Baltic Shield. The seismic data were acquired with 5 explosive sources and 270 receivers onshore; 16 ocean bottom seismometers and air gun shooting from the vessel Hakon Mosby were used to collect both offshore and onshore.We present the results from raytracing modelling of the seismic velocity structure along the profile. The outputs of this experiment will help to solve high onshore topography and anomalous and heterogeneous bathymetry of the continental lithosphere around the North Atlantic Ocean. The results show crustal thinning from the shield onto the continental shelf and further into the oceanic part. Of particular interest is the velocity below the high topography of the Scandes, which will be discussed in relation to isostatic equilibrium along the profile.

With balanced spatial resolution, imaging depth, and functional sensitivity, photoacoustic tomography (PAT) hold great promise for human brain imaging. However, the strong acoustic attenuation and aberration of the human skull (∼8 mm thick) are longstanding technical challenges for PAT of the human brain. In this work, we numerically investigated the impacts of the stratified human skull on photoacoustic wave propagation (i.e., the forward model) and PAT image formation (i.e., the inverse model). We simulated two representative transcranial PAT implementations: photoacoustic computed tomography (PACT) and photoacoustic macroscopy (PAMac). In the forward model, we simulated the detailed photoacoustic wave propagation from a point or line source through a digital human skull. The wave attenuation, refraction, mode conversation, and reverberation were thoroughly investigated. In the inverse model, we reconstructed the transcranial PACT and PAMac images of a point or line target enclosed by the human skull. Our results demonstrate that transcranial PAMac suffers mainly from wave reverberation within the skull, leading to prolonged signal duration and reduced axial resolution. Transcranial PACT is more susceptible to the skull’s acoustic distortion, mode conversion, and reverberation, which collectively lead to strong image artifacts and deteriorated spatial resolutions. We also found that PACT with a ring-shaped transducer array shows more tolerance of the skull’s adverse impacts and can provide more accurate image reconstruction. Our results suggest that incorporating the skull’s geometry and acoustic properties can improve transcranial PAT image reconstruction. We expect that our results have provided a more comprehensive understanding of the acoustic impact of the human skull on transcranial PAT.

The estimation of a reliable velocity–depth model from towed streamer marine seismic data recorded in deep water, especially with a complex seafloor environment, is challenging. The determination of interval velocities from the normal move-out (NMO) of the reflected seismic signals for shallow reflectors (

Recently, several applications leveraging unconventional manipulation of electromagnetic radiation based on parity-time symmetry have been proposed in the literature. Typical examples include systems with unidirectional invisibility and asymmetric refraction. Such applications assume an inherent system stability and no occurrence of unbounded signal growth or unwanted self-oscillations. Here, a general instability issue of parity-time-symmetric systems is investigated, with particular emphasis on a recently proposed system based on resistive metasurfaces. Explicit closed-form stability criterion is derived, crosschecked and verified by both time-domain transient simulations and the measurements on an experimental demonstrator operating in a lower radiofrequency range. Results of this study lead to the conclusion that any parity-time-symmetric system is necessarily marginally stable. Finally, it is shown that such a marginally stable system may easily become unstable if not designed carefully.

In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topological modes, which is found to be solely determined by the relative resonant strength between the scatterers, significantly affects the refraction patterns. More interestingly, the outgoing traveling wave through a zigzag interface becomes evanescent when operating at deep sub-wavelength scale. This is realized by tuning the average resonant strength. We show that the evanescent modes only exist along a particular type of outlet edge, and that they can couple with both topological interface states. We also present two designs of topological functional devices, including an elastic one-way transmission waveguide and a near-ideal monopole/dipole emitter, both based on our phononic structure.

The article examines the influence of refraction on the results of measuring the horizontal angle in special places. In the conditions of the hot and arid climate of Uzbekistan in the polygonometric network of river banks, according to the results of field experiments, the new version of the developed methodology of the GIS makes it possible to increase the accuracy of measuring horizontal angles and lengths of lines. Significant temperature changes along the water and the coast, on rocks, in the upper layers of sand-concrete pavements are also explained by the properties of the heat and radiation balance.

Summary Seismic refraction tomography (SRT) can be a useful tool for detecting lateral velocity changes in the subsurface. In this work, we leverage a traditional seismic reflection offshore dataset to image a high velocity structure imbedded in sediments. The studied profile is located in the western edge of the South Orkney Microcontinent (SOM). Seafloor depth in this sector ranges between 268 and 304 m. The multichannel streamer of 120 channels and 1.4 km length allowed to detect refraction arrivals from the subsurface and used them as input for SRT to reconstruct a P-wave velocity model of the near–structure. A layered initial model provided the best result retrieving a sharp image of the velocity anomaly. Interpretation of this anomaly was supported by the comparison between the SRT velocity model and the multichannel seismic reflection image. Shallow subparallel layers of sediments characterized by velocities between 1500 and 2000 m/s overly a zone with older deformed sedimentary layers related to velocities ranging between 2500 and 3000 m/s. Within this second layer, a high-velocity anomaly (more than 4000 m/s) is delineated. Geological context supports interpreting this anomalous structure as metamorphic rocks or gabbroic bodies from PMA (Pacific Margin Anomaly) as part of the basement.

