High Wave Speed Research Articles

Insights into the structure of the upper mantle beneath the Murray basin from 3D teleseismic tomography

Distant earthquake records from a passive array of 20 short-period seismometers are used to image the 3D P-wave velocity structure of the upper mantle beneath the Murray Basin in southern New South Wales and northern Victoria. During the five-month deployment period of the array, 158 teleseisms with good signal-to-noise ratios were recorded, allowing 3085 relative arrival time residuals to be picked with high accuracy. These arrival time residuals are mapped as 3D perturbations in P-wave velocity with respect to the ak135 global reference model using teleseismic tomography. The resulting images exhibit lateral variations in wave speed in the upper mantle to depths of nearly 300 km, and help to reveal the deep structure beneath a region almost devoid of Palaeozoic outcrop. Of particular significance is an east – west high – low – high relative wave speed variation that is present throughout the upper mantle between 70 and 250 km depth. The transition from faster to slower wave speeds in the west is indicative of a change from Proterozoic to Phanerozoic lithosphere that has also been observed further south in a previous teleseismic study. The transition from slower to faster wave speeds in the east has a less obvious association, but may well signal an underlying change in lithospheric structure related to the convergence of the western and central Lachlan subprovinces. At shallower depths (<70 km), the structural pattern is dominated by a fast perturbation (>3.5%) which overlies the slower region across the northern margin of the Bendigo Zone, and may be a consequence of localised thrusting and emplacement of denser lithosphere during the Early – Middle Devonian Tabberabberan Orogeny.

Seismic detection of folded, subducted lithosphere at the core–mantle boundary

Seismic tomography has been used to infer that some descending slabs of oceanic lithosphere plunge deep into the Earth's lower mantle. The fate of these slabs has remained unresolved, but it has been postulated that their ultimate destination is the lowermost few hundred kilometres of the mantle, known as the D'' region. Relatively cold slab material may account for high seismic velocities imaged in D'' beneath areas of long-lived plate subduction, and for reflections from a seismic velocity discontinuity just above the anomalously high wave speed regions. The D'' discontinuity itself is probably the result of a phase change in relatively low-temperature magnesium silicate perovskite. Here, we present images of the D'' region beneath the Cocos plate using Kirchhoff migration of horizontally polarized shear waves, and find a 100-km vertical step occurring over less than 100 km laterally in an otherwise flat D'' shear velocity discontinuity. Folding and piling of a cold slab that has reached the core-mantle boundary, as observed in numerical and experimental models, can account for the step by a 100-km elevation of the post-perovskite phase boundary due to a 700 degrees C lateral temperature reduction in the folded slab. We detect localized low velocities at the edge of the slab material, which may result from upwellings caused by the slab laterally displacing a thin hot thermal boundary layer.

Three-Dimensional Compressional Wavespeed Model, Earthquake Relocations, and Focal Mechanisms for the Parkfield, California, Region

We present a new three-dimensional (3D) compressional wavespeed ( V p) model for the Parkfield region, taking advantage of the recent seismicity associated with the 2003 San Simeon and 2004 Parkfield earthquake sequences to provide increased model resolution compared to the work of Eberhart-Phillips and Michael (1993) (epm93). Taking the epm93 3D model as our starting model, we invert the arrival-time data from about 2100 earthquakes and 250 shots recorded on both permanent network and temporary stations in a region 130 km northeast–southwest by 120 km northwest–southeast. We include catalog picks and cross-correlation and catalog differential times in the inversion, using the double-difference tomography method of Zhang and Thurber (2003). The principal V p features reported by epm93 and Michelini and McEvilly (1991) are recovered, but with locally improved resolution along the San Andreas Fault (saf) and near the active-source profiles. We image the previously identified strong wavespeed contrast (faster on the southwest side) across most of the length of the saf, and we also improve the image of a high V p body on the northeast side of the fault reported by epm93. This narrow body is at about 5- to 12-km depth and extends approximately from the locked section of the saf to the town of Parkfield. The footwall of the thrust fault responsible for the 1983 Coalinga earthquake is imaged as a northeast-dipping high wavespeed body. In between, relatively low wavespeeds (<5 km/sec) extend to as much as 10-km depth. We use this model to derive absolute locations for about 16,000 earthquakes from 1966 to 2005 and high-precision double-difference locations for 9,000 earthquakes from 1984 to 2005, and also to determine focal mechanisms for 446 earthquakes. These earthquake locations and mechanisms show that the seismogenic fault is a simple planar structure. The aftershock sequence of the 2004 mainshock concentrates into the same structures defined by the pre-2004 seismicity, confirming earlier observations (Waldhauser et al. , 2004) that the seismicity pattern at Parkfield is long lived and persists through multiple cycles of mainshocks. Online material : 3D V p model and earthquake relocations.

