Surface Wave Paths Research Articles

Metasurface Cloaking Lens Designed by the Ray Insertion Method

This paper presents a metasurface cloak with the ability to make regions of any shape and size on the flat lens invisible in the microwave band. The gradient refractive index (GRIN) of the metasurface is designed by the ray insertion method (RIM), which enables the ray paths of electromagnetic surface waves to be tailored in a desired fashion. The lens is composed of periodic metallic square patches etched onto a grounded dielectric substrate to synthesize the required GRIN of the metasurface. The design technique is validated by simulations using a commercial software, which demonstrate the successful bending of impingent waves according to the prescribed paths and thus achieving the desired cloaking effect. A prototype of the GRIN metasurface cloak was manufactured and measured, yielding results that verify the theoretical predictions.

A scalar radiative transfer model including the coupling between surface and body waves

SUMMARYTo describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry with mixed boundary conditions. In this model, Green’s function can be represented as a sum of body waves and surface waves, which mimics the situation on Earth. In a first step, we study the single-scattering problem for point-like objects in the Born approximation. Using the assumption that the phase of body waves is randomized by surface reflection or by interaction with the scatterers, we show that it becomes possible to define, in the usual manner, the cross-sections for surface-to-body and body-to-surface scattering. Adopting the independent scattering approximation, we then define the scattering mean free paths of body and surface waves including the coupling between the two types of waves. Using a phenomenological approach, we then derive a set of coupled transport equations satisfied by the specific energy density of surface and body waves in a medium containing a homogeneous distribution of point scatterers. In our model, the scattering mean free path of body waves is depth dependent as a consequence of the body-to-surface coupling. We demonstrate that an equipartition between surface and body waves is established at long lapse-time, with a ratio which is predicted by usual mode counting arguments. We derive a diffusion approximation from the set of transport equations and show that the diffusivity is both anisotropic and depth dependent. The physical origin of the two properties is discussed. Finally, we present Monte Carlo solutions of the transport equations which illustrate the convergence towards equipartition at long lapse-time as well as the importance of the coupling between surface and body waves in the generation of coda waves.

Using alpha-phase modulation method to solve range ambiguity for high frequency surface wave radar

A new type of high frequency surface wave radar (HFSWR) system consisting of a close-range detection using surface wave path and a long-range detection using skywave path are proposed in this paper. An important portion of this system is to design a signal that can detect longer distance targets, which is the main content of this paper. To minimize the changes to the existing radar system, this paper phase-modulates the original transmitted signal to mitigate range ambiguity. This method is applicable to all kind of single pulse repetition frequency (PRF) original transmitted signal and can manage the received signal in the region of eclipse (where the received signal is incomplete). The simulation results of different original transmitted signals (constant-frequency pulse and P4 phase-coded signals) verify that the long-range target can be correctly detected through this method. Finally, the real data collected at Weihai, China is processed. Comparing the flight information of Automatic dependent surveillance-broadcast (ADS-B) at the time when the data was recorded, two tracks that match the actual flight information in course and positions were found near 900 km (Shuozhou), flying to Hohhot.

Lateral variation in crustal and mantle structure in Bay of Bengal based on surface wave data

Surface waves generated by earthquakes that occurred near Sumatra, Andaman-Nicobar Island chain and Sunda arc are used to estimate crustal and upper mantle S wave velocity structure of Bay of Bengal. Records of these seismic events at various stations located along the eastern coast of India and a few stations in the north eastern part of India are selected for such analysis. These stations lie within regional distance of the selected earthquakes. The selected events are shallow focused with magnitude greater than 5.5. Data of 65, 37, 36, 53 and 36 events recorded at Shillong, Bokaro, Visakhapatnam, Chennai and Trivandrum stations respectively are used for this purpose. The ray paths from the earthquake source to the recording stations cover different parts of the Bay of Bengal.Multiple Filtering Technique (MFT) is applied to compute the group velocities of surface waves from the available data. The dispersion curves thus obtained for this data set are within the period range of 15–120s. Joint inversion of Rayleigh and Love wave group velocity is carried out to obtain the subsurface information in terms of variation of S wave velocity with depth. The estimated S wave velocity at a given depth and layer thickness can be considered to be an average value for the entire path covered by the corresponding ray paths. However, we observe variation in the value of S wave velocity and layer thickness from data recorded at different stations, indicating lateral variation in these two parameters. Thick deposition of sediments is observed along the paths followed by surface waves to Shillong and Bokaro stations. Sediment thickness keeps on decreasing as the surface wave paths move further south. Based on velocity variation the sedimentary layer is further divided in to three parts; on top lay unconsolidated sediment, underlain by consolidated sediment. Below this lies a layer which we consider as meta-sediments. The thickness and velocity of these layers decrease from north to south. The crustal material has higher velocity at the southern part compared to that at the northern part of Bay of Bengal indicating that it changes from more oceanic type in the southern part of the Bay to more continental type to its north. Both Moho and lithosphere − asthenosphere boundary (LAB) dips gently towards north. Thicknesses of both lithosphere and asthenosphere also increase in the same direction. The mantle structure shows complex variation from south to north indicating possible effect of repeated changes in type of tectonic activity in the Bay of Bengal.