Summary Seismic data processing by pre-stack depth migration (PrSDM) requires a reliable initial velocity model. An accurate velocity model secures pre-stack gather flatness by short offset spread; however, a vertical transverse isotropy (VTI) model, for characterizing horizontal layering, should be sufficiently considered to extend offset usage and maximize image quality. This study sought a robust workflow of Thomsen VTI parameters, e and δ, estimation to stabilize anisotropic tomography analysis. Vertical and deviated wells offered the opportunity to derive the target parameters in a rather simple and elegant way. Anisotropic Backus averaging combined intrinsic and apparent anisotropy at seismic scale. In our case study, the calculated anisotropic parameters profiles were validated by WAVSPs and by the surface seismic data, which could be flattened effectively all the way to the largest offsets. In particular, steps like refraction FWI need an accurate anisotropic starting model to converge effectively. Cross-spread 3D seismic surveys are particularly ill suited for deriving shallow anisotropic velocity models and the vertical and deviated wells method provides a welcome alternative.

An alternative experimental approach and a numerical analysis for the study of destabilization by localized fluidization of an immersed dense granular material are presented. To visualize the evolutions of the internal structure of the granular medium, the hydrogel beads, composed of about 99% of water and having substantially the same refraction indexes, are used as solid phase. A LED lighting system is used in place of a laser lighting system. As a result, the optical access restriction of porous structure is removed. A real economic alternative for the experimental study of fluid-grain coupling during destabilization by localized fluidization of a granular material is created. The experimental phenomenology presented in the literature is verified: the system passes successively through three different stationary regimes: static regime, fluidized cavity regime, and fluidized chimney regime. Some restrictions of using hydrogel beads as particles in the study of liquid-solid interaction are also discussed.

Summary In November 2020, a passive and active seismic investigation was applied to the large slow-moving landslide of Hell-Bourg, Reunion Island. The objective of this survey is to provide relevant information for the characterisation of the internal structure and hydrogeology of the landslide. The first joint application of geophysical methods, geomorphological surveys, field observations and measurement has already led to the general characterisation of this complex landslide up to 200 m depth. The initial results from the seismic survey obtained from the P-wave refraction tomography allow confirming the existence and continuity of the main sliding surface, which had previously pointed out by resistivity model from aerial electromagnetic data. Furthermore, thanks to this data discontinuities that affect both the landslide and the substratum up to 450 m deep have been detected, suggesting a strong relation between the dynamic of the landslide and the substratum geometry. These initial results are promising and thus suggest that the seismic data we are currently processing will reveal new insights to improve our knowledge of the structure and dynamics of the Hell-Bourg landslide.

In this paper, considering the far-field seismic input, an accelerogram recorded in the bedrock at Wuquan Mountain in Lanzhou city during the 2008 Wenchuan Ms8.0 earthquake was selected, and numerical dynamic analyses were conducted. The one-dimensional equivalent linear method was implemented to estimate the ground motion effects in the loess regions. Thereafter, slope topographic effects on ground motion were studied by applying the dynamic finite-element method. The results revealed the relationship between the PGA amplification coefficients and the soil layer thickness, which confirmed that the dynamic response of the sites had obvious nonlinear characteristics. The results also showed that there was an obvious difference in the dynamic magnification factor between the short-period and long-period structures. Moreover, it was found that the amplification coefficient of the observation point at the free surface was greater than the point inside the soil at the same depth, which mainly occurred in the upper slope. Through this study, the quantitative assessment of ground motion effects in loess regions can be approximately estimated, and the amplification mechanism of the far-field ground motion mechanism can be further explained. In addition to the refraction and reflection theory of seismic waves, the resonance phenomenon may help explain the slope topographic effect through spectrum analysis.

Summary The Agbami field is a major field offshore Nigeria, covered with two towed-streamer and three ocean bottom node (OBN) seismic surveys. The existing processed data and associated velocity model gives satisfactory seismic images at the center of the field. However, near-surface velocity anomalies adversely affect the image in the northwest area. To address these issues a full 4D co-processed preprocessing workflow followed by a two-step top down velocity model building workflow consisting of both refraction FWI and ray-based reflection tomography using the 4D OBN data was implemented: a first for time-lapse processing in West Africa. In this paper, we present the results from the TTI FWI velocity model building and imaging. The work-flow allowed the incorporation of detailed shallow structures into the output model which enhanced the migrated images. Ultimately, this facilitated a better understanding of the reservoir architecture to aid with de-risking of any future drilling.

