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Structures and infrastructures can modify aeolian sedimentary dynamics as has occurred in the arid transgressive dunefield of Maspalomas (Gran Canaria, Canary Islands), where an aeolian shadow zone has been formed leeward of a tourist resort (Playa del Ingles). The aim of this paper is to analyse spatial and statistically the influences of vegetation and topography on wind flow across this shadow zone. An experiment was carried out in March 2017, collecting wind speed and direction from 5 transects with anemometers at 0.40 m height. Simultaneously, a drone flight was carried out, from which an orthophoto and digital elevation and surface models (DEM and DSM) were obtained. Distance from the resort, and the presence of vegetation were found to influence transects dominated by erosional processes. Transects that do not display erosional processes were primarily affected by the presence of vegetation. The local wind field changes at a similar distance across the transects downwind from the resorts indicating an acceleration or reattachment of the wind at this distance downwind. The vegetation role in this aeolian shadow zone could be a key to the future evolution of the area resulting in either further stabilization, or alternatively, the continued deflation of the area.

This paper describes the world's first successful simulation for lateral cutoff phenomena of sonic boom far from the flight path due to variation in atmospheric temperature with altitude. A flow field around an axi-symmetric paraboloid has been analyzed by the full-field simulation method that solves the three-dimensional Euler equations with a gravity term to create a horizontally stratified atmosphere. A solution-adapted structured grid is constructed to align the grid lines with the front and rear shock-wave surfaces in the entire domain, including the near field around a supersonic body and far field reaching the ground beyond lateral cutoff. The flight is assumed to have a speed of Mach 1.2 at an altitude of 10 km, and the computational domain ranges over a distance of 30 km from the axis of symmetry. The computational results show that the evanescent wave in the shadow zone beyond lateral cutoff decays exponentially and changes into a progressive rounding waveform. The characteristics of the waveform transition are in good agreement with those observed in the flight tests. Therefore, the full-field simulation is recognized as a promising approach for investigating sonic boom strength in the full extent of sonic boom noise, including lateral cutoff and evanescent waves. Moreover, the computational results clarify that sonic boom focusing occurs above the ground, except for the vicinity of the ground, and the focusing strength along the lateral cutoff curve detected from the three-dimensional shock-wave surface increases with altitude. The results of ray tracing analysis collaborate the reasonability of the simulation results, and the caustic of downward convex agrees well with the lateral cutoff curve. In the shadow zone, the magnitude of exponential decay increases with altitude, and the lateral distance where the pressure rise decreases rapidly shortens with altitude.

Parallel barriers are widely adopted to control environmental noise, but their performance may be inferior to that of a single barrier owing to the formation of multiple reflection waves between the parallel barriers. To improve the performance of parallel barriers, single or multiple Helmholtz resonators (HRs) are proposed to be mounted on the barrier surface. An acoustic interaction occurs between the HR and open cavity formed by the rigid ground and a pair of barriers, whereby the acoustic modal response within the open cavity is significantly suppressed and the diffraction wave at the barrier top edge is reduced. A semi-analytical model for dealing with acoustic coupling between the open cavity and HRs in a two-dimensional configuration is established in order to understand the sound suppression mechanism within the shadow zone. This model is also helpful for generating a noise control strategy that involves varying the dominant modal response at the target frequency. With the optimal position of a single HR, the insertion loss of about 10 dB around the target frequency can be controlled, while less influence is exerted on the off-target frequency. Comparisons are conducted between the data predicted using the present model and the numerical results obtained using the boundary element method, and the agreement between them is observed. Furthermore, experimental results demonstrate that the use of HRs for reducing noise in the shadow zone is feasible.

Observational analysis has revealed an apparent immobility of giant sand waves on the Taiwan Banks, while sand waves on the eastern Taiwan Banks show distinct dynamics influenced by the underlying larger-scale sand ridge bedforms. In this study, the effects of these sand ridge bedforms on sand wave migration and the local hydrodynamic environment were investigated using bathymetric and hydrodynamic datasets from 2016 and 2018. Upon separating the NNW-SSE sand ridge crest, the opposing sand wave migration and complementary sediment loss/gain on either side of the sand ridge are interpreted as convergence processes that serve to maintain the shape of the sand ridge. Analysis of the hydrodynamics revealed that, during the flood phase, the northward directed flow on the western side of the ridge crest was enhanced due to rapid shoaling. This caused the development of a flow shadow zone on the eastern side of the ridge crest, where the flow was rotated and weakened. During a tidal cycle, the dominance of the flood current on the western side of the ridge resulted in northward migration of sand waves. Conversely, due to the weakened flood current on the eastern side of the ridge, sand waves migrated southward in response to the stronger ebb current. This study thus provides insights into bedform dynamics in complex morphological settings and the maintenance mechanism of morphodynamic bedform systems.

Multi-purpose Artificial Reefs (MPARs) are structures that may provide aesthetically acceptable coastal protection and improve recreational outcomes. Twenty years after construction of the first MPAR, Narrowneck Reef on the Gold Coast of Australia, most of the available literature is still focused on the planning, design and construction of such structures and peer-reviewed publications on their post-construction monitoring, interaction with sediment transport and impacts on coastal morphology are lacking. The aim of this paper is to evaluate how does Narrowneck Reef influence the sediment transport, and morphological changes around the anthropogenic structure, two decades after construction. To do so, a combination of ten high spatial resolution topo-bathymetric surveys from the top of the dune to the 10 m depth captured over 21 months and a series of 60 simulations using a calibrated numerical model were used. Our results demonstrate that: although not expected during design or reported in similar structures, sand can bypass the MPAR around its offshore end; under oblique waves, the longshore currents are deflected as they pass the reef, resulting in a shadow zone on the downdrift side where sand deposits; the bar crest tends to be higher on the reef's updrift side compared to downdrift, indicating that the MPAR can act as a store for sediments, as initially designed. Furthermore, the MPAR can act to stabilise the bar as it moves onshore with a downdrift offset of the inner bar as a result of low oblique wave incidence. The results presented here demonstrate that the short-term response to the MPAR twenty years after construction is more closely related to the updrift build up of sand and the deflection of longshore currents as they encounter the reef than to the dissipation of wave energy. This is because MPARs are designed to dissipate just enough wave energy so that they can achieve their recreational goal (surfing).

