弱间断

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下：第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型，证明了该边值问题弱解的存在唯一性，在此基础上研究了自然电位测井电阻率识别问题：然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法，利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响，取得了满意的结果。

The correct weak form of basic equations in elasticity is presented by means of dual space conception and basic theorem in functional analysis. The conditions on discontinuous surfaces of displacements or elasticity constants for continua are given.

因此从泛函分析的角度出发，基于共轭空间的概念和泛函分析的基本定理准确地给出了弹性力学基本方程的弱形式；给出了连续介质在位移或物理常数间断面上的条件。

To reduce the weak discontinuity or to make the interface micro-discontinuous are all beneficial to the enhancement of the capacity of the FGMs interface to resist impact fracture, i.e.

减小界面的弱间断程度或使 FGMs界面具备''微间断性''，都将利于提高功能梯度双材料界面抗冲击断裂能力，在一定程度上达到界面增韧的目的。

The complexity of the 660km discontinuity beneath MDJ shows that the subducting slab materials are piled above the discontinuity, and the existence of this discontinuity beneath HIA shows that the effect of the subducting slab on the discontinuity is very weak.

MDJ台下660km间断面的复杂性体现了俯冲带物质在660km间断面上的堆积，而HIA下660km间断面的存在情况，则表明俯冲带的影响已经相当地弱了。

The existences of these discontinuities show obvious regional characteristics that,(1) at the northern Izu-Bonin which is north to latitude of 33°, the SV-P converted phases following the phases from the 660km discontinuity are relatively weak,(2) at the southern part which is south to latitude of 29°, all phases are relatively strong, even some phases' amplitudes are comparative with those from the 660km discontinuity, and (3) at the part of Izu-Bonin between the latitude between 30°and 32°, all converted phases are relatively weak except the clear phases from the 660km discontinuity.

从各地震的波形叠加结果看，这些间断面的存在情况明显具有区域性特征：在北部，北纬33°以北在来自660km间断面的转换震相之后出现的SV-P转换震相相对较弱；在南部，北纬29°以南则各转换震相相对较强，有的幅度可以与来自660km间断面的转换震相的幅度相比；而北纬30°～32°之间除了来自660km间断面的转换震相存在比较清晰以外，后至的转换震相都相对较弱。

The results show that the electrojet belt is divided by Harang discontinuity into two parts: the minor eastward electrojet in afternoon sector and the major westward electrojet in midnight-morning sector.

研究表明，Harang间断把极光电集流带分为两段：下午—黄昏段的东向电集流带较弱，而晨侧和子夜—凌晨段的西向电集流带较强。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。