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A model is developed to test the hypothesis that kimberlites can form by low-degree melting of asthenospheric mantle followed by entrainment and assimilation of lithospheric mantle. The developed model uses inversion calculations based upon rare earth and compatible trace elements. For kimberlites (s.s.), an equation describing mass balance between a melt of unknown composition and a contaminant end-member of xenocrystic/assimilated material from the lithospheric mantle is inverted. This allows calculation of the mass fraction of xenocrystic minerals from the lithospheric mantle (olivine, orthopyroxene, clinopyroxene, garnet, ilmenite) entrained in the kimberlitic magma, as well as the source mineralogy and melt degree in the source region. The composition of the parental melt prior to interaction with the lithosphere is not assumed a priori but is calculated by the model. The CO2, H2O, K2O and P2O5 contents of the source are estimated assuming batch melting and the inversion models. The range and coupling of the model parameters are found using a non-linear most-squares inversion procedure, and the model space is visualised using a Self-Organising Map approach. Our earlier work supporting assimilation of xenocrystic opx is, however, not a precondition but provides a post-processing constraint , as well as the selection of a more likely set of solutions from the Self-Organising Map. The calculation is applied to a data set from the Majuagaa kimberlite dyke (southern West Greenland) including added whole rock analyses for CO2 and H2O. Major variations in whole rock compositions are related to flow differentiation of olivine macrocrysts. The textures of opx, cpx, gt and ilm megacrysts show evidence for reaction with the transporting melt and physical erosion in the kimberlitic mush. Using the bulk rocks in our inversion scheme results in a silico-carbonatite parental melt with major element concentrations consistent with experimental melts. The ol, opx, and cpx mass fractions in the source are not well-resolved by this calculation, but the proportion of gt in the source is comparatively well defined at 15–22 wt% and cpx is constrained to less than 14 wt%. The source assemblage required is 36–80 wt% ol, 2–49 wt% opx, 0–6 wt% cpx, and 15–19 wt% gt. This suggests a peridotitic rather than an eclogitic source. The inversion model gives an overall mass fraction of xenocrystic material in the Majuagaa kimberlite magma of 41–51 wt% The mass fractions of the xenocryst phases are as follows: 71–85 wt% ol, 0–13 wt% opx, 5 ± 1 wt% gt, and 10–14 wt% ilm. There is less than 3 wt% cpx in the xenocrystic and assimilated assemblage. These results agree with petrographic observations. Processing the model results using the Self-Organising Map clearly displays the extent and coupling within the statistically acceptable region of the model space and leads us to a preferred model of 49 wt% xenocrysts with a xenocryst assemblage of 71–76 wt% ol, 8–13 wt% opx, 4 wt% gt and 12 wt% ilm. A source with a REE pattern similar to that of primitive mantle is sufficient to form the parental melt and consistent with generation of the initial kimberlite melt in the convecting mantle. Calculated CO2 and H2O concentrations in the source of the Majuagaa kimberlite of 230–860 μg/g and 223–741 μg/g, respectively, are within the range of independent convecting mantle estimates. This is equivalent to <0.17 wt% magnesite and the H2O budget of the mantle source can be accommodated via storage in nominally anhydrous silicate phases. When applied to Majuagaa kimberlite, the inversions are consistent with a conceptually simple model of kimberlite formation: (1) low degree melting in carbonated asthenospheric peridotite, (2) melt extraction and concentration, and (3) entrainment and reaction with lithospheric mantle material. [ABSTRACT FROM AUTHOR]