We propose and evaluate methods for the integration of automatic implicit geological modelling into the geophysical (potential field) inversion process. The objective is to enforce structural geological realism and to consider geological observations in a level set inversion, which inverts for the location of the boundaries between rock units. We propose two approaches. In the first approach, a geological correction term is applied at each iteration of the inversion to reduce geological inconsistencies. This is achieved by integrating an automatic implicit geological modelling scheme within the geophysical inversion process. In the second approach, we use automatic geological modelling to derive a dynamic prior model term at each iteration of the inversion to limit departures from geologically feasible outcomes. We introduce the main theoretical aspects of the inversion algorithm and perform the proof of concept using two synthetic studies. The analysis of the results using indicators measuring geophysical, petrophysical, and structural geological misfits demonstrates that our approach effectively steers the inversion towards geologically consistent models and reduces the risk of geologically unrealistic outcomes. Results suggest that the geological correction may be effectively applied to pre-existing geophysical models to increase their geological realism and that it can also be used to explore geophysically equivalent models.