What decides whether a fault slips slowly or in earthquakes?
In plain words
Some faults release stress in slow slip events lasting days to months, with faint tremor instead of shaking. What property of a fault makes its slip slow instead of fast is not established.
Precise statement
Slow slip events and tectonic tremor at subduction zones move at slip rates of order $1e-6 \text{ to } 1e-5\,\mathrm{cm/s}$, roughly $10 \text{ to } 100$ times the plate rate and about $1e7 \text{ to } 1e8$ times slower than earthquake slip (near $1e2\,\mathrm{cm/s}$). Identify the physical control: near-neutral rate-and-state frictional stability ($a - b \text{ near } 0$) with high pore-fluid pressure, dilatancy strengthening, mixed frictional-viscous rheology, or fault-zone heterogeneity, and whether and when slow slip triggers large earthquakes. An answer is a constitutive model, tested against laboratory data, that reproduces the observed moment-duration scaling, recurrence and tremor of slow slip (review: Burgmann, EPSL 2018, https://doi.org/10.1016/j.epsl.2018.04.062).
What would settle it
Laboratory friction experiments on natural fault-zone materials under in situ fluid pressure that reproduce slow slip, matched to geodetic and tremor catalogs.