Atmospherically corrected thermal infrared spectra of large regions of the Martian surface from the Mars Global Surveyor Thermal Emission Spectrometer (MGS TES) previously have been interpreted to represent two general spectral classes. One class represents a basalt to basaltic andesite composition, and the other class represents a basaltic andesite to andesite composition. We have performed new linear deconvolutions of the two Martian surface type spectra with an end-member set tailored to represent volcanic rock types. Our preparatory study of laboratory spectra of terrestrial volcanic rocks (acquired at 2 cm-1 sampling), convolved to TES spectral sampling (10 cm-1), shows little degradation in deconvolution results when compared to results acquired using the higher spectral resolution data, indicating that the deconvolution technique is valid for analyzing data at TES resolution. Our spectral fits to the Martian data agree well with previous models and do not exhibit any notable deviations from the Martian spectra that would indicate the absence of any significant end-members in our model. Modal mineralogies obtained with these new spectral fits also compare favorably (within the previously stated uncertainties) to prior results. The newly derived modal mineralogies are used with new and traditional classification schemes for volcanic igneous rocks (introduced in a companion paper <Wyatt et al., this issue>) to classify the Martian compositions. Our results substantiate the previously proposed hypothesis that these two spectral classes on the Martian surface represent volcanic compositions with distinguishable differences in silica content ranging from basalt to andesite. ¿ 2001 American Geophysical Union