基于双相介质的地震波衰减特性油气检测方法

油气储层是典型的多相介质,目前油气检测中依据的单相介质理论容易造成预测结果的多解性。为了更准确地检测油气,以Biot双相介质理论为基础,推导吸收系数表达式,建立能量密度衰减方程,利用广义S变换对地震资料进行频谱分解,分析介质含不同流体后地震波各频率成分的衰减特征。结果表明:当双相介质中所含流体性质不同时,地震波的频率衰减也不尽相同,当储集层中含油气时,地震波频率衰减量显著增大,低频能量衰减小,高频能量衰减大,在频谱上表现为低频能量相对增强,高频能量相对减弱,整体能量向低频移动。对比实际工区的低、高频能量剖面和衰减剖面,将地震波的衰减规律运用到油气检测中取得较好的效果,理论模型和实际资料的运用表明该方法可行。

基于改进的双快速行进法的图像分割方法

由于回转窑烧结图像境界模糊、噪声严重,传统方法难以有效地分割出烧结图像中的物料区、火焰区、充分燃烧区和黑把子区等关心区域(ROIs)。提出了利用敏感区域改进双快速行进法与利用能量衰减方程除去区域间耦合的图象分割新方法。首先,在快速行进法中引入了敏感区域的概念,定义了新的终止条件,利用改进后的双快速行进法与图像融合方法进行物料区和黑把子区的粗分割;然后,提出了采用能量衰减方程除去烧结物料对火焰区的影响,利用大津方法对火焰区进行粗分割,并通过粗分割的火焰区与黑把子区的差分来进行火焰区的精分割。对回转窑烧结图像的分割试验表明,利用本方法能够有效地从回转窑烧结图像精确地分割出ROIs。

Weak solution for a fourth-order nonlinear wave equation

The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coefficients. In particular, some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.

UNIFORM DECAY RATE FOR THE TRANSMISSION WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

This paper considers the stabilization of the transmission problem of wave equations with variable coefficients. By introducing both boundary feedback control and distribute feedback control near the transmission boundary, the author establishes the uniform energy decay rate for the problem.

Energy Decaying and Blow-Up of Solution for a Kirchhoff Equation with Strong Damping

The initial boundary value problem for a Kirchhoff equation with Lipschitz type continuous coefficient is studied on bounded domain.Under some conditions,the energy decaying and blow-up of solution are discussed.By refining method,the exponent decay estimates of the energy function and the estimates of the life span of blow-up solutions are given.