Optimal Filtering for Incompletely Measured Polynomial Systems with Multiplicative Noise

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations with an arbitrary, not necessarily invertible, observation matrix is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. Thus, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. A transformation of the observation equation is introduced to reduce the original problem to the previously solved one with an invertible observation matrix. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of linear and bilinear state equations. In an example, the performance of the designed optimal filter is verified against those of the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman–Bucy filter. The authors thank the Mexican National Science and Technology Council (CONACyT) for financial support under Grants No. 55584 and 52953.     

A calculus for and termination of rippling

Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general formalization of rippling. We introduce a simple calculus for rewriting annotated terms, close in spirit to first-order rewriting, and prove that is has the formal properties desired of rippling. Next we develop criteria for proving the termination of such annotated rewriting, and introduce orders on annotated terms that lead to termination. In addition, we show how to make rippling more flexible by adapting the termination orders to the problem domain. Our work has practical as well as theoretical advantages: it has led to a very simple implementation of rippling that has been integrated in the Edinburgh CLAM system. Funded by the German Ministry for Research and Technology under grant ITS 9102. Supported by a Human Capital and Mobility Research Fellowship from the European Commission. Both authors thank members of the Edinburgh Mathematical Reasoning Group, as well as Alan Bundy, Leo Bachmair, Dieter Hutter, and Michael Rusinowitch, for their comments on previous drafts. Additional support was also received from the MInd grant EC-US 019-76094.     

高邮凹陷晚白垩世泰一段沉积时期物源及沉积相定量分析

寻找岩性油气藏目前已成为高邮凹陷深层勘探的主要方向,而对岩性体作出准确的预测,须对沉积时期的物源及沉积相作出准确的判断.依据不同地区砂岩碎屑组分特征及其胶结物的类型变化规律、稳定与非稳定类型重矿物组合在平面上的变化特征及地层厚度的分析,得出高邮凹陷晚白垩世泰一段沉积时期存在3个物源,其分别是凹陷南部的通扬隆起、北部的建湖隆起以及西部的菱塘低凸起.在物源分析的基础上,依据大量单井岩心观察和砂岩、砂砾岩资料统计,并结合各类沉积相发育的构造带位置和形成机制对研究区的沉积相进行了定量分析.定量分析结果表明:泰一段沉积时期,高邮凹陷主要发育的沉积相类型有冲积扇、扇三角洲、辫状河三角洲和滨浅湖相.     

裂缝各向异性对纵波叠加地震资料的影响

裂缝分布模式的差别导致了介质速度属性的不同，带来了共中心点道集的动校正剩余时差，进而影响了共中心点道集的叠加效果，增加了资料处理和解释的复杂性。而这些复杂性包含了裂发布特征的信息，通过不 同的处理方式提取和解释这些复杂性包含的信息，使得利用纵波地震资料寻找有利裂缝发育带成为可能。     

准噶尔盆地侏罗系三工河组层序界面结构分析

通过对露头，钻井测井和地震资料的研究，认为在准噶尔盆地侏罗系三工河组J1s^22砂体之中从反旋回的转折点上发育一侏罗系内部层序界面，该界面的识别标志明显，在露头，钻井，测井以及地震剖面中具有较好的反映，由于J1s^22砂体的组合关系在盆地不同部位具有较大的差别，因而导致该界面的表现样式具有极大的差别，主要表现为层序底界具有上下岩性接触关系复杂，沿层地球物理参数变化多端以及多端以及界面上下地震反射结构差异较大等特征，因此该界面在全盆范围内非均一性特征突出，而形成该界面均一性的主控因素为构造活动特别是盆地内的局部构造活动的差异性导致的不同区域可容空间的变化，此外沉积供给和气候的变化也是主要影响因素之一。