Judging by the size of the holes, voles (field mice) are likely to be the critters to trap.  Fortunately, voles can be managed with mouse traps for as long as you want to continue. Voles usually take the easy way out when seeking a home burrow; they locate and re-use those that have been abandoned.

Voles are especially prolific. “Voles can reproduce year-round, with a peak breeding period in the spring followed by a second, smaller breeding period in the fall. Females can reach reproductive maturity in 35 to 40 days. They average one to five litters per year, with three to six young per litter. Gestation length is approximately 21 days.” (Meadow Voles and Pocket Gophers: Management in Lawns, Gardens, and Croplands - http://www.cals.uidaho.edu/edComm/pdf/PNW/PNW0627.pdf)

See “Vole management in home backyards and gardens” (http://cru.cahe.wsu.edu/CEPublications/FS094E/FS094E.pdf). “What is Tunneling in My Yard?” may also be useful to you: http://cru.cahe.wsu.edu/CEPublications/FS143E/FS143E.pdf