Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory

We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore

Transformation of Multidirectional Sea Field and Computational Study

A computational model based on the evolution equation for water waves (Li, 1994b) derived from the original Berkhoffs (1972) "Mild Slope Equation" is tested against multidirectional sea data. The model accounts for reflection as well as diffraction-refraction processes, which is important for applications involving coastal structures. The accuracy and convergence of the numerical solution, as well as the possibility of the implementation of an adaptive numerical scheme are investigated and implemented. The model was firstly tested using laboratory measurements (Briggs et al, 1995) of random directional wave diffraction around a semi-infinite breakwater on a flat bottom. These tests confirm the need to use "directional modelling" (using the principle of linear superposition) for the prediction of wave heights behind the breakwater. The model was then tested using directional wave data records, which were chosen from 4500 wave records collected in the field campaign, by the University of Plymouth and the University of Brighton, at Elmer - Sussex, UK from September 1993 - January 1995. The results showed that the representation of the measured random sea by monochromatic wave runs can introduce a significant error in wave height predictions shoreward of the breakwaters in the diffraction region, thus confirming the importance of directional modelling for random wave simulation. Evidence strongly suggests that non-linear wave effects have a significant influence (40-60%) on the accuracy of the model. Consequently, further tests are needed, which should also consider the influence of wave-current interaction, wave breaking, bed fiiction and transmissive boundaries. Over all the model predictions are more accurate for the controlled environment in the laboratory (5-13%), than for field conditions where the directional modelling accuracy varied from 8 - 32%. A summary of the data, collected by the author as a member of the University of Plymouth Research Team and a database of spectral and directional parameters is also presented in this thesis. Field validation of the numerical model required accurate estimates of measured data. Emphasis was placed on identifying a suitable directional analysis method, which accurately predicted direction and directional spread in the far-field from structures where reflection is still present. The non-phase-locked (hfPL) methods developed for a homogeneous sea are found to be appropriate. The anzdysis of two NPL methods, the Maximum Likelihood Method (MLM) and Bayesian Directional Method (BDM), directional estimates for simulated data shows that both methods can predict accurate incident wave height and direction. Both methods tend to overpredict directional spread and give non-accurate reflection estimates. The MLM method is easier to implement than the BDM method, which is sensitive to the chosen starting value of the hyperparameter u. As the difference between estimates of the two methods for numerical data is small, the MLM method's estimates were chosen for model testing

Joint inversion of seismic PP- and PS-waves in the ray parameter domain

Seismic inversion is a quantitative analysis technique in reservoir geophysics to reveal subsurface physical properties from surface-recorded seismic data. But the most widely used inversion in oil and gas exploration for decades is PP-wave based. P-to-S converted wave, which has shown great success in the imaging of gas clouds, has a different response to rocks and pore-fluids from the PP-wave. A joint use of the PS-wave and PP-wave in the inversion can reduce the ill-posedness of the inverse problem and in particular enables simultaneous inversion for three independent elastic parameters. Conventionally, prestack seismic inversion is based on the incidence angle-dependent reflection coefficients. In my research, I define the seismic reflections and impedances along the ray paths of wave propagation, and these ray paths obey Snell’s law. I adopt the ray-impedance concept, which is a frequency-dependent parameter and is sensitive to fluid contents. Joined interpretation of PP- and PS-wave ray impedances can identify reservoirs, and also has potential in fluid discrimination. Joint inversion of PP- and PS-waves is performed on the constant ray parameter (CRP) profiles. For a constant ray parameter, a pair of PP- and PS-wave traces has exactly the same ray path between the source and the reflection point, which means the PP- and PS-wave reflection events represent exactly the same reflection point, in the horizontal direction. Therefore, PP and PS-wave calibration transforms PS-wave reflection events from PS-wave time to the corresponding PP-wave time, and reflections events in a pair of PP- and calibrated PS-wave traces with a constant ray parameter should correspond to each other, sample by sample, both horizontally and vertically. I also present a procedure which preserves the original wavelets in the transformed PS-wave trace. I use a bending ray-tracing method to construct the common image point (CIP) gathers in the ray-parameter domain. I estimate mixed-phase wavelets for each constant ray-parameter (CRP) profile through a frequency domain high-order statistical method, and then invert for the reflectivity series using weighted constraints. From the reflectivity sections, I estimate PP- and PS-wave ray impedances separately and also estimate three elastic parameters simultaneously in a joint inversion. I have applied the entire procedure to a couple of field data sets, to verify the robustness and effectiveness of the method, and to demonstrate the great potential of joint inversion in ray-parameter domain