Beneath Bass Strait: Linking Tasmania and Mainland Australia using Ambient Seismic Noise

One of the most hotly debated topics in Australian geology pertains to the tectonic relationship between Tasmania and mainland Australia. Among the main difficulties in reconciling mainland Australian and Tasmanian tectonics is the lack of Precambrian exposure in the Lachlan Orogen (Victoria), which contrast with the West Tasmania Terrane that exhibits numerous outcrops of Proterozoic rocks, apparently excluding any tectonic affinity between them. Furthermore, the West Tasmania Terrane differs significantly from the East Tasmania Terrane in that the latter does not contain any evidence of Precambrian rocks and no evidence of a Proterozoic continental basement has been reported, either in outcrop nor inferred from geophysical surveys. Furthermore, the presence of Bass Strait and the Mesozoic and Cainozoic sedimentary and volcanic sequences that mask the older terranes, makes the link between Tasmania and southeast mainland Australia even harder to decipher. This has significantly impeded the ability of conventional surface mapping to unravel the tectonic history of this area, which remains one of the great challenges of Australian Earth sciences. The focus of this study is ambient seismic noise data from 24 broadband stations, which span northern Tasmania, several islands in Bass Strait and southern Victoria, thus allowing a dense coverage of surface wave paths that can be exploited to image the 3-D structure of the crust joining Tasmania and Victoria in high detail. To produce the highest quality Greenâ??s functions, careful processing of the data has been performed, after which Group and Phase velocity dispersion measurements have been carried out using a frequency-time analysis method on the symmetric component (average of the casual and acasual signal) of the empirical Green functions. The next step is to invert the dispersion curves for maps of Group and Phase velocity, which is expected to shed new light on the structure beneath Bass Strait.

Locating earthquakes with surface waves and centroid moment tensor estimation

Traditionally, P wave arrival times have been used to locate regional earthquakes. In contrast, the travel times of surface waves dependent on source excitation and the source parameters and depth must be determined independently. Thus surface wave path delays need to be known before such data can be used for location. These delays can be estimated from previous earthquakes using the cut‐and‐paste technique, Ambient Seismic Noise tomography, and from 3D models. Taking the Chino Hills event as an example, we show consistency of path corrections for (>10 s) Love and Rayleigh waves to within about 1 s obtained from these methods. We then use these empirically derived delay maps to determine centroid locations of 138 Southern California moderate‐sized (3.5 > Mw> 5.7) earthquakes using surface waves alone. It appears that these methods are capable of locating the main zone of rupture within a few (∼3) km accuracy relative to Southern California Seismic Network locations with 5 stations that are well distributed in azimuth. We also address the timing accuracy required to resolve non‐double‐couple source parameters which trades‐off with location with less than a km error required for a 10% Compensated Linear Vector Dipole resolution.

Surface Wave Path Corrections and Source Inversions in Southern California

The cut-and-paste (CAP) method for retrieving earthquake source parameters has proven useful in many regions. Since CAP breaks three-component data into Pnl and surface wave segments and models them separately, imperfect 1D Green’s functions can be effectively used to model the records and determine source parameters. The resultant time shifts for different segments, for example, Pnl or surface waves, can provide valuable data for improving the velocity model or Green’s functions. Moreover, if these shifts can be known from empirical path calibrations or estimated from a tomographic map, we can recover both source mechanism and location with an extended procedure CAPloc (Tan et al., 2006). Here we present a complete workflow from path calibration to source inversion in southern California. In particular, we use the CAP results from about 160 events with known locations to derive the Rayleigh and Love wave group velocity maps. We take a tomographic approach to solve for lateral velocity variations in 10 km size cells in a uniformly 12 km thick seismogenic layer. Velocity variations of up to 15% are observed and the patterns correlate well with some geological features. Synthetic surface waves for 2D cuts throughout the model with a finite difference approach show significant improvement over 1D synthetics in fitting surface wave travel times, but little difference in waveforms, which suggests 1D synthetics are sufficient in modeling with simple time shifts. This simplification allows source inversion for both mechanism and location to be easily obtained with CAPloc. Finally, we test the effectiveness of CAPloc in determining source parameters, including both mechanisms and locations with such calibration maps in poorly monitored situations. In particular, we focus on two station inversions with two pioneer stations PAS and GSC, which have appropriate recordings since 1960. Considerable success is achieved when the events are bracketed.

