Method, source array and source element that generate seismic waves. The source element includes an enclosure having an opening covered by a piston; a local supply accumulator fluidly communicating with an interior of the enclosure, a pressure of the fluid inside the local supply accumulator being larger than a pressure of the fluid inside the enclosure; a local supply valve located between the local supply accumulator and the enclosure and configured to control a flow of the fluid from the local supply accumulator to the interior of the enclosure; and a controller configured to control the local supply valve such that the pressure inside the enclosure does not fall below a first preset value based upon an ambient pressure of the enclosure while seismic waves are generated.