Passive systems theory with narrow-band and linear constraints: Part II -- Temporal diversity

This paper is part of a series of three papers studying passive tracking problems arising in navigation and positioning applications. The basic question here lies with the determination of the position and dynamics of a point source being tracked by an omnidirectional observer, through demodulation of the Doppler effect induced on the radiated signals by the relative motions. A simple model, fitting a finite parameter nonlinear estimation context, is developed, the receiver designed, and its mean-square error performance studied. It is shown that, besides the speed and angle estimation, simultaneous global range passive tracking is possible. The signal model precludes range acquisition from synchronous measurement of the absolute phase reference: the global range estimation is attained by processing the higher order temporal modulations (varying Doppler). Quantifying the statistical and geometric performance tradeoffs, the work presents simple expressions and graphical displays that can be used as design tools in practical passive tracking problems. A subsequent paper considers the space/ time coupling issues, generalizing the study to the context where a moving source is tracked by a directional array.     

Passive systems theory with narrow-band and linear constraints: Part III -- Spatial/Temporal diversity

This is the last of a series of three papers studying the theory of passive systems. The model assumes that i) the narrow-band signals are transmitted through a Rayleigh channel, ii) the observing array is geometrically linear, and iii) the source motion is deterministic. Ranging techniques based on synchronized measurements of the travel time delay are precluded by the incoherent phase model considered. The paper explores alternative methods that process the phase modulations induced on the signal by the extended geometry and relative dynamics. The present work applies maximum likelihood theory to design the receiver, being concerned with the global identifiability of all parameters defining the relative source/receiver geometry and dynamics. The emphasis is placed on the passive range global acquisition. In contradistinction with the previous papers, where the time stationarity (Part I) or the space homogeneity (Part II) lead to a one-dimensional processor, here the receiver involves processing over both domains. The paper considers the issues of space/time factorability and coupling arising in nonhomogeneous passive tracking. The cross coupling, resulting in more complex filters, improves the receiver acquisition capability. Resorting to Taylor's series type studies, the paper quantifies these improvements, as well as the receiver's mean square error performance, in terms of intuitively satisfying analytical expressions.     

Design of a 3D Chirp Sub-bottom Imaging System

Chirp sub-bottom profilers are marine acoustic devices that use a known and repeatable source signature (1–24 kHz) to produce decimetre vertical resolution cross-sections of the sub-seabed. Here the design and development of the first true 3D Chirp system is described. When developing the design, critical factors that had to be considered included spatial aliasing, and precise positioning of sources and receivers. Full 3D numerical modelling of the combined source and receiver directivity was completed to determine optimal source and receiver geometries. The design incorporates four source transducers (1.5–13 kHz) that can be arranged into different configurations, including Maltese Cross, a square and two separated pairs. The receive array comprises 240 hydrophones in 60 groups whose group-centres are separated by 25 cm in both horizontal directions, with each hydrophone group containing four individual elements and a pre-amplifier. After careful consideration, it was concluded that the only way to determine with sufficient accuracy the source–receiver geometry, was to fix the sources and receivers within a rigid array. Positional information for the array is given by a Real Time Kinematic GPS and attitude system incorporating four antennas to give position, heading, pitch and roll. It is shown that this system offers vertical positioning accuracy with a root-mean-square (rms) error less than 2.6 cm, while the horizontal positioning rms error was less than 2.0 cm. The system is configured so that the Chirp source signature can be chosen by software aboard the acquisition vessel. The complete system is described and initial navigational and seismic data results are presented. These data demonstrate that the approach of using fixed source-receiver geometry combined with RTK navigation can provide complete 3D imaging of the sub-surface.     

