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This study aims to determine the 1D deep S-wave velocity structure for Çanakkale Province and the surrounding area (Biga Peninsula, NW Turkey) using the moderate (M ≥ 4.0) earthquakes from the last decade. A total of 540 velocity seismograms with a high S/N ratio are obtained from 218 three-component acceleration records of the 10 earthquakes (4.0 ≤ Mw ≤ 5.3) that occurred in the areas of Ayvacık, Saros, and Çan between 2010 and 2018. A total of 34 strong ground motion stations operated by AFAD are grouped in 27 azimuthal directions, and fundamental mode surface wave group velocity dispersion curves are obtained using the multiple-filter method. First, the observed dispersion curves are utilized for the inversion application to define the 1D deep Vs model. Then they are compared with the theoretical curves of the tuned 1D deep Vs models with the trial-and-error forward method after inversion. The RMS misfits between observed and calculated surface group velocities decrease from 0.6 to 0.2 on average. The dispersion analyses allow for improved seismic velocities and thicknesses of especially the uppermost 4–5 km. The defined 1D deep Vs model of 202 source-station paths are also inferred to obtain an average pseudo-3D deep Vs model. In addition, the velocity models are verified with 1D numerical ground motion simulations for 0.05–1 Hz, including the characterized source models of the earthquakes and 1D shallow soil amplifications. The simulation results are quantitatively evaluated with goodness-of-fit measures considering different frequency bands. Fairly good agreement for waveform first arrival and spectral amplitude (0.05–1 Hz) is achieved. However, the later wave packages at the sites located on thick sediment basins cannot be modeled because of the reverberations in the sediment overlying the engineering bedrock. The test of the pseudo-3D Vs model using broadband (0.05–10 Hz) simulation of the 2017 Lesvos mainshock (Mw 6.3) also indicates that both the phase arrival times (< 1 Hz) and the amplitude spectral decay in the high-frequency range of 1–7 Hz are well modeled.

Internal structure imaging of the Earth, along with determining basin structure, can aid in evaluating potential seismic hazards. However, the high operating cost limits the current geophysical exploration methods; moreover, it is difficult to apply these techniques over a large area, which limits our understanding of the Quaternary structure and the development of earthquake prevention science. A combination of dense array observation technology and ambient noise surface wave tomography is being rapidly developed as a high-resolution urban detection method. Here, we report the ambient noise imaging results of a high-density array experiment. In the ambient noise surface wave tomography method (e.g., surface wave tomography; Eikonal tomography), the signal is assumed to be a single mode. However, several multimode signals were detected in this dataset. With the use of traditional methods to measure the dispersion, mode confusion occurs and the extracted dispersion curve jumps. To solve this problem, by combining the advantages of phase-matched filtering and dispersion compensation, we realized the automatic pickup of fundamental group velocity using reference phase velocity. From this, a Rayleigh wave group velocity map was obtained. The regional average phase velocity information was included in the inversion steps to reduce the uncertainty in the inversion of shear wave velocity. Finally, an S-wave velocity structure model was obtained within a depth of 500 m. The velocity structure was roughly layered and grew with depth. In the depth range of 240–320 m, obvious decreases in the S-wave velocity were observed. Compared with geothermal drilling data, this was speculated to be the reflection of a water-rich (confined water) sand layer. This study provides a technical approach for and a processing example of a high-density array, and its velocity model can be used as a reference for urban subsurface structure, underground space utilization, and earthquake disaster prevention and control.

Aims: Shear wave elastography (SWE) is of great significance in measuring the elasticity and in evaluating mechanical properties of biological tissues. The elasticity of biological tissues can be reflected by measuring the propagation velocity of shear waves. Therefore, accurate estimation of shear wave velocity is crucial.Material and methods: In this study, we proposed a robust estimation method based on a cyclic shifting algorithm (CSA) for measuring shear wave group velocity in homogeneous media. To validate the utility of the algorithm, we conducted accuracy analysis and robustness analysis with different noise levels in the digital phantom used for the standardization of shear wave velocity by Quantitative Imaging Biomarker Alliance (QIBA) of the Radiological Society of North America.Results: The estimated shear wave velocities (SWV) of the elastic digital phantoms with Young’s moduli 3 kPa, 6 kPa, 15 kPa, 30 kPa are 1.0156 m/s, 1.4065 m/s, 2.1875 m/s, 3.1250 m/s, respectively. When adding Gaussian white noise with 0 dB, the relative errors of the estimated SWVs are 2.5%, 4.8%, 11.8%, 20.5%, respectively. The estimated SWVs in the gelatin phantom with gelatin concentration of 7% and 10% are 2.0442 m/s and 3.1237 m/s. Compared with the existing two representative estimation algorithms, the estimation algorithm proposed in this paper has a higher anti-noise performance due to effective energy accumulation in the frequency domain.Conclusions: The proposed SWV method based on CSA in frequency domain is a robust shear wave group velocity estimation method, which seems to be a useful tool in homogeneous media for ultrasound elastography.

