Oilfield wastewater disposal causes fluid pressure transients that induce earthquakes. Here we show that, in addition to pressure transients related to pumping, there are pressure transients caused by density differences between the wastewater and host rock fluids. In northern Oklahoma, this effect caused earthquakes to migrate downward at ~0.5 km per year during a period of high-rate injections. Following substantial injection rate reductions, the downward earthquake migration rate slowed to ~0.1 km per year. Our model of this scenario shows that the density-driven pressure front migrates downward at comparable rates. This effect may locally increase fluid pressure below injection wells for 10+ years after substantial injection rate reductions. We also show that in north-central Oklahoma the relative proportion of high-magnitude earthquakes increases at 8+ km depth. Thus, our study implies that, following injection rate reductions, the frequency of high-magnitude earthquakes may decay more slowly than the overall earthquake rate.