Surface Wave Processes on the Continental Shelf and Beach

There is a growing need for surface wave information on the continental shelf and beach to estimate sea state, and to provide input for models of currents, sediment transport, radar backscatter and aerosol generation. While surface wave spectra in the open ocean evolve slowly over distances of O(100-1000 km), wave properties on the continental shelf and beach are highly variable (typical length scales of 0.1-10 km) owing to a variety of topographic effects (e.g., shoaling, refraction, scattering) and strongly enhanced nonlinear interactions and dissipation. The long-term goal of this research is to develop a better understanding of the physical processes that affect the generation, propagation and dissipation of surface waves in shallow coastal waters, and improve the accuracy of models that predict the transformation of wave properties across the shelf and beach.Award Numbers: N0001497WR30010 N0001497WR30011 N0001497WR30012 N0001497WR3007

Ocean Remote Sensing with Synthetic Aperture Radar

The ocean covers approximately 71% of the Earth’s surface, 90% of the biosphere and contains 97% of Earth’s water. The Synthetic Aperture Radar (SAR) can image the ocean surface in all weather conditions and day or night. SAR remote sensing on ocean and coastal monitoring has become a research hotspot in geoscience and remote sensing. This book—Progress in SAR Oceanography—provides an update of the current state of the science on ocean remote sensing with SAR. Overall, the book presents a variety of marine applications, such as, oceanic surface and internal waves, wind, bathymetry, oil spill, coastline and intertidal zone classification, ship and other man-made objects’ detection, as well as remotely sensed data assimilation. The book is aimed at a wide audience, ranging from graduate students, university teachers and working scientists to policy makers and managers. Efforts have been made to highlight general principles as well as the state-of-the-art technologies in the field of SAR Oceanography

Acoustic classification of buried objects with mobile sonar platforms

Thesis (Ph. D. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (p. 229-237).In this thesis, the use of highly mobile sonar platforms is investigated for the purpose of acoustically classifying compact objects on or below the seabed. The extension of existing strategies, including synthetic aperture sonar and conventional imaging, are explored within the context of the buried object problem. In particular, the need to employ low frequencies for seabed penetration is shown to have a significant impact both due to the relative length of the characteristic scattering mechanisms and due to the interface effects on the target scattering. New sonar strategies are also shown that exploit incoherent wide apertures that are created by multiple sonar platforms. For example, target shape can be inverted by mapping the scattered field from the target with a team of receiver vehicles. A single sonar-adaptive sonar platform is shown to have the ability to perform hunting and classification tasks more efficiently than its pre-programmed counterpart. While the monostatic sonar platform is often dominated by the source component, the bistatic or passive receiver platform behavior is controlled by the target response. The sonar-adaptive platform trajectory, however, can result in the platform finishing its classification effort out of position to complete further tasks.(cont.) Within the context of a larger mission, the use of predetermined adaptive behaviors is shown to provide improved detection and classification performance while minimizing the risk to the overall mission. Finally, it is shown that multiple sonar-adaptive platforms can be used to create new sonar strategies for hunting and classifying objects by shape and content. The ability to sample the scattered field from the target across a wide variety of positions allows an analysis of the aspect-dependent behavior of the target. The aspect-dependence of the specular returns indicate the shape of the target, while the secondary returns from an elastic target are also strongly aspect-dependent. These features are exploited for improved classification performance in the buried object hunting mission.by Joseph R. Edwards.Ph.D.in Ocean Engineerin