COMPUTATIONAL STUDY OF INTERFACE EFFECT ON IMPACT LOAD SPREADING IN SiC MULTI-LAYERED TARGETS

The effect of finite strength interface with friction on lateral load spreading and phenomena of interface crack initiation and propagation in bonded multi-layered targets under high velocity impact are presented through axisymmetric finite element simulations. The finite element code DYNA2D, developed at the Lawrence Livermore National Laboratory, was augmented with a phenomenological damage model for the silicon carbide ( SiC ) ceramic and contact/cohesive interface model. Simulations were carried out for four target configurations under varying interface strength (Tm), critical strain energy release rate (Gc), and inter-layer friction coefficient (μL). It is shown that the high wave speed SiC remains a potential material for enhanced load spreading if the confinement is ensured to reduce/delay its damage. The load spreading also increases with the increase in μL that comes into play after the interface failure. However, the μL of unity or more needed to approach the upper bound of load spreading found in the perfectly bonded target layers is not practical. It is shown that the resilience of the multi-layered targets depends on Tm as well as the Gc. But, the lateral load spreading depends dominantly on Tm and reaches the upper bound with its increase. It is further shown that the interface cracks initiate and propagate in shear, mode II. The crack speed is invariably the maximum at initiation and is of the order of the longitudinal wave speed of materials on either side. The maximum initiation speed of 11.29Cs and 7.79Cs are predicted at the SiC -aluminum and steel- SiC interfaces for the frictionless case, where Cs is the shear wave speed of the more compliant aluminum or steel. The crack speed reduces monotonously after initiation, but it remains in the intersonic region for more than 150 ns. Whether the propagating crack tip attains the steady state speed depends on the available driving energy. The steady state crack speed of 0.86Cs to 1.21Cs is predicted only at the steel- SiC interface at 2 mm depth from the impact surface, lasts for more than 3 μs, is shown to be independent of the interface strength upto 300 MPa, and is also independent of the friction coefficient.

Mantle heterogeneity beneath eastern California from magnetotelluric measurements

A 300 km long magnetotelluric profile across the Great Valley, Sierra Nevada, and California Basin and Range reveals minimum resistivity differences of 1 order of magnitude at depths from Moho at 30–35 km to depths greater than 200 km. Horizontal wavelengths of 25 km are seen for these changes at depths shallower than 100 km, and the Isabella high seismic wave speed anomaly is present in the section between depths of 100 and 200 km as a minimum tenfold resistivity increase. A transformation from electrical resistivity to temperature and melt fraction using a petrological model and laboratory measurements reveals that partial melt is relatively uncommon and confined primarily to depths between 30 and 100 km. The remainder of the observed resistivity variation is attributed to lateral variations in temperature. Predicted melt fractions match those inferred from Miocene‐Quaternary xenoliths, but modeled temperatures are ∼200°C higher than inferred from thermobarometric analyses of the xenoliths. Possible causes for this discrepancy include an incorrect starting material for the petrological model, exotic conductive phases, higher conductivity due to oxidation state and/or iron content, and diffusion of ions through the solid matrix. I show that hydrogen diffusion or higher oxygen concentrations are plausible explanation for the higher model temperatures. Less than 200 ppm H/106 Si in olivine would increase the conductivity of the matrix sufficiently to allow temperatures inferred from the resistivity section to match those from the xenoliths. A possible source of the hydrogen would be fragments of sinking, metasomatized mantle lithosphere that melted during Cenozoic delamination.

Patterns and controls on the distribution of diamondiferous intrusions in Australia