Topographic site effects in anti-plane problems have been studied for four decades cause of the obtained analytical solutions. The authors have developed proposed hybrid methods combining Lamb's series with finite element method (FEM) to resolve the problem of anti-plane scattering; however, it has been difficult to account for site effects in in-plane problems due to mode conversion. In this study, we sought to resolve this issue by developing a novel hybrid method to investigate the site effects of a canyon subjected to longitudinal waves (P waves) as well as horizontal and vertical displacement amplitudes ( | u x | and | u z | ) near and along canyons of various shapes. A transfinite interpolation function (TFI) was used to obtain the coordinates of nodes and conduct node numbering in the inner finite region within the canyon. Combining hybrid method with TFI function, similar procedures can be used to resolve the scattering problems in both anti-plane and in-plane problems. Canyons are divided into three groups according to shape: 1) smooth shallow, 2) non-smooth, and 3) smooth deep. We also examine the incident angle of P waves ( θ ), the dimensionless frequencies ( η ), and the shape of a canyon in terms of their effect on | u x | and | u z | . These factors were shown to generate site effects, including canyon-decay-effect, oblique-effect, shield effect, and SDCP (slope discontinuous points) effect. The site effects induce variations in | u x | and | u z | with constructive interference in the illuminated zone, destructive interference in the shadow zone, and attenuation along the surface of the canyon.

To predict ice accretion on the helicopter rotor more accurately, a three-dimensional Eulerian method with a shadow zone dispersion model is developed for calculating the water collection efficiency on blades in the unsteady vortex flowfield of the rotor. Firstly, the unsteady vortex flowfield of the rotor is calculated using a CLORNS code. Secondly, considering the 3-D effect of the rotor deeply, the droplet flowfield on the same embedded grids is solved by the Eulerian method to overcome the defects of traditional 2-D calculation methods for predicting rotor icing. To increase the stability and efficiency of the Eulerian method, the shadow zone dispersion model is presented. Thirdly, the calculated results are respectively validated through the ice amount comparisons with experimental results of UH-1H rotor and SRB rotor. The simulated results show that the blade-tip vortex has a significant effect on the water collection efficiency and causes a drop in the water collection amount along the blade spanwise direction. Finally, the effects of the advance ratio and the forward tilting angle of the rotor shaft on the water collection efficiency are calculated and analyzed, and some new conclusions are obtained. In forward flight, the blade-tip vortex has a more obvious effect on the water collection efficiency in the advancing blade than that in the retreating blade, and this effect decreases with the increase of the advance ratio and the forward tilting angle.

Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography , which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Frechet derivative. We also included regularization to resolve the ill-posed inverse problem , and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.

This study aims to determine if large-scale choked panel destress blasting can provide sufficient beneficial stress reduction in highly-stressed remnant ore pillar that is planned for production. The orebody is divided into 20 stopes over 2 levels, and 2 panels are choke-blasted in the hanging wall to shield the ore pillar by creating a stress shadow around it. A linear-elastic model of the mining system is constructed with finite difference code FLAC3D. The effect of destress blasting in the panels is simulated by applying a fragmentation factor (α) to the rock mass stiffness and a stress reduction factor (β) to the current state of stress in the region occupied by the destress panels. As an extreme case, the destress panel is also modeled as a void to obtain the maximum possible beneficial effects of destressing and stress shadow. Four stopes are mined in the stress shadow of the panels in 6 lifts and then backfilled. The effect of destress blasting on the remnant ore pillar is quantified based on stress change and brittle shear ratio (BSR) in the stress shadow zone compared to the base case without destress blasting. To establish realistic rock fragmentation and stress reduction factors, model results are compared to measured stress changes reported for case studies at Fraser and Brunswick mines. A 1.5 MPa immediate stress decrease was observed 20 m away from the panel at Fraser Mine, and a 4 MPa immediate stress decrease was observed 25 m away at Brunswick Mine. Comparable results are obtained from the current model with a rock fragmentation factor α of 0.2 and a stress reduction factor β of 0.8. It is shown that a destress blasting with these parameters reduces the major principal stress in the nearest stopes by 10–25 MPa. This yields an immediate reduction of BSR, which is deemed sufficient to reduce volume of ore at risk in the pillar.

Correlations between the calculated Coulomb stress changes and observed seismicity rate changes after the Wenchuan earthquake are investigated in this article. Three improvements are made in the calculation of static stress change, including employing a dislocation method with triangular elements rather than traditional rectangular elements, setting up a more realistic source-slip model and a more complete receiver fault model, and resolving stress changes on assumed receiver faults with spatially variable focal mechanisms based on well-determined focal mechanisms at different calculation points. The recorded aftershocks are mapped for comparison with the spatial distribution of stress changes. The results indicate that the Wenchuan earthquake encourages not only three major fault systems (the East Kunlun, south of Xianshuihe and west of Qinling Southern Frontal) but also several other regions including Tazang, north of Min Jiang, north of Pingwu-Qingchuan and west of Chongqing. In particular, the eastern segment of Longriba is shown to be quite dangerous with dramatic stress increase. The influence of depth and frictional coefficient is analyzed. The depth of calculation beyond the depth range of the source model will make a significant difference to the stress-change map and thus cannot be neglected. Many aftershocks occurring in the stress shadow zone near the main rupture can be attributed to dynamic stress triggering and the fractal structure of the main fault. The observed seismicity rate changes are compared with the static stress changes. The results show that high background seismicity rates will amplify the effect of stress change. The observed seismicity rate changes support the forecast rate of 10-year seismicity after the Wenchuan earthquake based on the rate- and state-dependent friction model. Coulomb stresses increase on the focal mechanisms away from the main rupture, which demonstrates the influence of the Wenchuan earthquake over a wide range. Especially, the focal mechanism for Lushan earthquake undergoes a stress increase by more than 2.0 bars, which suggests that the Lushan earthquake has been effectively promoted by the Wenchuan earthquake.

