WASHINGTON — The rate of earthquakes in Oklahoma has dropped dramatically since late May, when the state limited wastewater injections into energy wells, an Associated Press statistical analysis shows. And a new scientific study says the state is on its way back to calmer times that prevailed before a huge jump in man-made quakes.

For quake-prone parts of Oklahoma, the state ordered what is essentially a 40 percent reduction in injection of the saltwater that scientists generally blame for the massive increase in earthquakes. This year, before the new rules went into effect on May 28, Oklahoma averaged 2.3 quakes a day. Since then the average dropped to 1.3 a day, based on AP's analysis of U.S. Geological Survey data of earthquakes of magnitude 3.0 or larger. But some of those fewer post-regulatory quakes have been large and damaging.

"Definitely the rate of quakes have gone down," said USGS geophysicist Robert Williams. "At the same time, we had more magnitude 5s this year than ever before historically in Oklahoma. It's good news on one hand. It's heading in the right direction, but troubling to see these large damaging quakes in Pawnee and Cushing."

Over the last couple years, scientists have linked a dramatic increase in earthquakes in Oklahoma, Kansas and Texas to the practice of injecting wastewater from hydraulic fracturing, or fracking, back underground after drilling for oil and gas. Higher volumes of wastewater injected are connected to more quakes with the fluids adding more pressure to tiny faults. After Kansas regulated wastewater volume in March 2015, a January AP analysis showed that Kansas felt fewer quakes, while less-regulated Oklahoma got more. In response, Oklahoma announced new regulations.