<p>Magnetic anomaly-derived lineaments, indicative of major dike swarms at shallow crustal levels, are common features associated with igneous provinces due to the contrasting magnetisation of diabase and dolerite compared to crystalline and sedimentary country rocks. Aeromagnetic datasets are useful for tracking the extension of subsurface structures, but the observed magnetic anomalies rarely correspond directly to the exposed dikes. Typically, a large number of dikes are inferred from airborne data, many of which are located at deeper levels, with few reaching the ground surface. To fully understand the effects of dikes in groundwater, geothermal, and petroleum and gas geosystems, accurate mapping of dike distribution and intrusion depths is required. Dikes are usually steeply dipping, elongated, and tabular bodies, allowing them to be represented as simple vertical thin-sheet models that do not explicitly account for their width. By exploring the correspondence of this parametrisation regarding the equivalence of the amplitude of the magnetic anomaly (AMA) with a field generated by a line of current situated at the thin-sheet top, it is possible to formulate the resulting field as equivalent to a Cauchy probability density distribution. This equivalence allows for model uncertainty inferences about depth estimates based solely on the observed AMA attributes, provides reliable automatic solutions for preliminary geological interpretation, and offers well-suited initial solutions for fast convergence of nonlinear data fitting to the observed magnetic anomaly. The developed procedure is applied to interpret a magnetic transect across dike swarms of the North Atlantic Igneous Province in Northern Ireland, where a minimum number of dikes at variable depths are inferred to explain the observed magnetic transect.</p>