Seismic observations involve signals that can be easily masked by noise injection. For InSight, NASA's lander on Mars, the atmosphere is a significant noise contributor for two thirds of a Martian day, and while the noise is below that seen at even the quietest sites on Earth, the amplitude of seismic signals on Mars is also considerably lower requiring an understanding and quantification of environmental injection at unprecedented levels. Mars' ground and atmosphere provide a continuous coupled seismic system, and although atmospheric functions are of distinct origins, the superposition of these noise contributions is poorly understood, making separation a challenging task. We present a novel method for partitioning the observed signal into seismic and environmental contributions. Pressure and wind fluctuations are shown to exhibit temporal cross-frequency coupling across multiple bands, injecting noise that is neither random nor coherent. We investigate this through comodulation, quantifying the signal synchrony in seismic motion, wind and pressure. By working in the time-frequency domain, we discriminate the origins of underlying processes and provide the site's environmental sensitivity. Our method aims to create a virtual vault at InSight, shielding the seismometers with effective post-processing in lieu of a physical vault. This allows us to describe the environmental and seismic signals over a sequence of sols, to quantify the wind and pressure injection, and estimate the seismic content of possible Marsquakes with a signal-to-noise ratio that can be quantified in terms of environmental independence. Finally, we exploit the temporal energy correlations for source attribution of our observations.