Track Parameter Estimation from Multipath Delay Information

It is desired to track the location of an underwater acoustic source with range difference measurements from a stationary passive array. Many times, the array has only one or two sensors, and the multipath and intersensor range difference measurements are insufficient to localize and track a source moving along an arbitrary path [1]. Here, we propose to track sources with one- or two-sensur stationary passive arrays by making the simplifying assumption that the source's path can be described by a small set of so-called track parameters. Range difference information can then be used to estimate the track parameter set rather than the source location as a function of time. In this paper, we choose the track parameters to specify a straight-line constant-velocity constant-depth path. Cramer-Rao bounds are presented for estimating these track parameters from the time history of multipath and intersensor range difference measurements. It is shown that this track parameter set cannot be accurately estimated from the time history of a single multipath range difference without side information (an independent velocity estimate, for instance), although multipath and intersensor range difference measurements from a two-sensor array are generally sufficient to estimate the track parameter set. Computationally efficient techniques are presented which estimate track parameters from range difference measurements taken from one- and two-sensor arrays. Monte-Carlo simulations are presented which show that these techniques have sample mean-square error approximately equal to the Cramer-Rao bound when a single multipath range difference and an independent velocity estimate are available. The sample mean-square error is shown to be in the range of two to ten times the corresponding Cramer-Rao bounds when these techniques are applied to two-sensor range difference data.     

Low-frequency acoustic wave-scattering phenomena under ice cover

Studies on low-frequency acoustic wave-scattering phenomena due to under-ice roughness made by utilizing a rough, thin-ice plate model are presented. The model naturally divides the reflected field solution into specular and off-specular components. The model for specular components can give an excellent propagation loss prediction if the combined effects of under-ice roughness scattering, ice absorptions, and ice thickness are taken into account. The model for scattered or off-specular components is evaluated for a point source and point receiver geometry to study various spreading phenomena     

Spatial diversity equalization applied to underwater communications

Underwater acoustic digital communication is difficult because of the nature of the fading multipath channels. Digital signal processing, such as adaptive equalization, is known to greatly improve the communication data rate by limiting intersymbol interference (ISI). However, existing underwater acoustic equalization studies are limited to single-channel techniques, and spatial diversity processing is limited to selection or combining. In this paper, we design minimum mean-square error (MMSE) equalizers jointly among all spatial diversity channels. We call this spatial diversity equalization (SDE). Results are based on a very sparse vertical array in a midrange underwater acoustic channel. We study the effect of element number and placement, the length of the equalization filters, and linear feedforward versus nonlinear decision feedback algorithms. A suboptimum equalizer combiner (EC) is studied to alleviate the computational intensity of JCE. We first design the system for a known acoustic channel; later, some results are verified using adaptive algorithms. Results are presented both in terms of the mean-square error (MSE) and the probability of a symbol error. The latter is important as it is the ultimate interest for a digital communication system. We found that system performance improves rapidly with an increase in the number of spatial channels     

On Performance of Array Signal Processing

A unified treatment for performance evaluation of various array signal processors is presented. Detection performance is expressed in terms of the parameter of the power-type receiver operating characteristic (ROC) for optimum, beamformer, and null-steerer detectors. Estimation performance is analyzed in terms of the normalized mean-square error (MSE) for minimum mean-square error (MMSE) and maximum likelihood estimators (MLE's) under a varying noise environment. Sensitivity of the detection/estimation performance to the varying internal and directional noise sources is investigated. An interesting inverse relationship is presented between the normalized MSE of the MMSE estimator and the power-type ROC parameter for the optimum detector.     

A modeling study of acoustic propagation through movingshallow-water solitary wave packets

Propagation of 400-Hz sound through continental-shelf internal solitary wave packets is shown by numerical simulation to be strongly influenced by coupling of normal modes. Coupling in a packet is controlled by the mode coefficients at the point where sound enters the packet, the dimensions of the waves and packet, and the ambient depth structures of temperature and salinity. In the case of a moving packet, changes of phases of the incident modes with respect to each other dominate over the other factors, altering the coupling over time and thus inducing signal fluctuations. The phasing within a moving packet varies with time scales of minutes, causing coupling and signal fluctuations with comparable time scales. The directionality of energy flux between high-order acoustic modes and (less attenuated) low-order modes determines a gain factor for long-range propagation. A significant finding is that energy flux toward low-order modes through the effect of a packet near a source favoring high-order modes will give net amplification at distant ranges. Conversely, a packet far from a source sends energy into otherwise quiet higher modes. The intermittency of the coupling and of high-mode attenuation via bottom interaction means that signal energy fluctuations and modal diversity fluctuations at a distant receiver are complementary, with energy fluctuations suggesting a source-region packet and mode fluctuations suggesting a receiver-region packet. Simulations entailing 33-km propagation are used in the analyses, imitating the SWARM experiment geometry, allowing comparison with observations     

