The Australian Greens will explore avenues to appeal a decision allowing seismic testing off the coast of Kangaroo Island.

The application by Canadian company Bight Petroleum to conduct seismic testing as a precursor to oil and gas drilling has been approved by NOPSEMA, despite strong community opposition.

Australian Greens Senator for South Australia Penny Wright said she would explore avenues for appeal when further documents are released.

South Australian Greens Senators Sarah Hanson-Young and Penny Wright have slammed the Coalition's first budget, which slugs SA families while letting big business off the hook.

"This is a brutal budget by a cruel Coalition," Senator Wright said.

"Not only has Education Minister Christopher Pyne turned his back on SA school students by ripping the heart out of the Gonski reforms, he wants to make it harder and more expensive to go to university.