The wave equation as derived in Section 7.1 and used so far in this book, is valid for sound propagation in lossless media. The Helmholtz form of this equation is

As building blocks of acoustic metamaterials, resonant scatterers have demonstrated their ability to modulate the effective fluid parameters, which subsequently possess extreme properties such as negative bulk modulus or negative mass density. Promising applications have been shown such as extraordinary absorption, focusing, and abnormal refraction for instance. However, acoustic waves can be further controlled in Willis materials by harnessing the coupling parameters. In this work, we derive the closed forms of the effective parameters from the transfer matrix in three asymmetric and reciprocal one-dimensional resonant configurations and exhibit the differences in terms of coupling coefficients. The way in which Willis coupling occurs in spatially asymmetric unit cells is highlighted. In addition, the analysis shows the absence of odd Willis coupling for reciprocal configurations. These effective parameters are validated against experimental and numerical results in the three configurations. This article paves the way of a novel physical understanding and engineering use of Willis acoustic materials.

Summary Full waveform inversion (FWI) has been applied with great success to build velocity model, which is typically used in RTM or least squares reverse time migration (LSRTM) to produce high resolution images. With the fast advancements in the computer industry and the progress of the FWI algorithm, high resolution FWI has become common practices. Nevertheless, it is still computationally expensive to invert a velocity model that is directly interpretable using FWI. In this paper, we propose a unified approach for the inversion of velocity model and the image. Starting at lowest frequency possible that the input data support, FWI gradually moves to higher frequencies, which allows it to invert a broad band velocity model. A reflectivity model is then computed directly from a velocity model inverted from FWI without the need of migration as it is in a typical workflow. Numerical examples show that the reflectivity image derived from a 15 HZ FWI velocity model have better resolution and improved continuity compared to the images from RTM and LSRTM. These benefits partially come from the contribution of both refraction and reflection energy used in FWI.

Summary Various velocity parameterizations are used in Bayesian first-arrival tomography. We conduct a short review of the existing approaches and suggest the natural neighbor interpolation as a viable alternative. This parameterization possesses numerous useful properties. It provides naturally smooth models, which is particularly suitable for a refraction setting. It does not need any specific treatment at model boundaries, and, finally, does not need any additional parameters apart from velocities defined on a set of nodes. We compare this parameterization with a more conventional linear barycentric approach on a synthetic near-surface seismic dataset. The comparison shows that natural neighborbased tomography results in a more accurate estimation of seismic velocity inside the near-surface low-velocity anomaly and provides a lower estimate of velocity uncertainty in the whole model.

In this paper we present a methodology and first results of seafloor compressional sound speed estimation in a compacting passive margin setting of the southeastern Mediterranean Sea, offshore Israel. The estimation was obtained through a coupled wide-angle reflection-refraction travel time analysis of standard commercial 2D multichannel seismic data, acquired with a 7.2km long horizontal receivers array, and geoacoustic inversion. We found that three parameters were needed to model the observed travel times: 1) the compressional sound speed at water-sediment interface c0; 2) a constant velocity gradient K within the sub-bottom sediments layer; and 3) the thickness of the relevant sub-bottom layer H2. The model considered consists of a water layer with a vertically varying sound speed profile according to the season. The thickness of this layer is constrained by the pre-known seafloor bathymetric depth of 1200 m. The base of the model is the top of a regional salt layer, which underlies the investigated sub-bottom layer and constrains H2. The estimated c0 and K are 1550 m s−1 and 0.7 s−1, respectively. The proposed method allows to estimate a relatively low (∼1500-1650 m s−1) sound speed at water-sediment interface, where it is challenging to use conventional refraction-based methods.

This lecture aims to give an overview of water waves and their propagation in inhomogeneous media. Effects of varying bathymetries, varying currents, or structures including porous media are then considered. After some generalities on water waves, governing equations for regular plane waves for the study of wave scattering including reflection, refraction and diffraction, due to either varying bathymetry and currents or structures are presented for both 2D and 3D cases. Analytical and numerical solutions are then presented and compared to experiments. For 2-D cases, examples are given for wave reflection through interference process including Bragg resonance. For 3-D cases, various examples including wave scattering due to a shoal, a structure, periodic structures or varying currents are given. Applications to both shore protection solutions and wave energy are also presented.

The work is concerned with the wave propagation at the interface of isolated exponentially graded couple stress thermoelastic media under initial stress and gravity. We analyse the influence of initial stress and gravity on reflection and refraction coefficients for both upper and lower couple stress thermoelastic half-spaces. Further, we found there are three waves, viz. quasi-SV and set of two longitudinal waves propagating with different speeds. The phase speeds, equation of motions, reflection and refraction coefficients are calculated in closed form. The impact of gravity and initial stress parameter has also been calculated numerically and shown graphically.