There is an issue dealing with the fixed coefficient of , that I believe is not a problem, but I place it under ``future work'' anyway because I expect it to come up occasionally. Our PEFs, , have a fixed coefficient that is defined to have the value 1. We actually estimate , which is related by , which means we should load our initial model guess, , with some other value in the fixed coefficient, that will be integrated by to give 1's. This is a hassle because our software has the value 1 built in. Luckily, the problem seems to disappear. Wherever the forward operator is applied, it looks like , which is the same as .The adjoint is used to calculate the change in the roughened model variable : , where is the residual. Whatever change is made to the fixed coefficient is zeroed by .In other words, it seems we never need to know the fixed coefficient of .

7/5/1998