Werner Deconvolution: Analyzing Magnetic Field Anomalies for Source Parameters

1. Werner deconvolution, like Euler deconvolution, is more properly thought of as an inverse method: we analyze the observed magnetic field and solve for source parameters. The initial assumption for total field analysis is thin, sheet like bodies. But that anomaly is equal to the horizontal gradient of the total field anomaly over a semi-infinite half space. Thus, Werner deconvolution is applied to dikes and layers and has been extended to polygons. The general equation over an inclined sheet of dipoles is: The unknowns are: xo = source location d = source depth A & B are combinations of constants, magnetization, and dip. We rewrite this as a matrix equation and, given four observed points on a magnetic profile, we have four equations in four unknowns.

2. Werner deconvolution is a ‘sliding window’ technique. We move the operator along the profile and continually solve for the unknowns. The figures show solutions for depth and location from sliding window step-sizes ranging from one grid unit to nine. Window lengths either too short or long yield spurious solutions. Note the solutions from the shortest operators.

3. Selecting the solutions from operator ranges which show the best clustering regularly yields good estimates.

4. Interfering anomalies complicate the issue. Yet, there is still good clustering over the tops of the dikes. As before, removing the solutions with poor clustering improves the situation.

5. Selecting the best clustered solutions yields improved results. Yet, there are still spurious solutions from the interference of the two anomalies. And, these anomalies have no geologic nor measurement error. Regardless of these difficulties, the Werner method is time-tested and yields valuable information for further analysis and modeling, particularly when the assumptions for the thin sheet or half-space conditions are met.

6. Here’s what can happen when you make the wrong assumption on the type of source. These are Werner solutions for the horizontal derivative of the dike anomaly. Analyzing the horizontal derivative is the procedure for estimating source parameters for the vertical contact of a semi-infinite half space. Clearly, the choice of an incorrect model results in lesser solutions. The recommended approach is to use both procedures, look carefully at clustering, compare the results to other techniques, and consider the actual anomalies.

7. The prism in this example is somewhere in between a thin dike and a semi-infinite half space. It is much thicker then deep, but the anomalies from the edges (contacts) still overlap over the center. When actually assessing clusters, it helps to use no vertical or horizontal exaggeration. Here, the edge detection of the best clustering is still good, but the depth estimates are too deep.

8. Assuming vertical contacts and thus calculating Werner solutions on the horizontal derivative still yields scattered solutions for short window lengths.

9. Even with interference from the insufficiently separated lateral edges, the clustered solutions provide good guidance for modeling.