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A strong, repeatable seasonal cycle in the background methane mixing ratio has been observed at the Gale Crater landing site of the Mars Science Laboratory rover with the Tunable Laser Spectrometer of the Sample Analysis at Mars instrument. However, as of yet, no physical process has been proposed that can explain both the timing and amplitude of the observations. Here we show that a one-dimensional numerical model considering adsorption onto and diffusion through the regolith can reproduce the variation, including a phase lag, if the regolith is impregnated with methane from a prior plume or supplied from below by microseepage. Combining the model results with geological constraints, we estimate that the amount of microseepage at Gale is at most 3 x10(-5)tonnes km(-2) yr(-1). Gale's unique dynamical environment makes such seeps easier to detect in surface sampling measurements. Over most of the Martian surface, atmospheric mixing is stronger or atmospheric transport more effective, and we expect the amplitude of the seasonal cycle to be smaller for the same strength of seep.