Coherent reflection of an acoustic plane wave from a random sediment layer over an elastic sea floor

The problem of coherent reflection of an acoustic plane wave from a seabed consisting of a randomly inhomogeneous sediment layer overlying a uniform elastic sea floor is considered in this analysis. The random perturbation in the sediment layer is attributable to the sound-speed variations, resulting in volume scattering due to medium inhomogeneities. An approach based upon perturbation theory, combining with a derived Green's function for a slab bounded above and below, respectively, by a fluid and an elastic half-space, is employed to obtain an analytic solution for the coherent field in the sediment layer. A linear system is then constructed to facilitate the computation of the coherent reflection field. The results of the coherent reflection coefficient for various sediment randomness, frequency, sediment thickness, and sea floor elasticity have been numerically generated and analyzed. It is found that the higher/larger the randomness, frequency, thickness, and shear-wave speed, the lower is the coherent reflection. Physical interpretations for the characteristics of the various results are provided.     

Acoustic wave scattering from a rough seabed over a sediment layer with generalized-exponential density and inverse-square sound speed profiles

This paper considers acoustic plane wave scattering from a rough seabed on a transition sediment layer overlying an elastic sea basement. The transition sediment layer is assumed to be fluid-like, with density and sound speed distributions behaving as generalized-exponential and inverse-square functions, respectively. This specific class of density and sound speed profiles deserves special attentions not only because it is geologically realistic, but also renders analytical solutions to the Helmholtz equation, making it particularly useful in the study of ocean and seabed acoustics. Based upon a boundary perturbation approach, the computational algorithm for the spatial spectrum in terms of the power spectral density of the scattered field has been developed and implemented. The results have shown that, while the coherent field mainly depends upon the gross structure of the seabed roughness, e.g., RMS roughness, the scattered field is significantly affected by the details of the roughness distributions specialized by the roughness power spectrum and the spatial correlation length of the rough surface. The dependence of the power spectral density of the scattered field on the various types of sediment stratifications, including the constant and the k²-linear sound speed distributions, is also included in the analysis.     

The asymmetric elastic wavefields in a model comprising a liquid layer overlying an anisotropic solid seabed due to an arbitrary source within the solid

The asymmetric three-dimensional radiation pattern and resultant elastodynamic response of stress waves in a model comprising a compressible water column overlying a transversely isotropic seabed in which a time-harmonic source acts is theoretically investigated. The use of potential functions, the Hankel transform, and a Fourier series expansion are adopted to deal with the equations of motion for both media. Closed-form integral expressions are developed for the potentials and the stress/displacement components. The expressions and introduced procedure are sufficiently flexible to incorporate various types of source loads. To evaluate the field quantities, the residue method and a robust integration scheme are utilized to handle the poles and branch points within the integrand. Any possible number of dispersive propagation modes are taken into account in the integral evaluation. The deduced velocity dispersion curves depict the characteristics of the various modes. They also indicate the existing singular points (poles) for a specific dimensionless frequency and the surface wave type associated with each pole. Numerical results are presented for the hydrodynamic pressure and displacement in the liquid layer and stress and displacement components in the solid seabed due to distributed and concentrated source excitations. The formulation and the numerical scheme are valid for calculating the wavefield anywhere within the model including both far- and near-field effects. The sensitivity of the results to different parameters is also analyzed. Both analytical and numerical comparisons with existing solutions for simpler cases are made to confirm the validity of the results. The results are especially useful in seismic hazard assessment of submarine earthquakes, landslides, and tsunamis. They can also be extended to deal with the fluid-solid-structure interaction problems.     

Acoustic plane-wave reflection from a rough surface over a random fluid half-space

Plane-wave reflection from a rough surface overlying a fluid half-space, with a sound speed distribution subject to a small and random perturbation, is considered. A theory based upon a boundary perturbation method in conjunction with a formulation derived from Green's function for the coherent field in the random medium have been applied to a typical oceanic environment to study their effects on the plane-wave reflection. By considering the coherent field itself, the plane-wave reflection may be obtained straightforwardly through a procedure consistent with the formalisms currently employed in rough surface scattering. The results show that both the rough surface and medium inhomogenieties may reduce the plane-wave reflection, however, the characteristics of the curves representing their effects are different, enabling us to identify the dominant scattering mechanism. The results for the coherent reflection due to the individual scattering mechanism are compatible with those found in the existing literature.     