Movable-bed large-scale laboratory experiments were conducted to examine the fate and quantify the benefits of nearshore placed dredged material. Two tests were performed on a beach classified as eroding [19] for mounds placed in the active zone described by Hands and Allison [12] at two depths. Mound sand was dyed to provide contrast and to differentiate it from the native sand beach. Beach surveys were performed intermittently during each experiment with a laser scanner. In addition to beach change elevations, the scanner provided RGB color components, which permitted tracking of the mound sand. The experiments showed that the mound sand dispersed rapidly and was transported mainly downdrift. Sand accumulation was observed on the beach onshore and adjacent to the mounds mainly due to wave sheltering of the mounds described as the longshore effect by [28] . There was little contribution to onshore accretion from cross-shore migration of the mounds. Beach response was similar to that of an offshore breakwater in which the mounds provided a wave shadow zone to the leeward beach. The results from the experiment will provide validation data for the numerical morphological model C2SHORE [15] .

Biophysical interactions of the mesopelagic fauna and hydrodynamic features were investigated at a shallow, tall seamount in the tropical Northeast Atlantic based on data from three inter-disciplinary surveys collected between 2009 and 2015. Senghor Seamount is located close to the equator in a unique but underexplored oceanographic setting, where classical seamount effects are expected to be small. Shipboard Acoustic Doppler Current Profiler (ADCP) and remote sensing data revealed flow phenomena strongly varying over different temporal and spatial scales. The quasi-steady, longer period flow at the seamount was largely unchanged by flow-topography interaction with the exception of a persistent and recurring shadow zone of weaker currents downstream of the summit. Senghor Seamount is exposed to energetic mesoscale eddy activity in surrounding waters with potentially large physical and biological implications. At higher frequencies, tidal currents interacting with the seamount generated large-amplitude internal waves propagating horizontally and vertically away from the summit. Analysis of acoustic backscatter data and micronekton biomass displayed prominent near-surface night time and deep (>400 m) day time scattering layers associated with the diurnal vertical migration of the mesopelagic fauna. An intense and previously unreported aggregation of acoustic scatterers was detected in the depth range 150–300 m inside a radius of 3 km along the upper slopes of the seamount summit. ADCP measurements over a full semi-diurnal tidal cycle suggest that biophysical interactions were present in near-seafloor waters around the upper seamount as evidenced by plankton distributions that were modified by topographic blocking during descent and aggregation in waters characterised by internal waves and enhanced tidally-driven energy dissipation.

Transversely polarized seismic waves are routinely observed in ambient seismic energy across a wide range of periods, however their origin is poorly understood because the corresponding source regions are either undefined or weakly constrained, and nearly all models of microseism generation incorporate a vertically oriented single force as the excitation mechanism. To better understand the origin of transversely polarized energy in the ambient seismic wavefield we make the first systematic attempt to locate the source regions of teleseismic SH waves observed in microseismic (2.5–20 s) noise. We focus on body waves instead of surface waves because the source regions can be constrained in both azimuth and distance using conventional array techniques. To locate microseismic sources of SH waves (as well as SV and P waves) we continuously backproject the vertical, radial, and transverse components of the ambient seismic wavefield recorded by a large-aperture array deployed in China during 2013–2014. As expected, persistent P wave sources are observed in the North Atlantic, North Pacific, and Indian Oceans, mainly at periods of 2.5–10 s, in regions with the strong ocean wave interactions needed to produce secondary microseisms. SV waves are commonly observed to originate from locations indistinguishable from the P wave sources, but with smaller signal-to-noise ratios. We also observe SH waves with about half or less the signal-to-noise ratio of SV waves. SH source regions are definitively located in deep water portions of the Pacific, away from the sloping continental shelves that are thought to be important for the generation of microseismic Love waves, but nearby regions that routinely generate teleseismic P waves. The excitation mechanism for the observed SH waves may therefore be related to the interaction of P waves with small-wavelength bathymetric features, such as seamounts and basins, through some sort of scattering process.

Despite advances in understanding processes of sand transport by saltation and reptation, which are involved in the formation of sand ripples, the mechanisms that determine the linear dependence of ripple spacing on wind speed and their relative importance are yet unknown. In a pivotal study, Sharp (1963) proposed that this linear dependence arises from the scaling of the ripples’ shadow zone – the part of the ripple devoid of particle impacts – with the wind speed. Here, we test this hypothesis by integrating wind tunnel experiments with numerical simulations of saltation. Specifically, we measured the effective shadow zone by using sand traps designed for this purpose and found a linear relationship between the shadow zone and the wind shear velocity, consistent with Sharp’s hypothesis. However, contrary to what Sharp assumed, we found that the shadow zone is not completely screened from particle impacts, which as indicated by numerical simulations is due to the wide distribution of impact angles. Nonetheless, the shadow zone can be one of the major mechanisms contributing to the linear increase of the ripple wavelength with wind speed at the nonlinear growth stage of the ripples where merging events between small ripples take place. However, for the initial stage of ripple development, when the ripple dimension is small, other mechanisms can be dominant, such as the recently suggested resonant saltation trajectory (Duran et al., 2014).

Background The curved shoreline shape of embayed beaches is one of its most notable characteristics and can be described using the parabolic bay shape equation (PBSE). Wave diffraction in and around the shadow zone is often regarded as the primary forcing mechanism leading to the prominent curvature of the shoreline. However, wave climate variables (wave direction, directional spreading and wave height) are shown to be influential in redistributing wave energy throughout the bay and in the shadow zone. Methods In this study, a process-based morphological model (Delft3D) is used for hydrodynamic and morphodynamic simulations of a schematic embayed beach. Wave forcing conditions are systematically varied between a mixture of time-invariant and time-varying cases. Results The role of diffraction is shown to be dominant only when the wave conditions are both narrow-banded ( 30°). Otherwise, as little as 6% variation in wave direction within a 90° range can account for the shoreline curvature in and around the shadow zone. Conclusion The degree to which wave direction and directional spreading vary through time therefore has a large effect on the equilibrium orientation and shoreline planform of the bay.

Terrestrial LiDAR (light detection and ranging) and a transit compass were used separately to collect discontinuity orientation data at an abandoned quarry in the vicinity of Claytor Lake Dam, southwest of Christiansburg, Virginia. DIPS software program was used to process the data obtained by the two methods. Stereonet plots of orientation data, generated by the DIPS program, were used to determine the principal discontinuity sets present at the quarry. Statistics provided by the DIPS program were compared to evaluate the variability of discontinuity orientation data between the two methods. The purpose was to evaluate the reliability of LiDAR-derived data, by comparing it with manually collected data, and to investigate whether the two datasets yield similar discontinuity orientations. Results of the study show that both data sets are able to identify bedding and two other joint sets. However, one gently dipping joint set, identified by the manually collected data, is either under-represented or missing from the LiDAR data. Possible factors influencing this difference in the two datasets include: (1) shadow zone (related to sampling bias), (2) patch size, and (3) spatial variation of discontinuity orientations. We suggest a protocol for minimizing the influence of these factors on discontinuity mapping by the LiDAR method.