The distribution of kimberlite, lamproite and related alkaline volcanism in Australia can be broadly related to the structure of the Australian continent and lithosphere. Diamondiferous kimberlites and lamproites, with the apparent exception of the weakly diamondiferous Orrorro kimberlites in the Adelaide Fold Belt, lie within the large Precambrian shield where seismic tomographic models and heat flow data indicate the presence of relatively cold, high seismic wave speed lithosphere (tectosphere) typically some 200 km thick or more beneath the Archaean cratons and up to 300 km in parts of central Australia. Many of the diamondiferous intrusions appear to lie at the margins rather than in the centre of the lithosphere domains. The highest concentration of diamondiferous intrusions (kimberlites and lamproites) is on and around the Kimberley Craton where seismic data indicate crustal thicknesses of 35–40 km and a lithosphere up to 275 km thick that is distinct from Proterozoic northern Australia. Many, but clearly not all, of the intrusions show evidence of regional and local structural controls. Some are spatially associated with known crustal structures, especially regional faults. Others are aligned, either singly or in clusters, along or near discontinuities and/or gradients evident in regional scale potential field data, especially the total horizontal gradients of gravity data continued upward tens to hundreds of kilometres. Many of these features are not evident in the original datasets as their signatures are masked by shorter wavelength (near surface) anomalies. In some cases, the kimberlites and associated rocks lie within crustal blocks and domains defined by discontinuities in the potential field data rather than at domain boundaries. Our overview suggests that analysis of potential field data, especially horizontal gradients in upwardly continued potential field data, at all scales can assist definition of crustal and, potentially, lithospheric structures that may influence the distribution of diamond pipes. However, more definitive mapping of Australia's diamond prospective regions requires the integration of data on crustal structures, especially trans-lithospheric faults, and geodynamic settings with high resolution tomographic models and other geophysical, petrologic, and isotopic information on the nature of the lithosphere beneath the Australian continent.

Mantle structure and composition to 800-km depth beneath southern Africa and surrounding oceans from broadband body waves

Average one-dimensional P and S wavespeed models from the surface to depths of 800 km were derived for the southern African region using travel times and waveforms from earthquakes recorded at stations of the Kaapvaal and South African seismic networks. The Herglotz–Wiechert method combined with ray tracing was used to derive a preliminary P wavespeed model, followed by refinements using phase-weighted stacking and synthetic seismograms to yield the final model. Travel times combined with ray tracing were used to derive the S wavespeed model, which was also refined using phase-weighted stacking and synthetic seismograms. The presence of a high wavespeed upper mantle lid in the S model overlying a low wavespeed zone (LWZ) around 210- to ∼345-km depth that is not observed in the P wavespeed model was inferred. The 410-km discontinuity shows similar characteristics to that in other continental regions, but occurs slightly deeper at 420 km. Depletion of iron and/or enrichment in aluminium relative to other regions are the preferred explanation, since the P wavespeeds throughout the transition zone are slightly higher than average. The average S wavespeed structure beneath southern Africa within and below the transition zone is similar to that of the IASP91 model. There is no evidence for discontinuity at 520-km depth. The 660-km discontinuity also appears to be slightly deeper than average (668 km), although the estimated thickness of the transition zone is 248 km, similar to the global average of 241 km. The small size of the 660-km discontinuity for P waves, compared with many other regions, suggests that interpretation of the discontinuity as the transformation of spinel to perovskite and magnesiowüstite may require modification. Alternative explanations include the presence of garnetite-rich material or ilmenite-forming phase transformations above the 660-km discontinuity, and the garnet–perovskite transformation as the discontinuity.

Load spreading and penetration resistance of layered structures—a numerical study

The objectives of this study were to gain insight into the penetration resistance of layered structures, and to examine the effects of layer damage and imperfect interfaces on load spreading and projectile defeat capabilities of the layers. To investigate the overall penetration process instead of just the terminal state, we examined the time history of the energy transfer between the projectile and the target, and between the layer and the substrate. Under idealized conditions, without layer damage or an imperfect interface, a target with a single thick high-strength, high-wave-speed layer offers the best penetration resistance. The high impedance and strength of the layer enhance the projectile defeat capability of the target; more impact energy is dissipated in the projectile and less energy is delivered to the target. The high wave speed of the layer allows the impact load and energy imparted to the target to be absorbed more quickly and distributed widely in the substrate. Both layer damage and an imperfect interface degrade the target's capability to defeat the projectile and to spread the load. However, the former has a more detrimental effect than the latter.

Three‐dimensional crustal structure of Long Valley caldera, California, and evidence for the migration of CO2 under Mammoth Mountain

A temporary network of 69 three‐component seismic stations captured a major seismic sequence in Long Valley caldera in 1997. We performed a tomographic inversion for crustal structure beneath a 28 km × 16 km area encompassing part of the resurgent dome, the south moat, and Mammoth Mountain. Resolution of crustal structure beneath the center of the study volume was good down to ∼3 km below sea level (∼5 km below the surface). Relatively high wave speeds are associated with the Bishop Tuff and lower wave speeds characterize debris in the surrounding moat. A low‐Vp/Vs anomaly extending from near the surface to ∼1 km below sea level beneath Mammoth Mountain may represent a CO2 reservoir that is supplying CO2‐rich springs, venting at the surface, and killing trees. We investigated temporal variations in structure beneath Mammoth Mountain by differencing our results with tomographic images obtained using data from 1989/1990. Significant changes in both Vp and Vs were consistent with the migration of CO2 into the upper 2 km or so beneath Mammoth Mountain and its depletion in peripheral volumes that correlate with surface venting areas. Repeat tomography is capable of detecting the migration of gas beneath active silicic volcanoes and may thus provide a useful volcano monitoring tool.

