The conventional formulation of 3D Euler deconvolution assumes that the observed field in each Euler window varies in all directions. Where the source is 2D, this assumption leads to the production of poorly constrained solutions. If the source is 2D, the problem leads to a rank deficient normal equations matrix having an eigenvector associated with a zero eigenvalue. This vector lies in the horizontal plane and is pointing along the strike direction, thus allowing for the identification of a 2D structure and its strike. Finding a pseudoinverse via eigenvector expansion allows accurate source location, and the strike information allows the automatic implementation of profile-based techniques like extended Euler deconvolution to gridded data, thus allowing for the first time the estimation of strikes, dips, and susceptibilities from grids using an automatic process. We present a grid-based version of Euler deconvolution that has the ability to define within an Euler operating window whether the source is 2D or 3D in character so that the solutions can be treated differently. We illustrate the new approaches on model and real data.