Complaints concerning wind turbine noise have been more widespread in recent years. This is a modeling paper on noise generated by a three blade wind turbine. A single blade is treated as a linear source with the sound power growing from the hub to the tip. The main contribution of this study is the idea of the partially ensonified zone (PEZ), which separates the fully ensonified zone (close to the turbine) and the shadow zone (far away from the turbine). PEZ comes from a blade – a linear source and the wind shear refraction. The commonly used methods provide the A-weighted time average, L AeqT , inside the fully ensonified zone. The main finding is the method of L AeqT estimation within PEZ.

Near surface seismic investigations are expensive and time-consuming. Moreover, seismic processing usually focuses on one particular type of wave and wastes much of the information contained in seismic records that could be used to make near surface seismic surveys more valuable and cost effective. A workflow is proposed herein that combines seismic refraction tomography, multichannel analysis of surface waves (MASW), and seismic reflection using P-waves and SV-waves, which takes advantage of P-wave first arrivals, Rayleigh waves, and P-wave and SV-wave reflections, respectively. The use of the proposed methodology is shown through three case studies carried out in the Outaouais region, Quebec, Canada, using a 24-channel seismograph, vertical geophones, and a sledgehammer. The results show that it is possible to acquire SV-reflections at sites where a strong velocity reversal is present at the surface using only vertical geophones. Under that condition, or more generally when two component geophones are used, the proposed workflow leads to two complementary stacked sections: 1) an SV-wave section that has a high resolution even at shallow depths but can lack coherency and 2) a P-wave section that has better coherency but is blind at shallow depths. Two velocity models are also produced: an SV-wave model that combines the results from MASW and SV-wave reflections and a P-wave model that combines the results from seismic refraction and P-wave reflections. The workflow uses the frequency variant linear move-out (FV-LMO) surface wave filter, which is much more efficient than band pass or f-k filters to process SV waves. The value of many near surface seismic surveys can thus be enhanced by processing all propagation modes, especially when SV-wave reflections are present due to their high resolution.

Sea-surface movement in the ocean induces a time-varying acoustic channel which affects underwater system including acoustic communication. For an investigation of surface movement effects on communication channel parameters (delay time, amplitude, etc.), acoustic transmission and reception experiments were conducted in the water tank. The delay time and amplitude of single surface bounce path from the measurement data show periodic time dependence, which is caused by a travelling periodic sinusoidal surface. A ray-based propagation model is applied to the experimental environment to estimate communication channel parameters. A comparison between measurement data and model result permit a physical interpretation of the communication channel parameters. The difference of single surface bounce path delay times from the model and measurement data are within small error bound. The delay times oscillate around the delay time of single surface bounce path when the surface is flat and show the periodic sine function. The amplitudes from the model are in agreement with those from the measurement data except at low amplitude region. Slight angle and frequency dependencies of source and receiver and noise in the water tank account for the disagreement in this region. Since the crest and trough of surface wave respectively make the acoustic energy emitted from the source converge and diverge, the amplitudes have high fluctuation and same phase with the delay time. The ray model is applied to an environment in the ocean. A striation pattern appears in surface reflected signal due to shadow zone on the surface.

We developed a new back-projection method that uses teleseismic P-waveforms to integrate the direct P-phase with reflected phases from structural discontinuities near the source and used it to estimate the spatiotemporal distribution of the seismic energy release of the 2011 Tohoku-oki earthquake. We projected a normalized cross-correlation of observed waveforms with corresponding Green's functions onto the seismic source region to obtain a high-resolution image of the seismic energy release. Applying this method to teleseismic P-waveform data of the 2011 Tohoku-oki earthquake, we obtained spatiotemporal distributions of seismic energy release for two frequency bands, a low-frequency dataset and a high-frequency dataset. We showed that the energy radiated in the dip direction was strongly frequency dependent. The area of major high-frequency seismic radiation extended only downdip from the hypocenter, whereas the area of major low-frequency seismic radiation propagated both downdip and updip from the hypocenter. We detected a large release of seismic energy near the Japan Trench in the area of maximum slip, which was also the source area of the gigantic tsunami, when we used only the low-frequency dataset. The timing of this large seismic energy release corresponded to an episode of smooth and rapid slip near the Japan Trench, and reflects the strong dependence of the seismic energy distribution obtained on the frequency band of the input waveform dataset. The episode of smooth and rapid slip may have been the trigger for a release of roughly all of the accumulated elastic strain in the seismic source region of the 2011 Tohoku-oki earthquake.

Traditional methods of imaging the Earth's subsurface using seismic waves require an identifiable, impulsive source of seismic energy, for example an earthquake or explosive source. Naturally occurring, ambient seismic waves form an ever-present source of energy that is conventionally regarded as unusable since it is not impulsive. As such it is generally removed from seismic data and subsequent analysis. A new method known as seismic interferometry can be used to extract useful information about the Earth's subsurface from the ambient noise wavefield. Consequently, seismic interferometry is an important new tool for exploring areas which are otherwise seismically quiescent, such as the British Isles in which there are relatively few strong earthquakes. One of the possible applications of seismic interferometry is ambient noise tomography (ANT). ANT is a way of using interferometry to image subsurface seismic velocity variations using seismic (surface) waves extracted from the background ambient vibrations of the Earth. To date, ANT has been used successfully to image the Earth's crust and upper-mantle on regional and continental scales in many locations and has the power to resolve major geological features such as sedimentary basins and igneous and metamorphic cores. Here we provide a review of seismic interferometry and ANT, and show that the seismic interferometry method works well within the British Isles. We illustrate the usefulness of the method in seismically quiescent areas by presenting the first surface wave group velocity maps of the Scottish Highlands using only ambient seismic noise. These maps show low velocity anomalies in sedimentary basins such as the Moray Firth, and high velocity anomalies in igneous and metamorphic centres such as the Lewisian complex. They also suggest that the Moho shallows from south to north across Scotland which agrees with previous geophysical studies in the region.