Automated multimode phase speed measurements for high-resolution regional-scale tomography: application to North America

SUMMARY A fully automated method for obtaining multimode phase speed measurements from a single seismogram has been developed and applied to a large data set of three-component longperiod seismograms in North America, constructing high-resolution phase speed maps on a continental scale. The method of our phase speed estimation is based on a fully non-linear waveform inversion by Yoshizawa & Kennett working with a global search method (the Neighbourhood Algorithm). The entire process of waveform fitting and the evaluation of the estimated phase speed have been fully automated employing several empirical quantitative measures, assessing the quality of waveform fit and the relative contributions of each mode in a chosen time window. The measured phase speed data undergo automatic screening for quality control, comprising the threshold evaluation of their reliability and outlier detection and removal. This new automated method has been applied to a large data set recorded at North American stations, including the latest transportable stations of USArray. Using long-period three-component seismograms recorded during the past eight years, we have successfully retrieved large numbers of regional surface wave paths, including over 20000 paths for the fundamental-mode Rayleigh waves over a wide range of frequencies, and over 10000 paths for the higher mode Rayleigh as well as the fundamental-mode Love waves. The consistentresultsoftheautomatedmeasurementproceduresuggestthatthemethodworkswell at regional distances, allowing us to perform a high-resolution mapping of multimode phase speeds in North America. The results of the automated waveform analysis also indicate some intrinsic limitations in the higher mode phase speed measurements from a single seismogram particularly in the short period range, mainly due to the overlapping of higher mode arrivals as well as coupling between mode branches. Despite such an innate difficulty in the higher mode dispersion measurements, the automated method allows us to construct reliable multimode phase speed maps. The current data set of ray paths is significantly biased towards the western half of North America, resulting in non-uniform horizontal resolution across the continent. This issue will be resolved by the future migration of the USArray stations to cover the central and eastern United States. The new automated method can be a useful tool for high-resolution mapping of regional 3-D shear wave structure including possible anisotropy.

FEM-Based Surface Wave Multimixed-Path Propagator and Path Loss Predictions

A finite element method (FEM)-based surface wave propagation prediction simulator is developed. The simulator is tested and calibrated against analytical ray-mode models that also take into account the Millington recovery effects. It successfully calculates path losses over multimixed propagation paths at MF and HF frequency bands where the surface wave contribution is significant.

Numerical method for calculating the surface wave field in the presence of caustics

Due to the lateral heterogeneity of the upper layers of the Earth, paths of surface waves deviate from arcs of great circles. Because of the sphericity of the Earth, the paths intersect on a hemisphere opposite to the epicenter and form caustics consisting of two branches, with their tangent point being a cusp. For this reason, the field of surface waves cannot be analyzed in terms of the ray theory at distances larger than 90°. The asymptotic approach to the analysis of the field in the vicinity of such caustics is very ill-suited for numerical implementation. The difficulties of such an approach to the field calculation are aggravated by the fact that such caustics are superimposed in some regions. Therefore, it is suggested to use the theorem of representation, according to which the field within a certain contour is expressed as an integral whose integrand contains values of the function itself, its derivative along the normal to the contour, and Green’s function. The field on the contour (the circle bounding a hemisphere centered at the epicenter) is calculated by the ray method because rays do not intersect on this hemisphere. These data are used for the construction of the field on the opposite hemisphere assumed to be homogeneous, which enables the construction of Green’s function for this hemisphere. This limitation is not very stringent because the configuration of rays and caustics on this hemisphere is mainly determined by the field on the circle. The integral in the representation theorem is calculated numerically. Numerical examples are presented for models in which one caustic or two superimposed caustics form. These calculations yield constraints on variations in the amplitude and phase of the wave. Rayleigh wave fields are also calculated for a model of the real Earth. It is shown that, at some points, the Rayleigh wave spectrum can be strongly distorted because caustics corresponding to different periods differ in shape.

