波动方程三维吸收边界分解与拟合深度偏移方法

FACTORIZATION AND FITTING METHOD FOR 3-D WAVE EQUATION DEPTH MIGRATION WITHABSORBING BOUNDARY CONDITIONS

在偏移问题中引入吸收边界条件，既可以消除由人工边界激发的虚假反射，从而提高剖面质量。又可以减少计算工作量．本文讨论了三维吸收边界条件方程，提出了求解具有吸收边界条件的三维波动方程偏移定解问题的分解与拟合方法。理论分析与合成记录及野外实际地震资料处理结果表明，本文方法为一有效的三维吸收边界深度偏移方法。

The Introduction of absorbing boundary conditions not only can eliminate the false reflection excited by the artificial boundary,thus increasing reliability and quality of the seismic profile,but also can reduce the costs of computing.Because a great quantity of computing is needed in the 3-D migration problem,so absorbing boundary plays a very important role.In this paper the 3-D absorbing boundary migration problem is discussed.First,on the basis of the principle proposed in Fan Shangwu[7],the absorbing boundary condition equations are deduced for the boundary Planes of migration area.Then,we derive absorbing boundary condition equations for the boundary lines in reference to the absorbing equations about the boundary planes.The migration equation together with these boundary equations constitute 3-D absorbing boundary migration problem.When a partial differential equation problem is solved by splitting or decomposition method,it is difficult problem that how to deal with boundary condition to make the desired solution is one of the original problem.In order to overcome this difficulty,a fitting method is proposed to process boundary condition equation in this.paper.Using the factorization format of inner migration equation and the fitting format of boundary equation,the 3-D absorbing boundary migration can be realied.