Numerical prediction of hydrodynamic forces on a berthed ship induced by a passing ship in different waterway geometries

An investigation has been conducted to quantify the effect of waterway geometry on the form and magnitude of forces and moment experienced by a berthed ship due to a passing ship.By using the dynamic mesh technique and solving the unsteady RANS equations in conjunction with a RNG k?ε turbulence model,numerical simulation of the three-dimensional unsteady viscous flow around a passing ship and a berthed ship in different waterway geometries is conducted,and the hydrodynamic forces and moment acting on the berthed ship are calculated.The proposed method is verified by comparing the numerical results with existing empirical curves and a selection of results from model scale experiments.The calculated interaction forces and moment are presented for six different waterway geometries.The magnitude of the peak values and the form of the forces and moment on the berthed ship for different cases are investigated to assess the effect of the waterway geometry.The results of present study can provide certain guidance on safe maneuvering of a ship passing by a berthed ship.     

Modeling and interpreting the seismic-reflection expression of sandstone in an ancient mass-transport deposit dominated deep-water slope environment

Subsurface mass-transport deposits (MTDs) commonly have a chaotic seismic-reflection response. Synthetic seismic-reflection profiles, created from a precise lithological model, are used to interpret reflection character and depositional geometries at multiple frequencies. The lithological model was created from an outcrop of deep-water lithofacies where sandstone deposition was influenced by mass-transport deposit topography. The influence of MTD topography on sandstone distribution should be considered in reservoir characterization and modeling when MTDs underlie the reservoir, especially if the reservoir is thin relative to the scale of the topography. MTD topography up to several tens of meters in both the horizontal and vertical dimensions (relative to local elevation) compartmentalizes significant quantities of sandstone and is not resolved at lower seismic-reflection frequencies. The resolvability of thick (up to 70 m) sandstone packages is hindered when they are encased in MTDs of at least equivalent thickness. Lateral and vertical changes in seismic-reflection character (e.g., amplitude, polarity, geometry) of sandstone packages in the synthetic profiles are due to lithology changes, tuning effects, resolution limits, and depositional geometries, which are corroborated by the lithological model. Similar reflection-character changes are observed in an actual seismic-reflection profile, of comparable scale to the synthetic profiles, from the Gulf of Mexico, which demonstrates similar lithofacies distributions. Synthetic profiles, when constrained by a precise lithological model, are particularly useful analogues for interpretation of lithofacies relationships, and depositional geometries, in complicated depositional environments, such as deep-water slope deposits.     

The application of Hert'z contact theory to the problem of an offshore structure entering the seabed

This paper treats the problem of the penetration of a cylindrical leg of a fixed offshore structure into the sea. The problem is taken as a classic contact problem where the seabed is flat and two cases of structure geometry are considered. Comparisons of the flat and hemispherical bottom geometries indicate that the hemispherical geometry requires 2/3 the load of the flat bottom. This results leads to a preliminary conclusion that a hemispherical geometry is more efficient for initial penetration.     

A Portable Matched-Field Processing System Using Passive Acoustic Time Synchronization

A portable matched-field processing (MFP) system for tracking marine mammals is presented, constructed by attaching a set of autonomous flash-memory acoustic recorders to a rope to form a four-element vertical array, or "insta-array." The acoustic data are initially time-synchronized by performing a matched-field global inversion using acoustic data from an opportunistic source, and then by exploiting the spatial coherence of the ocean ambient noise background to measure and correct for the relative clock drift between the autonomous recorders. The technique is illustrated by using humpback whale song collected off the eastern Australian coast to synchronize the array, which is then used to track the dive profile of the whale using MFP methods. The ability to deploy autonomous instruments into arbitrary "insta-array" geometries with conventional fishing gear may permit nonintrusive array measurements in regions currently too isolated, expensive, or environmentally hostile for standard acoustic equipment     