海底沉积物实验室剪切波速度及其与沉积物的物理性质之间的关系

采用压电陶瓷弯曲元法和共振柱试验的方法对采自我国海域的一些典型海底浅表层沉积物样品进行了剪切波速测试,获得首批可信数据.两种方法所测得的剪切波速数据具有很好的一致性,且在数赫兹至数十千赫兹频段范围内剪切波速不具明显弥散性.剪切波速与沉积物类型关系密切,不同海区和不同类型海底沉积物的剪切波速有明显差异.近海较细颗粒沉积物粉砂的剪切波速在100m/s左右,细颗粒沉积物的剪切波速在100m/s以下;陆架较粗颗粒沉积物的剪切波速最大,超过100m/s;深海、半深海细颗粒沉积物的剪切波速最低,小于50m/s.剪切波速与含水量、密度、孔隙度、塑限和液限等沉积物物理参数之间具很好的相关性,反映了剪切波速和物理性质之间的密切关系.剪切波速与压缩波速呈正相关性,但在不同的波速范围剪切波速随压缩波速的变化有很大不同.     

A layer-stripping fast algorithm for reconstructing an elastic medium from its compressional wave reflection response

A fast algorithm for recovering profiles of density and compressional (P) and shear-vertical (SV) wave speeds as functions of depth for the inverse seismic problem in a continuous layered elastic medium is obtained. This algorithm differs from previous fast algorithms for this problem since it requires only the compressional wave P-P reflection response at the surface of the medium, for three different slownesses or angles of incidence. Previous algorithms have required shear stress data in the form of the P-SV and SV-SV reflection responses, making them unsuitable for an ocean environment. This algorithm is thus much more suitable for reconstructing the ocean floor from pressure data taken in the ocean. The algorithm is exact, and it includes the effects of multiple reflections and mode conversions. A computer run illustrates the performance of the algorithm on synthetic data.     

Effects of seabed properties on acoustic wave fields in a seismo-acoustic ocean waveguide

Acoustic wave fields in an ocean waveguide with a sediment layer having continuously varying density and sound speed overlying an elastic subbottom are considered in this analysis. The objective of this study is to investigate the effects of seabed acoustic properties, including the density and sound speed of the sediment layer and subbottom, on the characteristics of the wave fields. Examination of the reflection coefficient, wavenumber spectrum, and noise intensity of the sound field through numerical analysis has shown that the variation in the acoustic properties in the sediment layer is an important factor in determining the reflected or noise sound fields. In particular, the sediment thickness-to-wavelength ratio and the types of variation of acoustic properties inside the layer give rise to many characteristics that potentially allow for acoustic inversion of the seabed properties. With regard to the wave-field components in a shallow-water environment, the various types of waves existing in a seismo-acoustic waveguide have been illustrated. The results indicate that the effects of the sediment properties on the wavenumber spectrum are primarily on the continuous and evanescent regimes of the wave field. The noise intensity generated by distributive random monopoles at various depths, together with the effect of refractive sound-speed distribution in the water column, has been obtained and analyzed.     

Generation of a double Kelvin wave resulting from the reflection of the Rossby wave by the jump layer

This paper considers the evolution of a spatially-localized divergent Rossby wave field near the depth jump. If the jump magnitude is comparable to the depth, Rossby waves are fully reflected and a double Kelvin wave is then generated. The Rossby waves and the double Kelvin wave are described by the first- and zero-approximation fields of the asymptotic expansion, respectively. Over the characteristic Rossby wave period, the level elevation produced by the double Kelvin wave spreads over an extensive area, theraby making up for the change in the total fluid mass of the Rossby waves.Translated by Vladimir A. Puchkin.     

渗透海床上矩形Bragg防波堤对波浪反射的研究

与海床不可渗透的情况相比,波浪在可渗透海床上传播时会发生波能衰减。本文将基于可渗透海床上一维修正型缓坡方程,建立方程求解的有限差分模型。将通过与不可渗透海床上矩形Bragg防波堤对波浪反射系数解析解的对比,验证有限差分模型的正确性和适用性。将进一步研究海床可渗透情况下,海床的渗透性参数、坝体的相对宽度、数量、浸没度对波浪反射系数的影响及其与海床不可渗透情况下的差异。本文研究发现,Bragg共振发生时的反射系数随坝体数量的增多而增大,随海床渗透性参数和坝体浸没度的增大而减小,并且存在一个坝体相对宽度值会使Bragg共振反射达到最大。相较于海床不可渗透的情况,发生Bragg共振反射的波浪频率几乎相同,但反射系数减小,而且零反射（或全透射）现象不再存在。     

