Hamilton—Jacobi方法的新探讨

在广义的正则方程的基础上导出了用于Ｃｈｅｔｅａｖ型非完整约束的广义Ｈａｍｉｌｔｏｎ——Ｊａ－ｃｏｂｉ方法，并以引力场作用下尖缘圆盘在水平面上纯滚动的问题作实例，说明该方法的应用。

Correction of seabed layer thickness in processing subbottom profile data

The subbottom profiling is an important means of marine engineering survey, hazardous geology study and continental shelf scientific research. The accuracy of subbottom profile data interpretation has a direct impact on the research and investigation results. Because some of profilers’ transducer and hydrophone are separately installed, when the survey area is very shallow, distortion of shallow layers will be caused if it is seen as a self-excited and self-collected single-channel seismic system. According to the principle of subbottom profiler, the distortion correction formula is deduced and analyzed, providing actual value to using C-View software to interpret such subbottom profile data more accurately. In addition, the seabed sediments sound velocity is one of the key parameters when acquiring and processing the subbottom profile data. On the basis of comparing some sound velocity forecasting empirical equations, the LU Bo’s equation was considered the most appropriate to predict the seabed sediments, sound velocity at near-shore of China. In a survey of an artificial island site, the LU Bo’s equation and the porosity data obtained from geological drilling were utilized to predict the sediments sound velocity, and the sound velocity structure profile was plotted, which was applied in processing the subbottom profile data of the artificial island investigation. The method of using porosity data to predict sediments sound velocity in processing subbottom profile data can improve the interpretation accuracy and it’s of practical significance.

New Predictor-Corrector Methods Based on Exponential Time Differencing forSystems of Nonlinear Differential Equations

We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies.

Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

In this study,the cylindrical finite-volume method(FVM)is advanced for the efficient and high-precision simulation of the logging while drilling(LWD)orthogonal azimuth electromagnetic tool(OAEMT)response in a three-dimensional(3 D)anisotropic formation.To overcome the ill-condition and convergence problems arising from the low induction number,Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system.The electrical fi eld continuation method is applied to approximate the perfectly electrical conducting(PEC)boundary condition,to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels.On the base,the 3 D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries.The equivalent conductivity in a non-uniform element is determined by a standardization technique.The direct solver,PARDISO,is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem.To reduce the number of calls to PARDISO,the whole computational domain is divided into small windows that contain multiple measuring points.The electromagnetic(EM)solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix,relevant to all the transmitters in the same window,is changed.Finally,the 3 D FVM is validated against the numerical mode matching method(NMM),and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

Correction of Dynamic Error Result from Measurement System Limitations

The main cause of dynamic errors is due to frequency response limitation of measurement system. One way of solving this problem is designing an effective inverse filter. Since the problem is ill-conditioned, a small uncertainty in the measurement will came large deviation in reconstncted signals. The amplified noise has to be suppressed at the sacrifice of biasing in estimation. The paper presents a kind of designing method of inverse filter in frequency domain based on stabilized solutions of Fredholm integral equations of the fast kind in order to reduce dynamic errors. Compared with previous several work, the method has advantage of generalization. Simulations with different Signal-to-Noise ratio （SNR） are investigated. Flexibility of the method is verified. Application of correcting dynamic error is given.