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现在地球物理学家可以解决石油工业上的许多非常重要的问题,例如,油气通过褶皱、断裂的渗透层的扩散,在页岩弯曲的不均匀介质中的对流等。这些问题是不可能用解析法解决的,但可以通过数字方法解决。应用有限差分法是最容易的,但加勒金(Galerdin)法(和有限元法)对许多界面问题来说更为适宜。作为有限差分法的一个例子,给出了对流上地幔中各种模型的温度和流线。它们说明对流层的大纵横比是由于岩石圈的很高粘性和重软流圈的低粘性引起的。岩石圈本来就是热的和粘的边界层。对流图形使系统的拉格朗日算子减到最小的程度。
Nowadays, geophysicists can solve many very important problems in the oil industry. For example, oil and gas flow through folds, diffusion of fractured infiltration layers, convection in an uneven medium with shale bending, and the like. These problems can not be resolved analytically, but can be solved digitally. Finite-difference method is the easiest, but Galerdin method (and finite element method) is more suitable for many interface problems. As an example of the finite difference method, the temperature and flow lines of various models in the convective upper mantle are given. They show that the large aspect ratio of the troposphere is due to the high viscosity of the lithosphere and the low viscosity of the heavy asthenosphere. The lithosphere has always been a hot and sticky boundary layer. The convection graph minimizes the Lagrangeian of the system.