Two Dimensional Regularization Parameter in the Downward Continuation of Potential Fields

The search for the correct value of the regularization parameter is the crucial step in the concept of the Tikhonov regularization. The present sequential methods are using the specialized curves (L p norms or L curves) on which the points with given properties are searched and tested as desired values of the regularization parameter. Here, we extended one of those methods into two dimensions for the regularized downward continuation operator, while there are situations where the noise shows some directional dependence. The two regularization parameters—one for the each direction ( x and y ), could be the partial answer to these problems. The method is tested on the synthetic and two real data sets from detailed and regional magnetometry to demonstrate its possibilities.