The correct answer is A) Secure the engine and water wash the compressor off-line. The reasoning is that a slow but steady increase in gas turbine vibration and specific fuel consumption indicates a buildup of deposits on the compressor blades, which reduces the engine's efficiency. To correct this, the best maintenance technique is to shut down the engine and perform an off-line water wash of the compressor. This will remove the deposits and restore the engine's performance. The other options are incorrect because: B) Increasing the Variable Stator Vane setting would not address the root cause of the problem, C) water washing the power turbine would not affect the compressor deposits, and D) increasing the gas generator RPM would not fix the underlying issue and could potentially further stress the engine.