The two-layer problem has been solved completely. Considerable success with the three-layer problem has been attained by the extension of the two-layer methods of Tagg and Roman making use of the principle established by Hummel.Some of the limitations of these methods are examined by the comparison of theoretical curves for various values of h 2 , rho 2 , and rho 3 with help-curves computed using Hummel's principle. In general it is found that the three-layer problem of the type where a good conductor lies between two relatively poor conductors is more favorable for interpretation by the extension methods than is the opposite case where a poor conductor lies between two good conductors. The disadvantage in the latter case is that the field measurements must be carried to very much larger electrode spacings compared to the depth investigated.In all three-layer problems where h 2 < h 1 , a good interpretation for h 1 is difficult. The four-layer problem is much more difficult and only very special types lend themselves to the extension methods.The use of a large number of theoretical curves for curve matching is advocated both as a supplement to the extension methods and as a more powerful but slower method for the less favorable three-layer problems as well as for problems of four or more layers.

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