  Subsurface sandstone reservoirs sealed by overlying, low-permeability layers
provide capacity for long-term sequestration of anthropogenic waste. Leakage
can occur if reservoir pressures rise sufficiently to fracture the seal. Such
pressures can be generated within the reservoir by vigorous injection of waste
or, over thousands of years, by natural processes. In either case, the precise
role of intercalated mudstones in the long-term evolution of reservoir pressure
remains unclear; these layers have variously been viewed as seals, as pressure
sinks or as pressure sources. Here, we use the geological record of episodic
fluid venting in the Levant Basin to provide striking evidence for the
pressure-source hypothesis. We use a Bayesian framework to combine recently
published venting data, which record critical subsurface pressures since
$\sim$2~Ma, with a stochastic model of pressure evolution to infer a
pressure-recharge rate of $\sim$30~MPa/Myr. To explain this large rate, we
quantify and compare a range of candidate mechanisms. We find that poroelastic
pressure diffusion from mudstones provides the most plausible explanation for
these observations, amplifying the $\sim$3~MPa/Myr recharge caused primarily by
tectonic compression. Since pressurised mudstones are ubiquitous in sedimentary
basins, pressure diffusion from mudstones is likely to promote seal failure
globally.
