By making use of the vector product in R^3, a commuting operation is introduced so that R^3 becomes a Lie algebra. The resulting loop algebra R^-3 is presented, from which the well-known AKNS hierarchy is produced. Ag...By making use of the vector product in R^3, a commuting operation is introduced so that R^3 becomes a Lie algebra. The resulting loop algebra R^-3 is presented, from which the well-known AKNS hierarchy is produced. Again via applying the superposition of the commuting operations of the Lie algebra, a commuting operation in R^6 is constructed so that R^6 becomes a Lie algebra. Thanks to the corresponding loop algebra R^3 of the Lie algebra R^3, the integrable coupling of the AKNS system is obtained. The method presented in this paper is rather simple and can be used to work out integrable coupling systems of the other known integrable hierarchies of soliton equations.展开更多
Frequency attenuation occurs when seismic waves propagate through the porous reservoirs containing hydrocarbons. Current researches on the seismic frequency attenuation mainly focus on the post-stack domain instead of...Frequency attenuation occurs when seismic waves propagate through the porous reservoirs containing hydrocarbons. Current researches on the seismic frequency attenuation mainly focus on the post-stack domain instead of the prestack domain. Here we propose the frequency attenuation gradient vs. offset （FAGVO） based on the amplitude variation with offset and frequency attenuation integral equations. We derive the FAGVO equation that equals to zero in a full-elastic medium and is negative in a viscoelastic medium. FAGVO is affected by the viscosity of the medium, the coefficients of reflection, the frequency variation, and high-frequency attenuation. FAGVO uses the differences of partially stacked data to decrease the interference caused by subsurface strata affecting the frequency attenuation, highlights the frequency attenuation gradient anomalies in hydrocarbon-bearing reservoir pores, and finally realizes the hydrocarbon fluid identification. The method was verified using a two-dimensional wave equation forward model and was found to be cost effective. Furthermore, the method does not require well information, which can be applied in the stage of seismic exploration, especially, in the exploration of a none-well project.展开更多
文摘By making use of the vector product in R^3, a commuting operation is introduced so that R^3 becomes a Lie algebra. The resulting loop algebra R^-3 is presented, from which the well-known AKNS hierarchy is produced. Again via applying the superposition of the commuting operations of the Lie algebra, a commuting operation in R^6 is constructed so that R^6 becomes a Lie algebra. Thanks to the corresponding loop algebra R^3 of the Lie algebra R^3, the integrable coupling of the AKNS system is obtained. The method presented in this paper is rather simple and can be used to work out integrable coupling systems of the other known integrable hierarchies of soliton equations.
基金supported by the Major National Science&Technology Project(No.2016ZX05003-003)the National High Technology Research and Development Program of China(863 Program)(No.2013AA064201)
文摘Frequency attenuation occurs when seismic waves propagate through the porous reservoirs containing hydrocarbons. Current researches on the seismic frequency attenuation mainly focus on the post-stack domain instead of the prestack domain. Here we propose the frequency attenuation gradient vs. offset （FAGVO） based on the amplitude variation with offset and frequency attenuation integral equations. We derive the FAGVO equation that equals to zero in a full-elastic medium and is negative in a viscoelastic medium. FAGVO is affected by the viscosity of the medium, the coefficients of reflection, the frequency variation, and high-frequency attenuation. FAGVO uses the differences of partially stacked data to decrease the interference caused by subsurface strata affecting the frequency attenuation, highlights the frequency attenuation gradient anomalies in hydrocarbon-bearing reservoir pores, and finally realizes the hydrocarbon fluid identification. The method was verified using a two-dimensional wave equation forward model and was found to be cost effective. Furthermore, the method does not require well information, which can be applied in the stage of seismic exploration, especially, in the exploration of a none-well project.
