North American oil services are in decline, with rigs and permits falling in fourth-quarter 2012, a sign to some that the industry may have bottomed out.

Rig counts dropped 15% year over year across the legacy shales, such as the Barnett and for Eagle Ford gas. Most prominent was a 37% freefall in the Woodford, said Scott Gruber, senior research analyst, U.S. oil services and equipment, for Sanford C. Bernstein & Co.

Still, 2013 is shaping up as a year of moderate growth in global exploration and production spending, according ...