Statistical distribution of nonlinear random wave height

A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

Measurements of ocean wave and current field using dual polarized X-band radar

A new ocean wave and sea surface current monitoring system with horizontally-(HH) and vertically-(VV) polarized X-band radar was developed. Two experiments into the use of the radar system were carried out at two sites, respectively, for calibration process in Zhangzi Island of the Yellow Sea, and for validation in the Yellow Sea and South China Sea. Ocean wave parameters and sea surface current velocities were retrieved from the dual polarized radar image sequences based on an inverse method. The results obtained from dual-polarized radar data sets acquired in Zhangzi Island are compared with those from an ocean directional buoy. The results show that ocean wave parameters and sea surface current velocities retrieved from radar image sets are in a good agreement with those observed by the buoy. In particular, it has been found that the vertically-polarized radar is better than the horizontally-polarized radar in retrieving ocean wave parameters, especially in detecting the significant wave height below 1.0 m.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

叠前叠后联合反演技术及其在QHD32-6油田的应用研究

What geophysical inversion studied includes the common mathematics physical property of inversion and the constitution and appraisal method of solution in geophysics domain, i.e. using observed physical phenomenon from the earth surface to infer space changing and physical property structure of medium within the earth. Seismic inversion is a branch of geophysical inversion. The basic purpose of seismic inversion is to utilizing seismic wave propagating law in the medium underground to infer stratum structure and space distribution of physical property according to data acquisition, processing and interpretation, and then offer the vital foundation for exploratory development. Poststack inversion is convenient and swift, its acoustic impedance inversion product can reflect reservoir interior changing rule to a certain degree, but poststack data lack abundant amplitude and travel time information included in prestack data because of multiple superimpose and weaken the sensitiveness which reflecting reservoir property. Compared with poststack seismic inversion, prestack seismic inversion has better fidelity and more adequate information. Prestack seismic inversion, including waveform inversion, not only suitable for thin strata physical property inversion, it can also inverse reservoir oil-bearing ability. Prestack seismic inversion and prestack elastic impedance inversion maintain avo information, sufficiently applying seismic gathering data with different incident angle, partial angle stack, gradient and intercept seismic data cube. Prestack inversion and poststack inversion technology were studied in this dissertation. A joint inversion method which synthesize prestack elastic wave waveform inversion, prestack elastic impedance inversion and poststack inversion was proposed by making fully use of prestack inversion multiple information and relatively fast and steady characteristic of poststack inversion. Using the proposed method to extract rock physics attribute cube with clear physical significance and reflecting reservoir characterization, such as P-wave and S-wave impedance, P-wave and S-wave velocity, velocity ratio, density, Poisson ratio and Lame’s constant. Regarding loose sand reservoir in lower member of Minghuazhen formation, 32-6 south districts in Qinhuangdao,as the research object, be aimed at the different between shallow layer loose sand and deep layer tight sand, first of all, acquire physical property parameters suitable for this kind of heavy oil pool according to experimental study, establishing initial pressure and shear wave relational model; Afterwards, performing prestack elastic wave forward and inversion research, summarizing rules under the guidance of theoretical research and numerical simulation, performing elastic impedance inversion, calculating rock physics attributes; Finally, predicting sand body distribution according to rock physics parameters, and predicting favorable oil area combine well-logging materials and made good results.

基于量子蒙特卡罗的地震波反演方法

The primary approaches for people to understand the inner properties of the earth and the distribution of the mineral resources are mainly coming from surface geology survey and geophysical/geochemical data inversion and interpretation. The purpose of seismic inversion is to extract information of the subsurface stratum geometrical structures and the distribution of material properties from seismic wave which is used for resource prospecting, exploitation and the study for inner structure of the earth and its dynamic process. Although the study of seismic parameter inversion has achieved a lot since 1950s, some problems are still persisting when applying in real data due to their nonlinearity and ill-posedness. Most inversion methods we use to invert geophysical parameters are based on iterative inversion which depends largely on the initial model and constraint conditions. It would be difficult to obtain a believable result when taking into consideration different factors such as environmental and equipment noise that exist in seismic wave excitation, propagation and acquisition. The seismic inversion based on real data is a typical nonlinear problem, which means most of their objective functions are multi-minimum. It makes them formidable to be solved using commonly used methods such as general-linearization and quasi-linearization inversion because of local convergence. Global nonlinear search methods which do not rely heavily on the initial model seem more promising, but the amount of computation required for real data process is unacceptable. In order to solve those problems mentioned above, this paper addresses a kind of global nonlinear inversion method which brings Quantum Monte Carlo (QMC) method into geophysical inverse problems. QMC has been used as an effective numerical method to study quantum many-body system which is often governed by Schrödinger equation. This method can be categorized into zero temperature method and finite temperature method. This paper is subdivided into four parts. In the first one, we briefly review the theory of QMC method and find out the connections with geophysical nonlinear inversion, and then give the flow chart of the algorithm. In the second part, we apply four QMC inverse methods in 1D wave equation impedance inversion and generally compare their results with convergence rate and accuracy. The feasibility, stability, and anti-noise capacity of the algorithms are also discussed within this chapter. Numerical results demonstrate that it is possible to solve geophysical nonlinear inversion and other nonlinear optimization problems by means of QMC method. They are also showing that Green’s function Monte Carlo (GFMC) and diffusion Monte Carlo (DMC) are more applicable than Path Integral Monte Carlo (PIMC) and Variational Monte Carlo (VMC) in real data. The third part provides the parallel version of serial QMC algorithms which are applied in a 2D acoustic velocity inversion and real seismic data processing and further discusses these algorithms’ globality and anti-noise capacity. The inverted results show the robustness of these algorithms which make them feasible to be used in 2D inversion and real data processing. The parallel inversion algorithms in this chapter are also applicable in other optimization. Finally, some useful conclusions are obtained in the last section. The analysis and comparison of the results indicate that it is successful to bring QMC into geophysical inversion. QMC is a kind of nonlinear inversion method which guarantees stability, efficiency and anti-noise. The most appealing property is that it does not rely heavily on the initial model and can be suited to nonlinear and multi-minimum geophysical inverse problems. This method can also be used in other filed regarding nonlinear optimization.