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Equivalence causes non-uniqueness in interpretations of the grounded-wire transient electromagnetic method (TEM). Many different layered models may produce the same response curves practically. However, the conventional theory of equivalence is based on the three-layer geo-electric models while the earth may not be reducible to a simple three-layer structure. Therefore, it is important to perform research on equivalence based on more complex models to reduce the uncertainty the grounded-wire TEM interpretations. Here, we extend the theory of equivalence based on a multi-layer target in the grounded-wire TEM, consisting of SS-, HH-, and TT-type. The analysis of relative error is applied to investigate the effect of measured components and receiver locations on equivalence. The results show that equivalence of multi-model occurs when any of three conditions is satisfied: the longitudinal conductance is constant in the far area, the thickness of targets do not change, or the transverse conductance of a multilayer target remains unchanged. In order to largely resolve the effect of equivalence on data interpretation, a strategy combined with short-offset survey and joint inversion of the electric component and magnetic component is presented and verified by the field survey in Shanxi Province, China. • Equivalence causes non-uniqueness in interpretations of the grounded-wire TEM method. • The conventional theory of equivalence is based on the three-layer geo-electric models. • It is important to perform research on equivalence based on more complex models. [ABSTRACT FROM AUTHOR]