Seifert matrix for the unknot

Question

I am a little bit confused about the Seifert matrix for the unknot. A Seifert surface for this knot it surely $F=\mathbb{D}^2$. If a chose a generator $a$ of $H_1(F)$ and I denote $a^+$ the push-out of a out of $F$, then I get $\text{lk}(a,a^+)=0$. So the Seifert matrix should be the zero matrix, but then the Alexander polynomial would be $\det (t 0-0^T)=0$, but it should be $1$.