深海海面目标单水听器被动测距方法与验证

基于射线理论分析了在深海情况下海面声源产生声场的频率-距离干涉结构,给出了影区内声场频率-距离干涉结构的近似理论表达式,分析得到影区内声场频域干涉周期随收发距离的增加而增大、随着接收水听器深度的增加而减小。因此由单水听器记录的声场干涉结构即可实现被动声源距离估计。在南海深海实验中观测到海面宽带噪声源在声场影区形成的声场干涉结构,对实验获得声场干涉结构的处理结果验证了深海声场影区干涉结构用于被动声源距离估计的有效性。与传统的匹配场被动定位方法相比,该方法不需要已知海底声学参数和大规模的拷贝场计算。     

Time-domain geoacoustic inversion of high-frequency chirp signal from a simple towed system

An inversion method using a towed system consisting of a source and two receivers is presented. High-frequency chirp signals that have been emitted from the source are received after multiple penetrations and reflections from the shallow water sub-bottom structure and are processed for geoacoustical parameter estimation. The data are processed such that a good resolution and robustness is achieved via matched filtering, which requires information about the source signal. The inversion is formulated as an optimization problem, which maximizes the cost function defined as a normalized correlation between the measured and modeled signals directly in the time domain. The very fast simulated reannealing optimization method is applied to the global search problem. The modeled time signal is obtained using a ray approach. An experiment was carried out in the Mediterranean Sea using a towed source and receiver system. The inversion method is applied to the experimental data and results are found to be consistent with previous frequency-domain analyses using measurements from a towed horizontal array of receivers and measurements on a vertical array.     

Modal Inversion Analysis for Geoacoustic Properties of the New Jersey Continental Shelf in the SWAT Experiments

In this paper, inversion for bottom sediment properties at a site on the New Jersey continental shelf is studied as part of the Shallow Water Acoustic Technology (SWAT) project. A source towed at a constant water depth over a range of some tens of kilometers transmitted low-frequency continuous wave (cw) signals, which were measured on a bottom-moored vertical line array of receivers. For the along-shelf geometry, the zeroth-order asymptotic Hankel transform is then applied to the acoustic field at 50 Hz measured on the resulting synthetic aperture horizontal array created at each receiver depth. The resulting horizontal wave number spectra, which have peaks corresponding to the mode eigenvalues, are observed to have slightly different values at different receiver depths, and therefore, stochastic mode inversion is exploited to utilize all of the observed peak position information. The estimated sound-speed profile (SSP) for the upper 10 m of sediment is then compared with an inversion result obtained using midfrequency (2–16 kHz) chirp sonar pulses reflected at normal incidence from the sediment. Although obtained using totally different inversion techniques, both estimated profiles are shown to be in good agreement in the top 10 m of sediment. The acoustic field simulated using the inverted SSP also agrees well with the measured acoustic field at each receiver depth. Furthermore, simulated sound fields which use this profile as input data are shown to be effective in predicting the measurements obtained at a different frequency (125 Hz) and for a different (cross-shelf) geometry.      

Foldbelts with early salt withdrawal and diapirism: Physical model and examples from the northern Gulf of Mexico and the Flinders Ranges, Australia

A physical experiment shows that shortening applied to existing diapirs and minibasins produces anomalous structural styles that are unlike those of more typical foldbelts. Strong minibasins remain largely undeformed while weak diapirs localize contractional strain. Short diapirs form the cores to folds and thrusted folds, whereas tall diapirs are squeezed and often welded, commonly leading to the extrusion of allochthonous material. Key features of the model are observed in real examples. In the northern Gulf of Mexico passive margin, minibasins were originally separated by a polygonal pattern of deep salt ridges, with diapirs located at ridge intersections. Gravity spreading resulted in squeezed diapirs (and associated allochthonous salt) connected by variably oriented contractional, extensional, and strike-slip structures. In the Flinders Ranges convergent-margin foldbelt of South Australia, preexisting diapirs were squeezed, welded, and thrusted, with anticlines plunging away in multiple directions, so that minibasins are surrounded by highly variable structures. A different geometry is observed in La Popa Basin, Mexico, where squeezing of a linear salt wall produced a vertical weld with diapirs at the terminations, rather than the culmination. In all areas, foldbelt geometries are strongly influenced by the preestablished salt-minibasin architecture.     

