Seifert matrices of cable knots
A formula for the Seifert matrix of an arbitrary satellite can be found in the proof of Theorem 6.15 of Lickorish's "An introduction to knot theory".
It also appeared in the article of H. Seifert as Theorem II:
Seifert, H. (1950). On the homology invariants of knots. The Quarterly Journal of Mathematics, 1(1), 23-32.