4M method vMAX – form (script) «
4M-BASE – all versions (→ illustrations)
Using the form (script) below, you can calculate the Mahalanobis distances (dM) and the level of similarity (Scluster) for an unknown meteorite using the 4M method. So make a classification – what type is it – H, L or LL! (For more details on the interpretation of the results (levels of similarity) see → Footnotes)
Enter the percentage values of the spectral areas obtained from Mössbauer spectroscopy in the text boxes below:
ol – value for olivine;
pyr – value for pyroxene;
met – cumulative value for the metallic phase (kamacite+taenite+tetrataenite);
tr – cumulative value for the sulfide phase (troilite+pyrrhotite).
(The script is based on the R statistics package installed on the server)
Meteorite is assigned to the type for which the level of similarity (Scluster) value is the highest! (BASE-vmax)
The results of the next calculations will be displayed here...
*————
A t t e n t i o n [-1]: The result is unreliable! A small maximum level of similarity (<20%) – perhaps: the specimen is heavily weathered / breccia / chondrite unequilibrated / incorrectly fitting results?!
A t t e n t i o n [-2]: The result is inconclusive! Difference in levels of similarity too small (<12,5%), the results lie „on the border” between two different types – perhaps: it is an intermediate type chondrite: H/L, L/LL or breccia?!
A t t e n t i o n [-3]: Unbelievable result! The maximum level of similarity is too low (<5%) – perhaps: value error / bad, incorrectly prepared sample / incorrect fit of the results / it's not chondrite...?!
A t t e n t i o n [-4]: Incorrect data!?! Not everything is ordinary chondrite 
(<1%)
A t t e n t i o n [∞]: BINGO! You've come in the center of cluster – such a high level of similarity (>99%) does not guarantee certainty
Abstract
The 4M method aims to determine the type of equilibrated ordinary chondrite only on the basis of the Mössbauer spectrum of the investigated meteorite. Mössbauer spectrum of non-weathered ordinary chondrite is comprised of four sub-spectra: two doublets and two sextets. One of the doublets consists of a signal from iron present in olivine and the other consists of a signal from iron present in pyroxene. Sextets on the other hand, contain signals from magnetically ordered iron. One sextet is related to the metallic phase (kamacite, taenite), whereas the second is related to troilite. A third of doublets, which emerges in weathered ordinary chondrites, is related to products of the oxidation of iron present in metallic phase. The spectral areas of olivine, pyroxenes, metallic phase and troilite, which were obtained from Mössbauer spectrum are proportional to the number of iron atoms present in relevant mineral phases. Some Mössbauer groups were inspired by this fact to construct different methods to determine the type (H, L, or LL) of investigated meteorites (Ga³¹zka-Friedman et al. 2019, Hyp. Inter. 241(1)). However, these methods, based on subjective criteria, were only qualitative. Our group elaborated a quantitative method, which is based on objective criteria. We called it the "4M method" (where M are derived from meteorites, Mössbauer spectroscopy, multidimensional discriminant analysis (MDA), Mahalanobis distance) (WoŸniak et al. 2019, MaPS).
This method was using only the Mössbauer experimental data, to which it applied advanced statistical methods. The base, which was created from Mössbauer data, consisted of three clusters H, L, LL. These clusters were constructed with sets of 4-dimensional vectors. The vectors are comprised of spectral areas of Mössbauer spectrum: ol (value proportional to iron present in olivine), pyr (value proportional to iron present in pyroxene), met (value proportional to iron present in metallic phase), tr (value proportional to iron present in troilite). To determine the type of investigated ordinary chondrite, its ol, pyr, met and tr values with average values of variables obtained for clusters H, L and LL need to be compared. The comparison can be performed with the use of MDA and Mahalanobis distance. Once Mahalanobis distance (dM) of the investigated meteoriteis is known, the level of similarity (Scluster) to three types of ordinary chondrites can be calculated.
Examples of such calculations were performed for seven ordinary chondrites: Goronyo, Carancas, New Concord, NWA 7733, Leoncin, So³tmany and Pu³tusk. They were made with the use of the new base composed of non-weathered ordinary chondrites. All results obtained with the 4M method yielded results consistent with traditional mineralogical methods.
Acknowledgments
We thank the author of the scripts, Janusz "Johnson" Lemañski. Without his knowledge and commitment, this website would not be created. We appreciate his patience and understanding for our whining, vague expectations and "lame" problems ;-)