A high-resolution seismic profiling system using a deep-towed horizontal hydrophone streamer

A seismic reflection profiling system utilising a surface air gun source and a deep-towed horizontal hydrophone streamer has been developed for high resolution studies in the deep ocean. The instrument is deployed on a conventional armoured single conductor cable at depths of up to 6 km. Seismic data from the 30 m long streamer is wide-band frequency modulated up the towing cable to the ship together with a high frequency monitor from a 3.5 kHz echo-sounder mounted on the instrument package. The geometry of the system allows an order of magnitude improvement in spatial resolution compared with that obtained from standard surface source/receiver configurations. The summed hydrophones of the streamer attenuate cable-generated mechanical noise, and the 3.5 kHz sea-surface and bottom reflected returns provide receiver positioning information. The system has been successfully deployed at depths of 5 km in the Vema Fracture Zone in the North Atlantic, and although initially difficulties were experienced in balancing the streamer, subsequent profiles across the transform fault show details of sub-bottom structure which on conventional surface records are generally masked by diffraction hyperbolae.     

Evaluation of cyclic and monotonic loading behavior of bucket foundations used for offshore wind turbines

Suction caissons are considered as an alternative foundation solution for offshore wind turbines. In the present study, three-dimensional finite element (FE) analyses are performed to assess the behavior of a bucket foundation and soil supporting the bucket under cyclic and monotonic loading conditions. A parametric study is also performed for a wide range of bucket geometries and two different soil densities. The results indicate that bucket geometry and soil properties significantly affect the foundation response due to cyclic loading conditions. The bucket with the smallest geometry installed in medium dense soil exhibits the lowest stiffness in initial loading and then with the progress of cyclic loads experiences lower stiffness compared to the caissons with larger geometries. The sensitivity of the foundation response to the soil density is higher than its geometry. The bucket under the lowest vertical load experiences the lowest stiffness in both virgin loading and during the progress of cyclic loads. The highest soil displacement is observed near the lid at the interior of the bucket. Stresses caused by cyclic loading belong to certain ranges. Additionally, increases in the skirt length result in increases in the stress ranges and shift the range to the right side. With respect to the monotonic loading conditions, normalized diagrams are proposed that can be used for the preliminary design of suction bucket foundations.     

Local scour prediction around piers with complex geometry

A laboratory study of local scour at complex piers under steady clear-water conditions is presented. The term complex piers is used to define a bridge pier comprising of a column, pile cap, and pile group. Comprehensive data over the full range of possible pile cap elevations for complex piers with different geometries were obtained using five complex pier models, which were scaled down from existing bridges in Malaysia. The data are used to evaluate existing methodologies for characterizing the effective width of complex piers with varying pile cap location relative to the undisturbed streambed. The effect of pile cap location on scour depth is also addressed. To improve the predictions of local scour at complex piers, the new data and some previous data are used to propose a new method to predict local scour depth at complex piers.     

Receiver depth selection for passive sonar systems

Since tactical acoustic systems such as towed arrays can be deployed at various depths, the authors address the question of what depth is optimal. This question is considered principally from the point of view of optimum propagation conditions, employing two deep-water scenarios representing summer and winter conditions in the western Mediterranean. Two simple rules-of-thumb are derived from these results: first, if the source depth is known, then the best receiver depth is either the source depth or the conjugate depth (where the sound speed is the same as that at the source). Second, if the source depth is unknown, then a receiver depth where the ocean sound speed is as low as possible is optimal. These two rules are qualified with a few disclaimers. In the first place they are derived under the assumption of a range-invariant environment. In addition, a definition of optimality requires numerous assumptions that may not always be appropriate. Both these guidelines and their domain of applicability are discussed