Proceeding from wave equations, the paper strictly deduced the dispersion relation equation of Love-type channel waves in Standard Linear Solid model. The e quation is a complex one with its real part signifying the d...Proceeding from wave equations, the paper strictly deduced the dispersion relation equation of Love-type channel waves in Standard Linear Solid model. The e quation is a complex one with its real part signifying the dispersion characteristics of the channel wave while the imaginary part, the attenuation characteristics. In calcu lating the attenuation value, the author has set up a mathematical model of a horizon tal symmetric sequence (a three layer sequence of rock-coal-rock), given out some physical parametersl and adopted the dichotomy method that is more of ten used in root resolving of an equatlon. The calculation indicates that the influence of non-elas tic absorption on the attenuation of the propagation of channel wave varies with the frequency. In the frequency band of the Airy phase, the attenuation increases steep like, which is unfavorable for the channel wave seismic prospecting. The study of channel wave attenuation has provided a theoretical basis for the compensation of at tenuation.展开更多
This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place onl...This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.展开更多
文摘Proceeding from wave equations, the paper strictly deduced the dispersion relation equation of Love-type channel waves in Standard Linear Solid model. The e quation is a complex one with its real part signifying the dispersion characteristics of the channel wave while the imaginary part, the attenuation characteristics. In calcu lating the attenuation value, the author has set up a mathematical model of a horizon tal symmetric sequence (a three layer sequence of rock-coal-rock), given out some physical parametersl and adopted the dichotomy method that is more of ten used in root resolving of an equatlon. The calculation indicates that the influence of non-elas tic absorption on the attenuation of the propagation of channel wave varies with the frequency. In the frequency band of the Airy phase, the attenuation increases steep like, which is unfavorable for the channel wave seismic prospecting. The study of channel wave attenuation has provided a theoretical basis for the compensation of at tenuation.
基金Supported by the Innovation Project for University Prominent Research Talents of Henan (2003KJCX008)
文摘This paper deals with two parabolic initial-boundary value problems in multidimensional domain. The first problem describes the situation where the spherical medium is static and the nonlinear reaction takes place only at a single point. We show that under some conditions, the solution blows up in finite time and the blow-up set is the whole spherical medium. When the spherical medium is allowed to move in a special space, we investigate another parabolic initial-boundary value problem. It is proved that the blow-up can be avoided if the acceleration of the motion satisfies certain conditions.
