Waves (such as EM waves) imply the change in some field, which is what they are trying to detect. After all, we already detect gravitational fields - after all,

Waves (such as EM waves) imply the change in some field, which is what they are trying to detect. After all, we already detect gravitational fields - after all, we are standing on the earth - what they're trying to detect are very specific changes to gravitational fields, thus waves.