Acoustic plane-wave scattering from a rough interface over an inhomogeneous transition fluid layer

Acoustic scattering of a plane wave incident upon a rough surface over a transition fluid layer within which both the density and sound speed vary with depth is considered. A theory based upon a boundary perturbation method has been applied to a typical seabed environment to study the power spectral density representing the energy distribution of the scattered field over the space. The effects of frequency and roughness properties, including the roughness height, spatial correlation, and power spectrum, on the power spectral density have been investigated. The results demonstrate that the power spectral density of the scattered field depends upon all the aforementioned parameters, particularly the correlation length and the power spectrum of the rough surface, a conclusion in distinct contrast to the results for the coherent field obtained in an earlier study. It was found that the constituents of the rough surface such as the correlation length and wavenumber spectrum dominate the angular distribution of the scattered energy. These results indicate that it is crucial to employ a suitable topological model in the study of rough seabed scattering.     

Global buckling of pipelines in the vertical plane with a soft seabed

Offshore pipelines are usually buried to avoid damage from fishing activities and to provide thermal insulation. Provided that the buried pipelines are sufficiently confined in the lateral direction by the passive resistance of the trench walls, they may be subject to vertical buckling caused by a rise in temperature. Vertical buckling is usually called upheaval buckling because the heated pipeline is assumed to move upwards conventionally. However, the seabed may be very soft, especially where a pockmark or abyssal ooze appears. Consequently, under thermal compressive force, the pipeline may buckle downward and penetrate into the seabed because the downward soil resistance is small. In this study, we extended an analytical solution for vertical pipeline buckling on a rigid seabed to a soft seabed, and the effects of soil resistance on pipeline stability, buckling mode and amplitude are illustrated and analyzed.     

Effects of a cover layer on wave-induced pore pressure around a buried pipe in an anisotropic seabed

In engineering practice, a cover layer of coarser material has been used to protect a buried marine pipeline from wave-induced seabed instability. However, most previous investigations of the wave–seabed–pipe interaction problem have been concerned only with such a problem either in an isotropic single layer or a rigid pipe. This paper proposes a two-dimensional finite element model by employing the principle of repeatability to investigate the wave-induced soil response around a buried pipeline. The elastic anisotropic soil bahavior and geometry of cover layer are included in the present model, while the pipe is considered to be an elastic medium. This study focuses on the effects of a cover layer (including thickness B and width W of the cover layer) on the wave-induced pore pressure in the vicinity of a buried pipeline.     

Analysis of optimal conditions for recording signals when studying the atmospheric boundary layer with the acoustic method of partial reflection

Equations for the coefficient of partial reflection K from stratified inhomogeneities in the atmospheric boundary layer have been derived on the basis of the Epstein transition and symmetrical layer models as functions of three dimensionless parameters, i.e., the relative layer altitude, its relative thickness, and the relative variations in the effective sound speed in a layer. The equations have been obtained for the relative layer altitude at which the total internal reflection appears; the behavior of the function K is studied at close altitudes. Significant weakening of the dependence of coefficient K on the relative layer thickness in these conditions is shown, which makes it possible to record partially reflected signals in a wide range of wave-lengths or frequencies of the sounding signal. In other cases, the coefficient of partial reflection K strongly depends on the layer thickness. According to experimental data on variations in the amplitude of received acoustic signals with an increase in the source-detector distance, a technique for the parameterization of the additional impedance attenuation of sound that propagates over the earth’s surface has been developed, and these parameters have been experimentally estimated for different stratification conditions and sounding signal frequencies. Many records of background acoustic noises typical for one or another measurement sites have been distinguished and classified, a technique for estimating the minimum signal amplitude distinguishable against noises has been developed, and the corresponding estimates have been made. Based on these data and the specifications of three different industrial acoustic sources, the parameter limits provided by these sources have been estimated for the method of partial reflection.     

Volterra series-based system analysis of random wave interaction with a horizontal cylinder

