A machine S/N would be a good start. There are a few procedures kicking around but knowing the boom type (mass, reach, etc) would help to narrow down the field a bit..
Is the crack located as shown by the area marked "1" on the drawing below..?
Without looking too deeply into it my suspicion is that in order to do a decent repair job: -
a) The boom will have to come off so it can be rotated - no vertical or overhead welding.
b) The boom box structure will need opening up so that the weld roots can be back-gouged and welded up with no possibility of leaving residual root cracks. Spendy but Eutectic Xuper Nucleotec 2222 electrodes are the dog's bollox for repairs like this. The weld has an eleongation spec of something like 50%.