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本文采用Ｈａｍｉｌｔｏｎ理论方法，研究反射地震记录域中地下同一反射点对应的反射走时随炮检距变化的特性，这在叠前地震资料处理中具有重要意义．由于走时函数可以表示成炮点位置、检波点位置、地震波射线出射角和接收角的函数，通过对共反射点走时与炮点位置变化关系的分析，提出了复杂介质中共反射点轨迹可用Ｈａｍｉｌｔｏｎ正则方程描述．在线性变速介质中，走时函数可以解析给出，由此可导出该介质中共反射点轨迹的Ｈａｍｉｌｔｏｎ正则方程．文中结合常速度、横向变速和线性变速介质模型，计算了地下不同反射面上各点相应的共反射点轨迹，阐明Ｈａｍｉｌｔｏｎ方法的一些特点，并首次引入Ｈａｍｉｌｔｏｎ理论方法描述共反射点走时随炮检距的变化特性，开创了该领域研究的一条新途径．
In this paper, the Hamiltonian method is applied to study the characteristics of the reflection time variation with the offset of the same reflection point in the reflection seismogram domain, which is of great significance in prestack seismic data processing. Because the traveltime function can be expressed as a function of the position of the shot point, the position of the detection point, the exit angle of the seismic wave and the acceptance angle, the analysis of the relationship between the travel time of the common reflection point and the position of the shot point shows that the trajectory of the common reflection point in the complex medium is Hamiltonian Equation description. In linear variable-speed media, the traveltime function can be given analytically, which leads to the Hamilton’s canonical equation for the point of the common reflection point in the medium. In this paper, the common reflection point trajectory of each point on different reflecting surfaces is calculated by combining the constant velocity, lateral velocity and linear variable medium model. Some characteristics of the Hamilton method are clarified. The Hamilton theory is introduced for the first time to describe the travel time of co- The changing characteristics of distance have opened up a new way of research in this field.