The response of a long flexible cylinder excited by random waves in a large model basin was investigated. The linear and non-linear physical mechanisms associated with the wave–cylinder interaction were analysed using system identification and modelling techniques. A third-order frequency domain Volterra model and its orthogonalized counterpart were used to analyse the relationships between wave elevations at various locations in the vicinity of the cylinder and cylinder acceleration data at various cylinder longitudinal locations. It was found that linear mechanisms dominate, particularly at the frequency band where the majority of the wave energy is located. At higher frequencies, the cubic component of the Volterra model is the main contributor to the total model coherence, i.e. the fraction of the measured output power that can be approximated by the model output, whereas the quadratic component's contribution to the total model coherence was in general quite small. This process of identification and quantification of the non-linear mechanisms of the unknown physical system can lead to the design of improved parametric models for the cylinder response, which should by design simulate non-linearities such as the ones identified by the Volterra model. The estimated linear and non-linear Volterra transfer functions were also used to predict the cylinder acceleration under excitation inputs not used in the estimation of the model transfer functions. The good match between predicted and measured output auto-power spectra suggests that the estimated transfer functions are indeed true models of the underlying physical mechanisms of the interaction. However, the latter can only be achieved if a minimum number of data segments, as determined by an error analysis involving modelling and prediction errors, is used in the estimation of the Volterra transfer functions.     

Characteristics of resuspended sediment from Georges Bank collected with a sediment trap

A sediment trap was deployed 3 m from the bottom at a water depth of 62 m on the southern flank of Georges Bank (41°02·2′N, 67°33·5′W) from 30 September 1978 to 10 March 1979 to qualitatively determine the size of sediments resuspended from the bottom by winter storms and to determine if seasonal changes in the phytoplankton could be observed in the trapped sediment.Bulk X-ray analyses of the trapped sediment showed layers of distinctly different textures preserved in the collection vessel. The median grain size of sampled layers ranged from 2·7 to 6·5 φ (fine sand to silt), but all layers contained a pronounced mode in the 3 φ (fine sand) range. Nine layers containing relatively large amounts of sand were present. The sand content was 75% in the coarest layers and about 32% in the fine layers. The median grain size of bottom sediments at the deployment site was considerably coarser than the trap samples, although the dominant grain size was also 3 φ.Average bottom-current speeds during the deployment period were about 30 cm s^?1 with a range of 10 to 50 cm s^?1. Bottom stress, computed from the observed currents and waves, suggest that 11 storms caused sufficient stress to resuspend 3 φ-sized sediments, in good agreement with the nine layers of relatively coarse sediments collected in the trap. Surface waves had to be included in the calculation of bottom stress because the bottom currents alone were insufficient to cause the resuspension of 3 φ-sized sediment.The trapped sediments contain numerous diatoms and coccoliths that are typical of late fall and winter assemblages. No clear seasonal difference in the flora was noted among sampled layers, probably due to the large influx of resuspended material and a reduced primary flux during this period. An undescribed species of Thalassiosira (G. Fryxell, personal communication), and siliceous scales of unknown systematic position were observed at all levels.     

A comparison of perturbation theory and the small-slope approximation for acoustic scattering from a rough interface for a Biot medium

In this paper, the lowest order small-slope approximation (SSA) scattering cross section for Biot theory is derived. Numerical results are obtained for both backscattering and bistatic scattering using a modified power law spectrum, and these results are compared with those of lowest order perturbation theory (PT). Frequencies ranging from 100 Hz to 3 kHz are used for surfaces with RMS heights h of 0.1 and 1 m and a correlation length l of 10 m. The angle of incidence for the bistatic results is limited to 45/spl deg/. It is found that for the smaller surface height roughness (h = 0.1 m), the SSA and PT give the same results for frequencies up to almost 1 kHz for both backscattering and bistatic scattering. For h = 1 m, the SSA and PT backscatter results are in good agreement at all frequencies for incident grazing angles up to approximately 45/spl deg/. For the bistatic results, the SSA and PT results agree only at low grazing angles of scatter. In the specular region, the results differ significantly.     

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x ^4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.     

Effect of the water-saturated sediment layer on recording seismic signals with a bottom seismometer

Recording seismic signals on the bottom is accompanied by specific distortions caused by resonance phenomena. In the literature, such distortions are explained by the natural vibration of the heavy housing of a seismometer on a soft elastic sediment layer. Meanwhile, there are experimental results that contradict this model. In the present paper, we consider the rheological properties of the bottom sediments, which in fact were not taken into account previously. The model of a viscoplastic medium was used (the Bingham model), and the parameters of the model were experimentally determined. The estimates show that, in the frequency range from 0.003 to 30 Hz used in broadband bottom seismology, the effect of the mass of the seismometer on the results of recording on a soft bottom is negligible. Large errors can be introduced only when a seismometer is placed on rubberlike media such as peat soil, algae aggregations, etc. Resonance phenomena in recording signals on the bottom can occur when seismic waves propagate through a layer of water-saturated sediments. These phenomena are more pronounced for shear waves, whereas the distortions of the longitudinal waves propagating through the water-saturated layer are relatively weak.