Abstract Second vertical derivative methods developed by Henderson and Zietz, Elkins, Rosenbach, and Danes are applied to various mathematical harmonic fields and the response of the methods is investigated. All methods give good results as long as the wavelength of the anomaly is large compared with station spacing. As the wavelength decreases, Elkins' formulae give progressively lower values. Rosenbach's values decrease slightly, but values are still very close to correct. Henderson and Zietz's values are about halfway between the above ones. Danes' results can be made correct to the degree of accuracy of the input data.