Hyperspectral RS to identify active faults is not the most convenient method, unless the fault trace influences the overlying / covering vegetation and / or soil composition (e.g. higher water content that should be detectable, different mineral composition - mylonites). Even then, one still has to ask if this due to recent fault activity or just because of the presence of a (paleo)fault.
Other methods in optical and NIR RS are based on identifying active faults on geomorphological criteria.
Much better however is to use SAR radar interferometry (inSAR).