A Matlab-based Virtual Propagation Tool: Surface Wave Mixed-path Calculator

A new Matlab-Based, user-friendly virtual propagation tool (VPT) that can be used for multi-mixed path surface wave path loss calculations has been designed. Any multi-mixed-path surface wave propagation scenario may be specified by the user together with all the necessary input parameters, and path loss vs. range plots may be produced. The effects of multi-mixed paths, electrical parameters of each propagation section, as well as the frequency can be observed and extra path losses can be predicted. The VPT can be used both for design and training purposes.

Shear waveQstructure and its lateral variation in the crust of China and surrounding regions

SUMMARY We have obtained three-layer crustal models of shear wave Q (Qμ) for several surface wave paths in China and peripheral regions using a single-station, multimode method in which amplitude spectra of fundamental-mode and higher-mode Rayleigh waves, computed for known source depths and mechanisms, are compared to measured spectra. The three layers, totaling 60 km in thickness, roughly comprise the entire crust in the Tibetan plateau and include both the crust and part of the uppermost mantle in other regions where the crust is thinner. Qμ in the shallowest layer, 10 km thick, is lowest (about 40) in the western portion of the Tibetan plateau and highest (about 250) in southeastern China. In the middle layer, at 10–30 km depth, Qμ is lowest (60–80) beneath Tibet and the Pamir thrust system and highest (120–140) in central China and parts of the Sino-Korean platform. Uncertainties of Qμ in the deepest layer, at 30–60 km depth, are much greater than in the upper two layers but available results suggest that Qμ is lowest (about 80) under the Pamir thrust system and highest (about 180) under southern Mongolia. The densities of event and station coverage, although wanting in some regions, allow us to develop the first regionalized maps of crustal Qμ variation for continents. The maps, for depth ranges 0–10 km and 10–30 km, generally show good agreement with Q results obtained earlier with other phases and good correlation with the tectonics of this active region.

Multimode surface wave tomography for the Australian region using a three‐stage approach incorporating finite frequency effects

A three‐stage inversion technique for surface wave tomography is applied to the Australian region. The inversion procedure consists of three independent processes. In the first stage, path‐specific one‐dimensional (1‐D) shear velocity profiles are derived from multimode waveform inversion to provide dispersion information. The information from all paths is then combined to produce multimode phase speed maps as a function of frequency. The first version of these phase speed maps is derived from linearized inversion based on the assumption of surface wave propagation along great circle paths. Subsequently, the 2‐D phase speed maps are updated by including ray tracing and finite frequency effects through the influence zone around the surface wave paths over which the phase is coherent. Finally, in the third stage the 3‐D shear wave speed distribution is reconstructed from the set of updated multimode phase speed maps. This three‐stage inversion of surface waves has significant benefits because it is possible to incorporate multimode dispersion, off‐great circle propagation, and finite frequency effects for surface waves in a common framework. The final 3‐D model, which includes the effects of ray bending and finite frequency, shows improvement in the definition of the model in regions with high gradients in shear velocity, such as near tectonic boundaries, especially in eastern Australia. Despite the natural smoothing imposed by considering the influence zone around the surface wave paths, the final models still require rapid change in shear wave properties in the neighborhood of the edge of the craton.

Determination of the influence zone for surface wave paths

SUMMARY An approximate description of the zone of influence around the propagation path for a surface wave is provided by investigating the Fresnel zones for the frequency range of interest. The influence zone about surface wave paths, over which surface waves are coherent in phase, is identified as approximately one-third of the width of the first Fresnel zone. A technique called Fresnel-area ray tracing (FRT) for surface waves has been used to estimate this region around the ray path for each frequency. The FRT technique is developed by combining two standard ray tracing methods, i.e. kinematic ray tracing (KRT) and dynamic ray tracing (DRT). To obtain the exact Fresnel area in a laterally heterogeneous structure would require the solution of a large number of KRT equations. In contrast, the FRT approach requires just a few ray tracing calculations. In the first step, the trajectory of the surface wave is computed by solving the KRT system for the phase-velocity distribution at the required frequency. In the next step, the behaviour of rays in the zone surrounding the KRT path is calculated by solving the DRT system twice; once from the source to the receiver and once more from the receiver to the source along the same trajectory. Finally, combining the solutions of these ray tracing systems using paraxial ray theory, the Fresnel area around a central ray can be estimated. Using FRT, stationary-phase fields can be constructed around a central ray path in a laterally heterogeneous structure. The influence zone around the ray path is then estimated from the stationary-phase function with simple assumptions concerning the perturbed wavefield. The estimate of the influence zone can be efficiently calculated in laterally heterogeneous structure by using the FRT technique, and allows an extension of current methods of surface wave analysis, which have commonly been based on geometrical ray theory and on the approximation of great-circle propagation. This approach allows the treatment of finite-width rays as well as deviations in propagation from the great circle induced by moderate lateral heterogeneity as revealed by recent tomography models. Such finite-width rays should be of major benefit in enhancing ray-based surface wave tomography.

