The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies f...The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.展开更多
ay equation migration of wide-angle reflections in 2-D medium is one kind of Kirchhoff prestack depth migration method. Based on ray theory, this method can be used extensively in 2-D inhomogeneous medium, and shows i...ay equation migration of wide-angle reflections in 2-D medium is one kind of Kirchhoff prestack depth migration method. Based on ray theory, this method can be used extensively in 2-D inhomogeneous medium, and shows its advantage in wide-angle reflection study. After calculating ray fields, we can get the wave fields of sources and receivers by interpolation, and the intensity (or amplitude) AP corresponding to the depth point P at travel-time tP=tSP+tPR can be found in seismograms. Ray equation migration is completed by transforming AP according to the specific relation, migrating it to the depth point, then calculating the ray fields of lots of sources and receivers in the same way and finally stacking the outcomes. Numerical calculation has yielded satisfactory results. Data processing of the Zhuangmu-Yuexi-Huangmei-Zhanggongdu profile passing through the Dabie orogenic zone provides a structural form of M-discontinuity along the profile. The result shows that the high pressure metamorphic rock zone of South Dabie rock mass is related to the uplifting of M-discontinuity here. 'Mountain root' exists under North Dabie rock mass, which conforms with gravity isostasy theory. The Xiaotian-Mozitan fault is a suture zone as a result of the collision of North China plate with Yangtze plate, and extends through M-discontinuity. The abyssal fault near Liu'an is the extended eastern section of the Luonan-Minggang fault, which is also confirmed here.展开更多
文摘The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.
文摘ay equation migration of wide-angle reflections in 2-D medium is one kind of Kirchhoff prestack depth migration method. Based on ray theory, this method can be used extensively in 2-D inhomogeneous medium, and shows its advantage in wide-angle reflection study. After calculating ray fields, we can get the wave fields of sources and receivers by interpolation, and the intensity (or amplitude) AP corresponding to the depth point P at travel-time tP=tSP+tPR can be found in seismograms. Ray equation migration is completed by transforming AP according to the specific relation, migrating it to the depth point, then calculating the ray fields of lots of sources and receivers in the same way and finally stacking the outcomes. Numerical calculation has yielded satisfactory results. Data processing of the Zhuangmu-Yuexi-Huangmei-Zhanggongdu profile passing through the Dabie orogenic zone provides a structural form of M-discontinuity along the profile. The result shows that the high pressure metamorphic rock zone of South Dabie rock mass is related to the uplifting of M-discontinuity here. 'Mountain root' exists under North Dabie rock mass, which conforms with gravity isostasy theory. The Xiaotian-Mozitan fault is a suture zone as a result of the collision of North China plate with Yangtze plate, and extends through M-discontinuity. The abyssal fault near Liu'an is the extended eastern section of the Luonan-Minggang fault, which is also confirmed here.
