ILL-POSEDNESS OF ABSORBING BOUNDARY-CONDITIONS FOR MIGRATION

被引:13
作者
HOWELL, LH
TREFETHEN, LN
机构
[1] MIT, Cambridge, MA, USA, MIT, Cambridge, MA, USA
关键词
ABSORBING BOUNDARY CONDITIONS - HYPERBOLIC DIFFERENTIAL EQUATIONS - WAVE-EQUATION MIGRATION;
D O I
10.1190/1.1442494
中图分类号
P3 [地球物理学]; P59 [地球化学];
学科分类号
0708 ; 070902 ;
摘要
Absorbing boundary conditions for wave-equation migration were introduced by Clayton and Engquist. We show that one of these boundary conditions, the B2 (second-order) condition applied with the 45 degree (third-order) migration equation, is ill-posed. In fact, this boundary condition is subject to two distinct mechanisms of ill-posedness: a Kreiss mode with finite speed at one boundary and another mode of a new kind involving wave propagation at unbounded speed back and forth between two boundaries. Unlike B2, the third-order Clayton-Engquist boundary conditions B3 is well-posed. However, it is shown that it is impossible for any boundary condition of Clayton-Engquist type of order higher than one to be well-posed with a migration equation whose order is higher than three.
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页码:593 / 603
页数:11
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