A study is conducted on minimizing the sum of the squared acoustic pressures with a linear array of control sources and a perpendicular linear array of error sensors, placed above the top of a noise barrier. Particular angular orientations, with respect to the center of the barrier top, and spacings of the linear arrays of control sources and error sensors result in moderate to significant additional reduction of the acoustic pressure in the shadow zone. Visual inspection of the sound pressure field, with and without active noise control, found that uniform and significant additional insertion loss can be generated near the barrier. Numerical simulations were conducted to test the proposed method. For separations between control sources and error sensors much less than a quarter wavelength of the primary noise disturbance, results show that the angular orientation, of the combined linear control source and sensor arrays, is a weak factor for acoustic pressure reduction in the shadow zone. Weak angle dependence serves as an advantage to the proposed method, which yields uniform performance for any angular orientation. An angular orientation involving the alignment of the furthest error sensor with the first diffracting edge of the barrier and the primary source was observed to perform well for a variety of frequencies, since the spacing between error sensors and between control sources is of the order of a quarter-wavelength. Improved noise control in the shadow zone of a barrier is achieved by the use of two control sources and angular orientation as mentioned above. Further spatial extension of the area of reduced acoustic pressure is possible by utilizing an increased number of control sources.

A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56m) grid covering 26.2km2 of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (Hs) values and a slight increase of Hs in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the Hs field. © 2011 Elsevier Ltd., Sonia Ponce de León is presently supported by the Ministry of Science and Innovation of Spain (MICINN-JDJ). J. H. Bettencourt is currently supported by the portuguese Foundation for Science and Technology (FCT).

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.

Seismic coda is composed of scattered waves originated from various kinds of heterogeneities, whose locations are not confined in the great-circle ray-path direction between the source and receiver. We devise a technique to image laterally varying regional heterogeneities using single-station seismograms for clustered events. We analyze regional seismic records of the Borovoye seismic station for the Balapan nuclear explosions in Kazakhstan. Scattered waves that arrive coherently over the source arrays, are extracted by directional beamformings. The locations of scatterers responsible for the scattered waves are mapped from the beamforming direction, travel time and slowness (equivalently, phase velocity). The illuminated locations of heterogeneities are highly correlated with the structural variations in surface topography, crustal thickness and sedimentary thickness. The influence of the structural variations on seismic waves is quantified in terms of scattering intensity and quality factor. The scattering properties are observed to vary with phase due to the difference in frequency content and phase velocity. The proposed technique appears to be useful for a study of active tectonic regions with limited monitoring stations.

Shallow high-resolution seismic reflection surveys have traditionally been restricted to either compressional (P) or horizontally polarized shear (SH) waves in order to produce 2-D images of subsurface structure. The northernmost Mississippi embayment and coincident New Madrid seismic zone (NMSZ) provide an ideal laboratory to study the experimental use of integrating P- and SH-wave seismic profiles, integrated, where practicable, with micro-gravity data. In this area, the relation between “deeper” deformation of Paleozoic bedrock associated with the formation of the Reelfoot rift and NMSZ seismicity and “shallower” deformation of overlying sediments has remained elusive, but could be revealed using integrated P- and SH-wave reflection. Surface expressions of deformation are almost non-existent in this region, which makes seismic reflection surveying the only means of detecting structures that are possibly pertinent to seismic hazard assessment. Since P- and SH-waves respond differently to the rock and fluid properties and travel at dissimilar speeds, the resulting seismic profiles provide complementary views of the subsurface based on different levels of resolution and imaging capability. P-wave profiles acquired in southwestern Illinois and western Kentucky (USA) detect faulting of deep, Paleozoic bedrock and Cretaceous reflectors while coincident SH-wave surveys show that this deformation propagates higher into overlying Tertiary and Quaternary strata. Forward modeling of micro-gravity data acquired along one of the seismic profiles further supports an interpretation of faulting of bedrock and Cretaceous strata. The integration of the two seismic and the micro-gravity methods therefore increases the scope for investigating the relation between the older and younger deformation in an area of critical seismic hazard.

A theoretical formula that is based on the geometrical theory of diffraction (GTD) is proposed for computing sound diffraction by multiple wedges, barriers, and polygonal-like shapes. The formula can treat both convex and concave edges, where edges may or may not be inter-connected. Comparisons of theoretical predictions with other results done by the BEM or experiments for scaled model confirm the accuracy of the present formula. Numerical examples such as double wedges and doubly inclined barrier show that when there exist several diffraction paths for given source and receiver positions, the insertion loss is dominated by the diffraction associated with the shortest propagation path. It is also found that although the partially inclined barrier increases the shadow zone as compared to the simple screen type of the same total height, it does not necessarily increase the insertion loss at all heights.

An integral representation of the wave field in the form of an interference integral is used to investigate the effects of near-solar plasma inhomogeneities on the propagation of radio waves. Asymptotic formulas are derived for the energy spectrum of spacecraft radio signals in the illuminated region and in the neighborhood of a caustic. Numerical simulations of the energy spectrum are performed for different parameters of the plasma inhomogeneities in the solar corona. In the caustic shadow region, where direct and Sun-reflected rays are formally excluded, it is shown that the form of the energy spectrum depends directly on the scattering inhomogeneity parameters. The additional information about the wave field structure in the presence of caustic focusing is a promising new diagnostic for coronal radio sounding investigations.

Simulation of thermal environment around buildings is of great importance for residential microclimate study. In this article, a numerical method is proposed to simulate the outdoor thermal environment around buildings. By the method, temperature distributions of the outdoor air, building surfaces and ground surfaces are achieved by combining computational fluid dynamics (CFD) calculation of air flow and energy balance equations calculation of surfaces. In every computing time step, the outdoor air distribution is calculated as quasi-steady condition. And the surface temperatures of buildings and ground are simplified as “shadow zone temperature” and “sunshine zone temperature” to reduce the calculating time and memory space. Response factor method is employed to deal with the transient heat transfer between outdoor air and surfaces of buildings and ground. The numerical method is validated by the measured data of outdoor thermal environment around one single building and the simulated temperature distributions are illustrated and analyzed at different time in a day.

