SUMMARY The ongoing InSight mission has recently deployed very broad band seismometers to record the Martian seismic activity. These recordings constitute the first seismic data set collected at the surface of Mars. This unique but sparse record compels for the development of new techniques tailored to make the best use of the specific context of single station-multiple events with several possible ranges of uncertainties on the event location. To this end, we conducted sets of Markov chain Monte Carlo inversions for the 1-D seismic structure of Mars. We compared two inversion techniques that differ from the nature of the parametrization on which they rely. A first classical approach based on a parametrization of the 1-D seismic profile using Bézier curves. A second, less conventional approach that relies on a parametrization in terms of quantities that influence the thermochemical evolution of the planet (mantle rheology, initial thermal state and composition), which accounts for 4.5 Gyr of planetary evolution. We considered several combinations of true model parameters to retrieve, and explored the influence of the type of seismic data (body waves with or without surface waves), the number of events and their associated epicentral distances and uncertainties, and the presence of potential constraints on Moho depth inferred from independent measurements/considerations (receiver functions and gravity data). We show that due to its inherent tighter constraints the coupled approach allows a considerably better retrieval of Moho depth and the seismic structure underneath it than the classical inversion, under the condition that the physical assumptions made in the coupled approach are valid for Mars. In addition, our tests indicate that in order to constrain the seismic structure of Mars with InSight data, the following independent conditions must be met: (1) The presence of surface waves triggered by an internal source to constrain the epicentral distance. (2) The presence of just a few well-localized impact sources, with at least one located at close epicentral distance (<5°) to illuminate independently the crust and the mantle. In addition to providing tighter constraints of Mars seismic structure, geodynamically constrained inversions allow one to reconstruct the thermochemical and rheological history of Mars until present. Therefore, even with a relatively small amount of large events and in absence of surface waves, constraining the present-day structure and long-term evolution of the red planet remains possible through the use of tailored hybrid inversion schemes.