Soliton-like solutions of higher order wave equations of the Korteweg–de Vries type

In this work we study second and third order approximations of water wave equations of the Korteweg–de Vries (KdV) type. First we derive analytical expressions for solitary wave solutions for some special sets of parameters of the equations. Remarkably enough, in all these approximations, the form of the solitary wave and its amplitude-velocity dependence are identical to the sech2 formula of the one-soliton solution of the KdV. Next we carry out a detailed numerical study of these solutions using a Fourier pseudospectral method combined with a finite-difference scheme, in parameter regions where soliton-like behavior is observed. In these regions, we find solitary waves which are stable and behave like solitons in the sense that they remain virtually unchanged under time evolution and mutual interaction. In general, these solutions sustain small oscillations in the form of radiation waves (trailing the solitary wave) and may still be regarded as stable, provided these radiation waves do not exceed a numerical stability threshold. Instability occurs at high enough wave speeds, when these oscillations exceed the stability threshold already at the outset, and manifests itself as a sudden increase of these oscillations followed by a blowup of the wave after relatively short time intervals.

Impact load spreading in layered materials and structures: concept and quantitative measure

We demonstrate a potentially new concept to enhance the resilience of structures to withstand rapid impulsive loading. The basic idea is to use a high wave speed layer to rapidly spread (μs time scales) the locally applied impact load. We also propose a quantitative measure based on normalized dissipative energy density (NDE) to characterize load spreading. Using this measure, we have studied numerically the effects of wave speed, layering geometry (thickness and configuration), and mechanical properties (impedance and strength) of the layer and substrate on load spreading. The numerical calculations make a good case for the load spreading concept. The NDE measure may also serve as a useful tool to examine the general response of layered composites to impact loading.

Arterial waves in humans during peripheral vascular surgery

The purpose of this study was to investigate the effect of aortic clamping on arterial waves during peripheral vascular surgery. We measured pressure and velocity simultaneously in the ascending aorta, in ten patients (70+/-5 years) with aortic-iliac disease intra-operatively. Pressure was measured using a catheter tip manometer, and velocity was measured using Doppler ultrasound. Data were collected before aortic clamping, during aortic clamping and after unclamping. Hydraulic work in the aortic root was calculated from the measured data, the reflected waves were determined by wave-intensity analysis and wave speed was determined by the PU-loop (pressure-velocity-loop) method; a new technique based on the 'water-hammer' equation. The wave speed is approx. 32% (P<0.05) higher during clamping than before clamping. Although the peak intensity of the reflected wave does not alter with clamping, it arrives 30 ms (P<0.05) earlier and its duration is 25% (P<0.05) longer than before clamping. During clamping, left ventricule (LV) hydraulic systolic work and the energy carried by the reflected wave increased by 27% (P<0.05) and 20% (P<0.05) respectively, compared with before clamping. The higher wave speed during clamping explains the earlier arrival of the reflected waves suggesting an increase in the afterload, since the LV has to overcome earlier reflected compression waves. The longer duration of the reflected wave during clamping is associated with an increase in the total energy carried by the wave, which causes an increase in hydraulic work. Increased hydraulic work during clamping may increase LV oxygen consumption, provoke myocardial ischaemia and hence contribute to the intra-operative impairment of LV function known in patients with peripheral vascular disease.

