III‐posedness of absorbing boundary conditions for migration
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° (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 condition B3 is well‐posed. However, we show 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.