Reflectance spectra of olivines spanning the forsterite-fayalite solid-solution series have been analyzed with the modified Gaussian model (MGM). The compositional variability of the three primary absorption bands that constitute the diagnostic 10-μm olivine feature has been quantified by examining the centers, widths, and relative strengths in 18 spectra ranging in composition from Mg-rich forsterite to Fe-rich fayalite. These analyses have also revealed several interrelationships among the three absorption bands that provide new insights into their crystallographic origins. The primary olivine absorptions near 1.0-μm are well behaved and provide a means to remotely identify and estimate the composition of olivine from reflectance spectra. However, the spectral resolution and signal-to-noise of current remotely acquired data, combined with the significant overlap in the 1.0-μm region, provide enough uncertainty to allow models based on simple least squares minimization to reach solutions that are mathematically satisfying yet physically unrealistic. More sophisticated models using inverse theory that incorporate constraints among the absorption bands as determined from these laboratory MGM analysis are shown to yield meaningful results which can be confidently used to estimate composition in remote data. The MGM and inverse theory are used to analyze the spectrum of the olivine-rich asteroid 246 Asporina and to quantitatively show that the olivine component on Asporina is magnesium-rich (i.e., forsteritic). In contrast to the systematic behavior of the three primary olivine absorptions, absorption features short of 0.7 μm are found to exhibit no obvious relationship to composition and as such are not recommended for use in remote applications.