The paper reports about an investigation of the erosion resistance of two types of hydraulic concrete, namely a plain hydraulic concrete (PC) and a steel-fibre reinforced hydraulic concrete (FRC). The flow erosion was simulated by high-speed water jets with velocities up to 234 m/s and impact angles of 15 ◦ and 90 ◦ , respectively. A general relationship could be found between relative erosion rate (g/g) and process parameters: ER ∝ v n f(θ), with n between 1.1 and 1.25. However, it was shown that the type of pump used for the experiments was critical to these results. The reason was that water flow velocity and water mass flow rate could not be varied independently. If the absolute erosion rate (g/s)—characterised by a constant water mass flow rate—was considered, a modified relationship ˙ ER ∝ v n+q F f(θ) was derived, where q considered water volume effects. Values for q were about unity. In general, erosion rate decreased if the concrete was reinforced. However, the influence of the fibre reinforcement was more pronounced for the lower impact angle. This is explained by the formation of a ‘shadow zone’ behind the fibres in case of shallow impact angle. © 2004 Elsevier B.V. All rights reserved.

In recent years there has been growing interest in the use of noise barrier profiles that can enhance the diffraction efficiency of plane barriers. These are placed on the top of the barrier in order to reduce sound diffracted into the shadow zone. A variety of shapes have been tested including T-shapes, multiple-edges and various cylindrical configurations. Despite numerous demonstrations that the profiles enhance performance there is no universal agreement on how the improvements can be quantified and incorporated into noise prediction models. Without such quantification it is likely that such profiles will not receive widespread acceptance. TRL has carried out an experimental investigation of the performance of novel-shaped barriers for the Transport Research Foundation. The approach relies on quantifying diffraction efficiency in the near field using a novel application of the Maximum Length Sequence (MLS)-based method. Measurements on 4 different profiles were taken in the vertical plane perpendicular to the barrier face. Two source and four receiver positions were used and results were obtained under a range of wind conditions. Results show large differences between the efficiency of the different options with the absorptive T-shaped and multiple-edge profiles performing best.

This paper is concerned with the influence of the diameter of the blocking plate on the gas flux density distribution in a typical calibration chamber. It was found that, at small values of the blocking plate diameter, the shape of the gas flux density function is similar to the sinus function, with zero deviation from the mean value of the gas flux density at mid-height of the chamber. As the blocking plate diameter increases a discontinuity appears at the edge of the “shadow zone”. Until the discontinuity occurs on the side wall, the difference between the maximum and minimum relative gas flux densities is about 3×10 −4 , then it grows to 3.7×10 −3 when the relative blocking plate diameter increases to 0.83 of the chamber diameter. If we confine our attention to the region between 0.33 and 0.67 of the whole chamber height, which is reasonable in practical terms, the maximum difference decreases to 6×10 −4 . Even in this case, this difference is twice as great as that in the case of the chamber without or with the smallest reasonable blocking plate.

Pre-drill reflection surface seismic was carried out in the Aigion city area in February 2001. The poor quality of seismic reflections obtained from standard processing did not allow us to refine the location of the vertical well AIG-10 to be drilled. Subsequently, a brief study of refracted seismic arrivals was attempted in order to better define the well location, in conjunction with observations from a shallow well. In 2002, after drilling, an innovative 6-VSP position well seismic survey was successfully run, using a four-component downhole sensor tool, i.e., three orthogonal geophones and a hydrophone. Refracted seismic events and first arrivals from VSP indicated the throw of the Aigion Fault and the fault plane dip; a secondary accident striking about south–north was detected about 100 m west of the well. No P–P seismic reflection was evidenced from standard VSP processing. To cite this article: C. Naville et al., C. R. Geoscience 336 (2004).

Atmospheric turbulence causes scattering of sound, which can reduce the performance of sound barriers. This is an important inclusion in prediction models to obtain a correct picture of the sound reduction at higher frequencies. Here a prediction method is applied that uses the strengths of the wind and temperature turbulence to estimate the scattered power into the shadow zone of a barrier. The predictions are compared to full-scale measurements on a thick barrier, where both acoustic and meteorological data were recorded simultaneously under both calm and windy conditions. Comparison between the measurements and the predictions indicate that the method gives reasonably accurate results for mid to high frequencies and a slight overestimation at very high frequencies.

In the present work the Green’s function of the mild-slope and the modified mild-slope equations is studied. An effective numerical Fourier inversion scheme has been developed and applied to the construction and study of the source-generated water-wave potential over an uneven bottom profile with different depths at infinity. In this sense, the present work is a prerequisite to the study of the diffraction of water waves by localized bed irregularities superimposed over an uneven bottom. In the case of a monotonic bed profile, the main characteristics of the far-field are: (i) the formation of a shadow zone with an ever expanding width, which is located along the bottom irregularity, and (ii) in each of the two sectors not including the bottom irregularity the asymptotic behavior of the wave field approaches the form of an outgoing cylindrical wave, propagating with an amplitude of order O(R−1/2), where R is the distance from the source, and wavelength corresponding to the sector-depth at infinity. Moreover, the weak wave system propagating in the shadow zone is of order O(R−3/2), and along the bottom irregularity consists of the superposition of two outgoing waves with wavelengths corresponding to the two depths at infinity.

Time domain 2.5-D finite-difference simulations of ground-penetrating radar (GPR) responses from models of buried human remains suggest the potential of GPR for detailed non-destructive forensic site investigation. Extraction of information beyond simple detection of cadavers in forensic investigations should be possible with current GPR technology. GPR responses are simulated for various body cross-sections with different depths of burial, soil types, soil moisture contents, survey frequencies and antenna separations. Biological tissues have high electrical conductivity so diagnostic features for the imaging of human bodies are restricted to the soil/skin interface and shallow tissue interfaces. A low amplitude reflection shadow zone occurs beneath a body because of high GPR attenuation within the body. Resolution of diagnostic features of a human target requires a survey frequency of 900 MHz or greater and an increment between recording stations of 10 cm or less. Depth migration focuses field GPR data into an image that reveals accurate information on the number, dimensions, locations and orientations of body elements. The main limitation on image quality is attenuation in the surrounding soil and within the body. 3-D imaging is also feasible.

