Advances in trace gas analysis allow localised, non-atmospheric features to be resolved in ice cores, superimposed on the coherent atmospheric signal. These high-frequency signals could not have survived the low-pass filter effect that gas diffusion in the firn exerts on the atmospheric history and therefore do not result from changes in the atmospheric composition at the ice sheet surface. Using continuous methane (CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$) records obtained from five polar ice cores, we characterise these non-atmospheric signals and explore their origin. Isolated samples, enriched in CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ in the Tunu13 (Greenland) record are linked to the presence of melt layers. Melting can enrich the methane concentration due to a solubility effect, but we find that an additional in situ process is required to generate the full magnitude of these anomalies. Furthermore, in all the ice cores studied there is evidence of reproducible, decimetre-scale CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ variability. Through a series of tests, we demonstrate that this is an artifact of layered bubble trapping in a heterogeneous-density firn column; we use the term "trapping signal" for this phenomenon. The peak-to-peak amplitude of the trapping signal is typically 5 ppb, but may exceed 40 ppb. Signal magnitude increases with atmospheric CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ growth rate and seasonal density contrast, and decreases with accumulation rate. Significant annual periodicity is present in the CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ variability of two Greenland ice cores, suggesting that layered gas trapping at these sites is controlled by regular, seasonal variations in the physical properties of the firn. Future analytical campaigns should anticipate high-frequency artifacts at high-melt ice core sites or during time periods with high atmospheric CH$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ growth rate in order to avoid misinterpretation of such features as past changes in atmospheric composition.