This research examines the overtopping volumes associated with focused wave groups on smooth dikes with an emerged toe. Focused wave groups are employed to represent the highest waves of random sea states in a compact form, obviating the need to model the entire irregular wave train. This study investigates how overtopping volumes are affected by focus location and phase. A total of 418 experimental tests were gathered and analyzed. Data with overtopping volumes below 600 L per meter (prototype conditions) were excluded in order to focus on extreme overtopping events, resulting in 324 relevant test cases. The experiments used first-order wave generation theory to analyze structural response. Subsequent studies will address the errors induced by this approximation and compare it with second-order wave generation. The experiments simulated extreme wave impacts on an idealized coastal layout, comprising a 1:6.3 foreshore slope and three different dike slopes, including vertical structures, with the initial still water level set below the dike toe. This study employed the NewWave theory to generate focused wave groups, with the objective of extending recent research on wave overtopping under varied conditions. The results, analyzed in both dimensional and non-dimensional forms, indicate that overtopping volumes are significantly influenced by the focus phase. Critical focus locations were identified at a distance of one-third of the deep-water wavelength from the toe.

Wave group focusing gives rise to the formation of large gravity waves at the surface of the ocean, some of which are called rogue waves and represent a natural hazard for ships and offshore platforms. For safety purposes, it is crucial to predict when and where these large waves will appear and how large they will be. This work focuses on crest velocities, a quantity that is relatively easy to extract from sea surface elevation fields. It is shown that there is a direct link between crest velocity gradient and wave group linear dispersive focusing. Studying analytically the focusing of one-dimensional Gaussian wave packets under linear evolution makes it possible to derive estimates of quantities at focus, based only on crest velocity measurements. In this way, the focusing time, focusing size and focusing amplitude (relative to instantaneous amplitude) of an isolated Gaussian wave packet can be estimated. Our work is also applicable to second-order non-linear waves. Limitations due to higher-order non-linear effects are studied in numerical simulations of the non-linear Schrödinger equation.

Since 2018, the research team has been investigating and developing a prototype sensor for recording seismic activity. An upgrade has been developed and must be evaluated, primarily to monitor ambient noise activities in the geothermal environment. This study aims to determine the group velocity of Rayleigh waves using ambient noise tomography (ANT) analysis in the Way Ratai geothermal region utilising four PiGraf seismograph prototypes. The acquisition method deploys a stationary inter-station around 5 kilometres (km) apart for seven consecutive days, with 100 samples per second (SPS). Fast marching surface tomography (FMST) has been utilised to generate group velocity from a cross-correlated time series, which produces tomographic images. The results showed that the ambient noise energy distribution originated from the northwest to the southeast, most likely from the sea. At the same time, the group velocity from the Green’s function group in the period range 0.2 s to 0.5 s, 0.5 s to 1 s, and 1 s to 5 s are 0.337 km/s, 0.415 km/s, and 0.427 km/s, respectively. These values are aligned within the dispersion curve’s velocity range of 0.3–0.8 km/s. The group velocity modelling of Rayleigh waves in the period range of 0.5 s to 1 s also identified a pattern corresponding with the geothermal potential area, confirming prior findings. However, the clarity of the cross-correlogram of the Green’s function group was identified as a topic for further investigation, suggesting adding more stations and longer measurement times.

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

The ringing of a floating barge’s roll motion under focused wave groups is studied using a fully nonlinear method in a numerical wave tank based on the potential flow theory. The higher order boundary element method (HOBEM) is used to solve the boundary value problem. The mixed Eulerian–Lagrangian (MEL) technique and the fourth-order Runge–Kutta time stepping scheme is used to simulate the interaction between the floating barge and focused wave groups. As the peak spectra frequency is set as one-third of the natural frequency of the barge’s roll motion, the influence of the peak wave amplitude of the incident focused wave groups on the roll response of the barge and wave loads is studied. The third-order components are found to be significant in both roll motion and moment as the incident peak wave amplitude increases. Relationship between the roll response of the barge and the peak spectrum frequency of the incident focused wave groups is also studied. The peak of the third-order roll response of the barge is found to decrease greatly as the triple peak spectral frequency deviates from the roll natural frequency.

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$ th-harmonic force scales with the $n$ th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

Wave crests of unexpected height and steepness pose a danger to activities at sea, and long-term field measurements provide important clues for understanding the environmental conditions that are conducive to their generation and behavior. We present a novel dataset of high-frequency laser altimeter measurements of the sea surface elevation gathered over a period of 18 years from 2003 to 2020 on an offshore platform in the central North Sea. Our analysis of crest height distributions in the dataset shows that mature, high sea states with high spectral steepness and narrow directional spreading exhibit crest height statistics that significantly deviate from standard second-order models. Conversely, crest heights in developing sea states with similarly high steepness but wide directional spread correspond well to second-order theory adjusted for broad frequency bandwidth. The long-term point time series measurements are complemented with space–time stereo video observations from the same location, collected during five separate storm events during the 2019/20 winter season. An examination of the crest dynamics of the space–time extreme wave crests in the stereo video dataset reveals that the crest speeds exhibit a slowdown localized around the moment of maximum crest elevation, in line with prevailing theory on nonlinear wave group dynamics. Extending on previously published observations focused on breaking crests, our results are consistent for both breaking and nonbreaking extreme crests. We show that wave crest steepness estimated from time series using the linear dispersion relation may overestimate the geometrically measured crest steepness by up to 25% if the crest speed slowdown is not taken into account.