The deep structure of the Australian continent from surface wave tomography

We present a new model of 3-D variations of shear wave speed in the Australian upper mantle, obtained from the dispersion of fundamental and higher-mode surface waves. We used nearly 1600 Rayleigh wave data from the portable arrays of the Skippy project and from permanent stations (from Agso, Iris and Geoscope). Agso data have not been used before and provide better data coverage of the Archean cratons in western Australia. Compared to previous studies we improved the vertical parameterization, the weighting scheme that accounts for variations in data quality and reduced the influence of epicenter mislocation on velocity structure. The dense sampling by seismic waves provides for unprecedented resolution of continental structure, but the wave speed beneath westernmost Australia is not well constrained. Global compilations of geological and seismological data (using regionalizations based on tectonic behavior or crustal age) suggest a correlation between crustal age and the thickness and composition of the continental lithosphere. However, the age and the tectonic history of crustal elements vary on wavelengths much smaller than have been resolved with global seismological studies. Using our regional upper mantle model we investigate how the seismic signature of tectonic units changes with increasing depth. At large wavelengths, and to a depth of about 200 km, the inferred velocity anomalies corroborate the global pattern and display a progression of wave speed with crustal age: slow wave propagation prevails beneath the Paleozoic fold belts in eastern Australia and wave speeds increase westward across the Proterozoic and reach a maximum in the Archean cratons. The high wave speeds associated with Precambrian shields extend beyond the Tasman Line, which marks the eastern limit of Proterozoic outcrop. This suggests that parts of the Paleozoic fold belts are underlain by Proterozoic lithosphere. We also infer that the North Australia craton extends off-shore into Papua New Guinea and beneath the Indian Ocean. For depths in excess of 200 km a regionalization with smaller units reveals that some tectonic subregions of Proterozoic age are marked by pronounced velocity highs to depths exceeding 300 km, but others do not and, surprisingly, the Archean units do not seem to be marked by such a thick high wave speed structure either. The Precambrian cratons that lack a thick high wave speed “keel” are located near passive margins, suggesting that convective processes associated with continental break-up may have destroyed a once present tectosphere. Our study suggests that deep lithospheric structure varies as much within domains of similar crustal age as between units of different ages, which hampers attempts to find a unifying relationship between seismic signature and lithospheric age.

The multiple-scale wave equation

An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ϵ 2 u tt = Δu + tf with high wave speed (ϵ ⪡ 1) is carried out. This study was initially motivated by meteorological observations which have indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storms, mainly from visible images of ripples in clouds in satellite photos. There is a question as to whether the presence of these waves is caused by the nearby storms. Since the linear wave equation is an approximation to the full system describing pressure waves in the atmosphere, yet is considerably more tractable, we have chosen to analyze the behavior of the linear nonhomogeneous wave equation with high wave speed. The analysis is shown to be valid in one, two, and three space dimensions. Partly because of the high wave speed, the solution is known to consist of behavior which changes on two different time scales, one rapid and one slow. Additionally, because of the presence of the nonhomogeneous forcing term tf, we show that there is a component of the solution which will vary only on a very large spatial scale. Since even the linearized wave equation can give rise to persistent large spatial scale waves under the right conditions, the implication is that certain storms could be responsible for the generation of large-scale waves. Numerical simulations in one and two dimensions confirm analytic results.

Three-dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland

SUMMARY The volcanic and geothermal areas of Iceland are rich sources of non-double-couple (non-DC) earthquakes. A state-of-the-art digital seismometer network deployed at the Hengill‐Grensdalur volcanic complex in 1991 recorded 4000 small earthquakes. We used the best recorded of these to determine 3-D V P and V P /V S structure tomographically and accurate earthquake moment tensors. The V P field is dominated by high seismic wave speed bodies interpreted as solidified intrusions. A widespread negative (’4 per cent) V P /V S anomaly in the upper 4 km correlates with the geothermal field, but is too strong to be caused solely by the eVect of temperature upon liquid water or the presence of vapour, and requires in addition mineralogical or lithological diVerences between the geothermal reservoir and its surroundings. These may be caused by geothermal alteration. Well-constrained moment tensors were obtained for 70 of the best-recorded events by applying linear programming methods to P- and S-wave polarities and amplitude ratios. About 25 per cent of the mechanisms are, within observational error, consistent with DC mechanisms consistent with shear faulting. The other 75 per cent have significantly non-DC mechanisms. Many have substantial explosive components, one has a substantial implosive component, and the deviatoric component of many is strongly non-DC. Many of the non-DC mechanisms are consistent, within observational error, with simultaneous tensile and shear faulting. However, the mechanisms occupy a continuum in source-type parameter space and probably at least one additional source process is occurring. This may be fluid flow into newly formed cracks, causing partial compensation of the volumetric component. Studying non-shear earthquakes such as these has great potential for improving our understanding of geothermal processes and earthquake source processes in general.

