This paper describes a spectrum-based algorithmic procedure for rapid reconnaissance for compact bodies at depths of interest using magnetic line data. The established method of obtaining depth to source from power spectra requires an interpreter to subjectively select just a single slope along the power spectrum. However, many slopes along the spectrum are, at least partially, indicative of the depth if the shape of the source is known. In particular, if the target is assumed to be a point dipole, all spectral slopes are determined by the depth, noise permitting. The concept of a 'depth spectrum' is introduced, where the power spectrum in a travelling window or gate of data is remapped so that a single dipole in the gate would be represented as a straight line at its depth on the y-axis of the spectrum. In demonstration, the depths of two known ironstones are correctly displayed. When a second body is in the gate, the two anomalies interfere, leaving interference patterns on the depth spectra that are themselves diagnostic. A formula has been derived for the purpose. Because there is no need for manual selection of slopes along the spectrum, the process runs rapidly along flight lines with a continuously varying display, where the interpreter can pick out a persistent depth signal among the more rapidly varying noise. Interaction is nevertheless necessary, because the interpreter often needs to pass across an anomaly of interest several times, separating out interfering bodies, and resolving the slant range to the body from adjacent flight lines. Because a look-up table is used rather than a formula, the elementary structure used for the mapping can be adapted by including an extra dipole, possibly with a different inclination.