Abstract

Euler deconvolution of magnetic fields, induced by sheets with nonnegligible widths, provides source-location estimates that are biased away from the true locations. I have derived formulas for these biases and used the equations to model diffuse solution patterns that are owing to the interplay between integer structural indices and finite sources. These patterns closely match solutions deconvolved from aeromagnetic data over northern Canada. Motivated out of the necessity that complete harmonics be integral degreed, I have investigated and discovered the ineffectiveness of noninteger structural indices in remediating the aforementioned biases. In fact, real numbers impart similar errors to multiple Euler solutions, causing ensembles of estimated origin loci to reside below the middle of the tops of wide sheets. I have devised an approach requiring the inclusion of a term in the Euler deconvolution kernel whose independent variable is the second horizontal derivative of the total field, and whose partial slope (to be solved) is the sheet width. This approach is appropriate only if the thickness does not exceed the depth. However, precision could be sacrificed in favor of accuracy because of the presence of the second derivative. The application to aeromagnetic data over a diabase dike in northern Canada yields a depth effectively coincident with a drilling depth.

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