Signal response of elastically coated plates

An analytical model of a compliant elastic coating attached to a submerged thin plate has been developed. A plane acoustic wave, representing the signal, is incident from the water on to the elastic coating. The normal and tangential velocity components induced in the coating by the acoustic wave are calculated. The effects of incidence angle, frequency, location throughout the coating, and coating properties on the signal response velocity components are evaluated. Many details of the coating velocity components are explained based on simple uncoupled waveguide characteristics of the coating. In general, the normal velocity components are several tens of decibels higher in amplitude than the tangential velocity components. It was shown, however, that the tangential velocity component could be increased by an average amount of about 20 dB, without serious degradation of the normal component, by altering the coating properties. In particular, combinations of high longitudinal wave speed and low shear wave speed were found to be advantageous.

Mechanisms of Differing Stone Fragility in Extracorporeal Shockwave Lithotripsy*

Clinical experience with extracorporeal shockwave lithotripsy (SWL) has demonstrated significant variations in stone fragility. To understand the physical mechanisms of the differences, we quantitatively determined shockwave-stone interaction under clinically relevant SWL conditions for six stone compositions: calcium oxalate monohydrate (COM), struvite (MAPH), calcium apatite (CA), uric acid (UA), brushite, and cystine. We also characterized the acoustic and mechanical properties of the stones using ultrasound and microindentation techniques. Our results show that renal calculi have distinctly different acoustic and mechanical properties. Higher wave speed, Young's modulus, and fracture toughness were measured from COM and cystine stones, whereas lower values of the corresponding properties were found in CA and MAPH, and the values for brushite and UA stones were in between. Computer modeling of shockwave propagation revealed that under the same shockwave intensity, larger deformation was induced in CA and MAPH stones than in COM and cystine stones. In addition, multiple reflected tensile waves were predicted for stones with concentric layer structure, indicating their susceptibility to shockwave fragmentation. These findings elucidate the mechanisms of the differences in stone fragility observed clinically. Their implications to SWL are discussed.

Decompression waves in fluidized beds

A packed bed of particles may be held against the permeable roof of a fluidized column by a fluid flux that is several times the minimum fluidization flux. When the fluid flux is sufficiently reduced, particles rain down and a decompression wave propagates into the packed bed. We report new data of the velocity of this wave, summarize previous work and compare with new analyses. The speed of the decompression wave cannot be predicted from continuum theories that contain a mutual drag force dependent only on the relative velocity and void fraction. Several hypotheses about additional forces are used to derive theoretical values of the decompression wave velocity which are compared with data. The three most successful hypotheses, which are shown to be roughly equivalent at the higher wave speeds, include: a force proportional to the second derivative of void fraction; a discrete averaging method over distances scaled by particle size; and a modification to the drag force using the geometrical relationship between area fraction and number density.

Interface reflection of spherical acoustic waves in the first- and second-order rational parabolic approximations and their artifacts

The accuracy of the first- and second-order rational parabolic approximations of the ‘‘vertical’’ slowness and the nature of the artifacts associated with them in the space-time solutions to the acoustic wave equations in a fluid medium are investigated. In particular, the reflection of an impulsive, point-source generated, spherical wave against the boundary with a medium with a higher wave speed is analyzed. From the space-time Green’s functions in the relevant two-media configuration, evaluated with the aid of the modified Cagniard method, it is found that, instead of generating the real, physical head wave, the approximations generate artificial head-wavelike arrivals. The analysis makes explicit in which regions of space and in which time interval the artifacts show up and of what nature they are. Numerical results are presented.

On the scattering of evanescent waves into sound

This paper concerns the conversion of momentum and energy from evanescent surface waves into sound. Exact results are obtained from surface waves of specified form on a confined region of an otherwise rigid plane surface. The model chosen is simple enough for exact analysis while approximating some of what we believe to be significant aspects of sound generation by vibrating surface panels.We find that the evanescent wave approaching an edge gives up all of its energy into sound, a sound which is beamed mainly parallel to the direction of the surface-wave phase velocity. The surface remains energetically inactive, but exerts a force on the fluid in the opposite direction to the incoming wave. This force is balanced by a nonlinear mean pressure gradient in the field of the evanescent wave, and by momentum in the sound field.Sound is also produced when a similar evanescent wave emerges from an edge. The surface has then to provide the necessary energy for both waves. These waves induce a mean axial force at the boundary which forces the fluid in the direction of the receding evanescent wave.A similar wave travelling across a finite panel in the otherwise rigid plane surface is observed to have some characteristics of the previous two cases, but there is no axial force arising from the mean pressure gradient.These results are applied to the problem of a semi-infinite tensioned membrane, and the energy radiation under light fluid loading is determined for the case of high and low free membrane wave speeds.