A seismic source signal generator includes a mass, a primary accumulator and a . secondary accumulator, the secondary accumulator having an internal volume smaller than an internal volume of the primary accumulator. A method for generating a signal using a seismic vibrator includes operating the seismic vibrator using hydraulic fluid, damping hydraulic pressure deviations in the hydraulic fluid using a first accumulator in hydraulic communication with the hydraulic fluid, and damping pressure deviations in the hydraulic fluid using a second accumulator in hydraulic communication with the hydraulic fluid, the second accumulator having an internal volume smaller than an internal volume of the first accumulator.