By using the semblance analysis of seismic noise prehistory of local earthquakes recorded by a dense seismic array, we reconstruct the image of distributed sources of weak seismic radiation beneath the Earth's surface. Array observations were carried out in the Nikko area, northern Kanto, Japan in 1993 by Joint Seismic Observation Team. The array consists of 195 three-component seismometers distributed along perpendicular profiles whose array diameters are 7 km. From the analysis of data, several active volumes in the upper crust were identified and new features of seismic emission discovered. A joint analysis of the coda and seismic noise shows that a mid-crustal magma body that was identified before by reflection analysis is both a scattering region and a source of seismic emission. Another large active volume is visible to the east of the array at depths of 2–15 km; it coincides with a known low-velocity and high-attenuation anomaly. This emission region corresponds to an area of large earthquakes.

In the present study, a special case of refraction due to wind blowing along the track is considered. Turbulence caused by wind eddies destroys the coherent nature of the ground effect. Due to upward refraction and the resulting shadow zone, only a segment of a track contributes to the noise in the receiver. The model contains three adjustable parameters that must be estimated at the site of interest.

Diffraction phenomena caused by edges and vertices are important in a number of studies and applications of wave propagation methods. Diffractions play a fundamental role, for example, in the interpretation of seismic data from faults and other complex geological structures in which petroleum reservoirs are located. The geometric theory of diffraction provides a good description of the diffraction of scalar waves from an edge in a homogeneous medium assuming free or rigid boundary conditions. The solution becomes infinite at the shadow boundary between the illuminated zone and the shadow zone, so that, within this region, a boundary layer solution must be used. This can be achieved by analytic continuation of the geometrical ray solution or, equivalently, using a one-dimensional or two-dimensional diffusion equation for modelling the amplitude of the diffracted wave. An alternative, older method for obtaining asymptotic expressions for different parts of the wavefield is by asymptotic expansion of the Kirchhoff integral. The authors have developed a new reciprocal surface-scattering integral by applying the divergence theorem to the Born volume integral. This new integral is called the Born–Kirchhoff (BK) integral. The scattering surface is a finite sum of smooth surfaces separated by smooth curves with a finite number of corners. The BK integral is now a sum of integrals over each smooth surface. These integrals are evaluated by the method of stationary phase, resulting in specularly reflected waves and boundary diffracted waves represented by a line integral along the boundary of each surface. Further asymptotic evaluation of these line integrals results in expressions for edge-and corner-diffracted waves. Smooth approximations of the wavefield are given for the case that a reflection point and an edge-diffraction point are close to each other, and when an edge-diffraction point and a corner-diffraction point are close to each other. These formulas can be cascaded to provide asymptotic expressions for multiple converted, reflected, transmitted and diffracted waves in anisotropic, inhomogeneous, elastic media. In the case that the rays are well separated from all shadow zones, the new expressions satisfy reciprocity.

The efficiency of a seismic network in providing information on the rate of seismicity, and on the inner structure of Mars, is estimated through a statistical analysis which takes into account the possible existence of a liquid core, the expected low rate of seismicity of Mars when compared to the Earths, and the attenuating properties of the mantle. The tests are performed for two frequency ranges (0.1–1.0 Hz and 0.5–2.5 Hz), for three instrumental noise amplitude densities ranging from 5 to 500×10 −10 m s −2 Hz −1/2 , and for three network configurations consisting of 4, 12 and 16 stations. Travel time tables are computed for P, S, PcP, ScS, and PKP phases using a simplified three layer model. Present-day estimates of liquid core radius induce a 25° wide shadow zone beginning at epicentral distances larger than 110°. Consequently, the best detection efficiency which can be expected from any network is of the order of 60% for mantle body waves. The detection efficiency is primarily controlled by the instrumental noise level. Since the amplitude of mantle body waves rapidly decreases with epicentral distance, high noise level instruments can only detect local events. Therefore, the detection score attained by 4 highly sensitive stations can be up to 30 and 7 times better than the score attained by 12 high noise level sensors, for mantle P and S waves, respectively. If crustal scattering is negligible, the record of mantle P waves on a network consisting of four low noise level instruments would permit to sample Mars mantle down to the core-mantle boundary. Conversely, the deepest penetration of rays recorded by a network of 12 high noise level sensors would hardly reach 300 km. In fact, strong crustal scattering might be the most important difficulty to be encountered in a seismic exploration of Mars. A possibility to deal with this problem would be to associate each of the four low noise instruments with three medium noise level sensors. This network strategy might permit to sample P and S mantle waves travelling down to 400–600 km, even if a lot of seismic energy is lost through crustal scattering.

A simple method is presented that requires measurements at only two positions. It can be used for the prediction of the time-averaged sound level, L AT , above a plain and homogeneous ground surface, in open space with no obstacles nearby. Upward and downward conditions are addressed, in addition to geometrical spreading and ground effect. The method makes it possible to predict L AT at the receiver, located beyond the shadow zone that is caused by upward refraction.

This paper examines the steady barotropic frictionally controlled circulation over a linear shelf which has an abrupt change in width. The model allows the net longshore transport to be specified and includes forcing due to: (1) flow through a gap in the coastline located along the discontinuity; and (2) longshore wind stress. Rapid longshore variations in the flow occur in the neighbourhood of the shelf width discontinuity and therefore both the cross-shelf and long-shore components of bottom friction must be retained. These give rise to a vorticity equation of elliptic character, in contrast to the parabolic “arrested topographic wave equation”. A “shadow zone” is produced on the wide shelf, adjacent to the shelf width discontinuity, in response to a uniform longshore wind stress. Within the shadow zone the fluid is almost stagnant. As friction increases, greater cross-isobath flow occurs, which reduces the area of the shadow zone. A combination of flow through the strait and longshore wind stress can generate complicated flow patterns in which eddies are ubiquitous. A combination of prescribed non-zero net poleward longshore transport and a uniform longshore wind stress generate a nearshore flow which is equatorward-poleward when the wind is directed equatorward-poleward. Further, the axis of the poleward longshore current migrates towards the shelf edge in response to an equatorward longshore wind stress of increasing magnitude. Seasonal variations in the nearshore flow off Vancouver Island, described by Hickey [(1979)Progress in Oceanography,8, 191–279] and Freelandet al. [(1984)Atmosphere-Ocean,28, 288–302] can be qualitatively reproduced by this simple method.

