若函数 $f(x)=\sqrt{\frac{1}{2} x+a^2}+\sqrt{x^2-1}-x$ 有零点, 则 $a$ 的取值范围是
A. $\left[-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right]$
B. $\left(-\infty,-\frac{\sqrt{2}}{2}\right) \cup\left(\frac{\sqrt{2}}{2},+\infty\right)$
C. $\left(0, \frac{1}{2}\right)$
D. $\left(\frac{1}{2},+\infty\right)$