The notional source method is posed in terms of linear algebra which admits a least squares approach and avoids the original iterative method. We extend the method to include the new concept of notional ghosts which do not need to be related to the notional sources by a linear filter. As a result, the free surface reflection details do not need to be specified. An example is used to demonstrate the new method. Not only does this new approach mean that the reflection process at the free surface may remain unknown, but also that it does not need to be linear. This aspect may turn out to be of considerable use.


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