Acoustic resonances of fluid-immersed elastic cylinders and spheroids: Theory and experiment

Frequency resonances in the scattering of acoustic waves from a target object are caused by the phase matching of surface waves repeatedly encircling the object. This is exemplified here by considering elastic finite cylinders and spheroids, and the phase-matching condition provides a means of calculating the complex resonance frequencies of such objects. Tank experiments carried out at Catholic University, or at the University of Le Havre, France by G. Maze and J. Ripoche, have been interpreted using this approach. The experiments employed sound pulses to measure arrival times, which allowed identification of the surface paths taken by the surface waves, thus giving rise to resonances in the scattering amplitude. A calculation of the resonance frequencies using the T-matrix approach showed satisfactory agreement with the experimental resonance frequencies that were either measured directly (as at Le Havre), or that were obtained by the interpretation of measured arrival times (at Catholic University) using calculated surface wave paths, and the extraction of resonance frequencies therefrom, on the basis of the phase-matching condition. Results for hemispherically endcapped, evacuated steel cylinders obtained in a lake experiment carried out by the NSWC were interpreted in the same fashion.

3-D surface wave group velocity distribution in central-southern Africa

Group velocities estimated from fundamental mode Love and Rayleigh waves are used in a tomography process in central-southern Africa. The waves were generated by eighteen earthquakes, which occurred along the East African Rift and recorded at BOSA, LBTB and SLR seismic stations in southern Africa. The group velocities from Love and Rayleigh waves were isolated using the Multiple Filter Technique (MFT) at the period range of 10 to 50 seconds. The tomography method developed by Ditmar and Yanovskaya (1987) and Yanovskaya and Ditmar (1990), was applied to calculate the lateral distribution of surface wave group velocities in central-southern Africa. The results of the tomographic inversion were plotted as distribution maps. In addition to the maps, I also produced two velocity cross-sections across the area of study. The velocity distribution maps show the regional tectonic units, though with poor resolution. The azimuthal bias of the surface wave paths is reflected in the distribution of the group velocities. The Moho depth appears to correlate with velocities at a period of about 30 s. A low velocity feature observed beneath the Zimbabwe craton implies a thickening upper asthenosphere and lithospheric thinning beneath the Zimbabwe craton. Also estimated was a shear wave velocity model beneath the Zimbabwe craton.

Stochastic modelling of target detection and tracking in surface wave HF radars

In this study, a software package is described which has been developed for the simulation of detection and tracking in surface wave high frequency (SW-HF) radars. The aim is to investigate the problems related to detection and tracking of surface targets at beyond the horizon ranges. In SW-HF radars target detection and tracking involves stochastic features such as target RCS fluctuations, atmospheric, galactic and/or man-made ambient interference components, and the sea clutter with the dominant resonant Bragg returns which affect target detection are all incorporated in the package. In the model, first, terrain data are fed into the simulator by means of a specially designed graphical user interface. Then, a scenario is prepared where the radar's location, coverage and operational parameters can be defined, together with different targets and their sailing routes. The radial propagation paths for angular resolution cells are extracted from the terrain data with the lengths of (possible) sea–island transitions. The surface wave path losses are calculated over the smooth spherical earth's surface with finite conductivity. Surface roughness and mixed-path propagation effects are also included in these calculations. The target detection is performed in the frequency domain after calculation of the noise floor, signal to noise (SNR) and clutter to noise (CNR) ratios. Since SW-HF radars yield coarse range and azimuth but accurate velocity measurements, different Kalman filter techniques are applied for the target tracking, and algorithms are added to improve the track–measurement data correlation. Various simulation tests are performed and the results are presented. © 1998 John Wiley & Sons, Ltd.