This review of dielectric aspects of relaxation processes begins with a survey of current experimental capabilities. These now extend from 10−4 Hz to 1010 Hz with comparative ease and good resolution by broad band methods. The increasing difficulties of measurements from much above 1010 Hz to 1012 Hz or more are considered together with the prospects for improvement. The need for and value of information in this ‘shadow zone’ is illustrated by several examples. Some limitations of dielectric probes of relaxation in general and of charge displacement in particular in relation to other approaches are indicated before turning to discussion of several classes of complex systems. Viscous liquids and their approach to their glass transitions are discussed, with particular attention to choice of representative examples and the need for studies of liquids composed of simpler molecules in order better to distinguish universality and individuality. Various possible origins of ‘excess absorption’ at higher frequencies other than stretched exponential or skewed arc behavior are also considered in this context. Two classes of molecular crystals that exhibit orientational relaxation effects, hydrogen halides and chlorinated methyl benzenes, receive attention because they both show changes from asymmetric to broad symmetric characteristic relaxation spectra associated with the state of order which may have more general implications. Problems with representation and interpretation of data for charge transport in ionic conducting glasses are indicated, with an indication of considerations to be kept in mind in resolving problems for conducting dielectrics generally, as are other generalities about dielectric and charge transport problems.

At long wavelengths, diffraction effects cause condensing lightpipes to have a significant response in directions within the geometric optics shadow zone. Here, using an analogy with the corrugated “scalar” horns often used in antenna engineering, we point out that a lightpipe with anisotropic surface impedance on its interior surfaces can have substantially reduced sidelobe levels. This may be important for measurements requiring high dynamic range, particularly in the far-infrared.

Ripples arise spontaneoulsy from sandy beds subjected to winds sufficient to cause the saltation of surficial grains. While the initially fastest growing wavelengths are 4–6 times the mean hop length of grains impelled downwind by long-trajectory high-energy saltating grains, the ripple wavelengths developed over long periods can be several times this. Numerical simulations based upon techniques pioneered by P.K. Haff and coworkers reveal that a complex process of ripple coalescence is responsible for this evolution of the ripple field. Small, fast-moving ripples catch up with and are absorbed by larger, slower forms, each such merger resulting in a growth of the mean wavelength and a decline in the relative dispersion of the wavelengths. An heuristic argument is presented which accounts for the fast initial growth and subsequent slowing of growth of the mean wavelength as the ripple field evolves. Ripple cross-sectional shape appears to be controlled in large part by a distrianment function which represents the declining likelihood of a grain stopping on a surface as it slopes more steeply downwind. That the resulting asymptotic wavelength in the simulations depends strongly upon impact angle supports Sharp's (1963) suggestion that the length of the shadow zone plays an important role in controlling the final ripple wavelength.

In the source region of a large shallow earthquake, there is likely to be a small spot characterized by the production of high accelerations and a gap in the aftershocks. On the seismograms of most large shallow earthquakes, and on some seismograms of moderate main shocks, two types of P-waves may be detected: the relatively low-amplitude waves following phase P 1 and the predominant high-frequency waves following phase P 2 . The duration of the seismic waves following phase P 1 (the P 1 −P 2 time) increases proportionately with the earthquake magnitude. This fact strongly suggests that the preliminary rupture period is closely related to the radiation of the predominant high-frequency seismic waves. To explain the above observation, the shear strain waves radiated from a moving rupture are calculated. Because the seismic wave velocity is generally higher than the rupture propagation velocity, maximum shear strains by seismic waves usually precede the rupture front. If the total shear strain, which is equal to the static pre-earthquake shear strain plus dynamic shear strain excited by seismic waves, exceeds the critical shear strain (~ 10 −4 ), the secondary ruptures break out in the forward direction from the initial rupture. The rupture processes of large or moderate earthquakes occur in two stages: one is the initiation of rupture corresponding to phase P 1 , and the other is the development of secondary ruptures triggered by seismic shear strain waves. The latter process generates an earthquake bright spot which radiates high-amplitude seismic waves.

Previous methods of determining the curved waterlines of bays which form on the coasts around the world have involved the logarithmic spiral. This has been applied to unstable bays which could erode back to a limit termed “static equilibrium” for which the constant in the spiral could be related to the obliquity of the wave crests to the control line, joining the upcoast headland to the downcoast extremity of the bay. It is shown that this applies mainly to the shadow zone behind the upcoast headland and not to the full bay periphery and does not have a fixed centre. A new method is proposed utilising arcs from the point of wave diffraction to the shoreline, whose lengths and angles to the wave crest line are related to those of the control line. Data and curves are presented for the static equilibrium shape by which the stability can be tested. They thus predict the waterline for the case of no sediment supply either from littoral drift or rivers debouching into the bay. An indentation ratio can also be derived to test stability.

The propagation of seismic waves through Earth models with slightly random lateral and vertical inhomogeneities superimposed on one composed of layers with vertical velocity gradients was investigated. The maximum deviation of velocity from a mean value at a given depth and a correlation distance derived from a two-dimensional smoothing filter were two parameters used to vary the amplitude and size of the velocity anomalies. The resulting models show short discontinuous reflectors scattered about at various depths throughout the model, and are thus in agreement with many deep seismic reflection experiments. On the other hand numerical experiments using ray-tracing techniques showed that the effect of the lateral and vertical velocity anomalies is to scatter the energy, and break up the continuous travel-time lines from vertical gradient models into travel-time segments with different slopes similar to those observed in many long range seismic refraction experiments, and to those resulting from layering effects in the media. Many of the numerical experiments which modelled the random crust produced a Pg segment and a P* segment with an apparent Conrad discontinuity at a depth of 10–20 km, this apparent depth being related to the correlation distance. When a seismic wave propagates through a heterogeneous Earth the amount of its energy which is converted into scattered energy will be a function of the inhomogeneous characteristics of the medium through which it has passed. If a ray passes through a homogeneous Earth the energy arriving at an array station should be relatively coherent whereas if the ray encounters lateral and vertical inhomogeneities its energy will be incoherent and much more complex. A series of coherency measurements done on array recordings of earthquakes at various distances showed that large lateral and vertical variations in complexity exist for different ray paths through the Earth with the region below the 650 km discontinuity in the mantle tending to be much simpler than the region just below the lithosphere.

THE SHORT-WAVE asymptotic form of Green's function for a section is investigated in the case of Neumann's boundary condition. From the solution represented as a contour integral, terms are extracted in the shadow zone and in the light zone, describing the diffracted wave radiated from the ends of the section. Then the corresponding single integrals reduce to expressions identical with the formulas of the geometrical theory of diffraction.