The Raman Maturity Method (RaMM) is a non-graphical technique for thermal maturity determination based on the multi-linear regression analysis of parameters derived from carbon Raman spectra of humic macerals. It is calibrated against vitrinite reflectance with a suite of Australian mostly Permian coals. In a previous communication an equation to cover the range 0.4-1.2% equivalent vitrinite reflectance was derived. In this report we extend the range with a second equation for the range 1.0-2.5%, and validate its use by testing a series of Australian Permian and German Carboniferous coals. The special features of the technique are that it is equally applicable to vitrinite and inertinite, it corrects internally for the suppression of vitrinite reflectance effect, grains as small as 5 mu m are suitable, and it does not require well depth information to be available. The technique has been applied to two wells, Cape Range-2 and Dampier-1, from the rift margin of the North West Shelf of Australia. Both wells intersect large thicknesses of fine-grained marine Jurassic and Cretaceous sediments including the major source rock formation of the Carnarvon Basin. There are no terrestrial sediments for control. There is good agreement between RaMM and VR results for VR > 12% for Cape Range-2. However within the oil window in both wells RaMM results indicate the vitrinites in many of the samples have reflectance suppression to such a degree that the VR results would be misleading or useless for maturity modeling. It is likely that this problem, which is well documented for marine influenced coals, to some degree affects organic matter in marine source rocks worldwide. (C) 2015 Elsevier B.V. All rights reserved.