The Backus-Gilbert inverse method relates model estimates to actual earth models by use of a resolving kernel. This inversion can in turn be related to various digital filter designs. If the second moment norm is used to define the resolving kernel, two types of filters are produced by an eigenvector decomposition of a time-weighted autocorrelation matrix. The eigenvector corresponding to the largest eigenvalue of this matrix is similar to the output energy filter, while the eigenvector for the smallest eigenvalue performs more like a deconvolution filter. Synthetic and real data examples demonstrate the characteristics of these filters and compare them to the familiar square norm filters. Our experiments suggest that second moment norm filters offer no significant advantages over their Euclidean norm relatives.

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