Application of the time-frequency polarization analysis to study the complexity of surface wave propagation

A new technique called the time-frequency polarization analysis was introduced in this paper. The technique combined the traditional surface wave analysis techniques (moving window and multi-filter) with the singular value decomposition method to measure the incidence azimuth of surface waves with different wavelengths. It was applied to study the progagation paths of surface waves across the different blocks of Chinese continent and different zones of Qinghai-Xizang (Tibet) plateau. The results show that the method can make full use of the differences in frequency compositions and arrival times of different surface wave modes, and give better polarization analysis results. The analysis by actual data shows that the lateral heterogeneity of the lithospheric structure influences the propagation paths of surface waves severely. Deviations of the paths across the Qinghai-Xizang plateau from great circle paths are great. Deviations of the surface waves across the different zones in Qinghai-Xizang plateau are different.

Variation in microseism power and direction of approach in northeast Greenland

AbstractPrevious work on background noise at seismic stations in Greenland has shown minimum seismic noise in the winter months for frequencies around 1 Hz and maximum seismic noise in the winter months for periods around 6 sec. We have analyzed microseism data from three new digital seismic stations installed during the summer of 1991 in northeast Greenland at Nord, Daneborg, and Scoresbysund. We determined seasonal and station-to-station variations in spectral power density between August and December in the frequency band between 10 sec periods and 5-Hz frequencies. These variations are in agreement with previous studies at periods of 1 and 6 sec. During the summer months, all three stations recorded a minimum for the average spectral power density in the microseism band between 10- and 5-sec periods. From about 3-sec periods to at least 5-Hz frequencies, the average spectral power density is at a maximum during the summer at all three stations. Conversely, the winter months have a maximum in spectral power density between 10- and 5-sec periods and a minimum between about 3-sec periods and at least 5-Hz frequencies at all stations. Station-to-station average-spectral-power-density comparisons show that Nord and Daneborg are roughly comparable over most of the frequency band between 10-sec periods and at least 5-Hz frequencies. Scoresbysund has a systematically higher spectral power density between 8-sec periods and at least 5-Hz frequencies. Overall, Nord had the lowest background seismic noise, at some frequencies approaching the values of a low noise model.We determined average direction of approaches in the 8- to 4-sec period band for each station during the months of August and November; these determinations agreed with previous studies. The predominant average direction of approaches were: southwest for Nord, south for Daneborg, and southeast for Scoresbysund. Although the microseism amplitude is larger and the direction-of-approach scatter is smaller during the winter months at all three stations, the direction-of-approach mean is apparently independent of season. A large number of storms develop around Iceland and typically track northeast, giving rise to large amplitude microseisms at Scoresbysund but relatively small amplitude microseisms at Daneborg and no microseism activity at Nord. This complete lack of microseism energy at Nord (and to a lesser degree Daneborg) from known frequent microseism sources in the Greenland Sea is shown for one 5-day period in August 1991. Other studies have shown that thick sediments in the Atlantic Ocean's continental margins are responsible for the absence of short-period surface waves from mid-ocean ridge earthquakes that have paths traversing such continental margins. Thick sediments act to attenuate, scatter, and disperse short-period surface waves. Indirect evidence indicates that the northeast Greenland shelf has thick and variable sediment layers. Because the paths of surface waves to Nord (and to a lesser extent Daneborg) originating from typical storms in the Greenland Sea have long path lengths traversing the northeast Greenland shelf, we conclude that this is the likely explanation for the lack of southeast directions from Nord (and to a lesser degree Daneborg) in the observed microseism direction of approaches.

Experimental study of sound scattering by elastic spheroids, and the excitation of their resonances

Experimental studies of ultrasonic scattering by submerged steel spheroids, both oblate and prolate, and of steel spheres have been carried out using incident short, sinusoidally modulated pulses. The time waveform and frequency responses of the scattering objects are obtained directly from experimental data via numerical processing. The sound pulses are incident in the axial direction and also in discrete oblique directions at every 5 deg from the axis. The sound paths of surface waves generated on the objects, causing a chain of echo pulses, are identified, echo arrival times are shown to agree with the surface wave interpretation, and resonanc spectra are extracted using the Numrich–de Billy method. For explaining the resonance spectrum, the phase-matching principle is employed. The target strength of the objects is extracted from experiment using various methods of interpretation (specular echoes, elastic-wave echoes, total echo energy, or entrance windows), and compared to the geometrical target strength. It is shown that specular echoes alone are not sufficient to explain the entire target strength, and the presence of elastic surface waves makes itself felt here.