Total derivative along a ray
= Total derivative along a ray
Along a ray $\mathbf x(t)$, the derivative of a field $f(\mathbf x,t)$ is
$$
\frac{df}{dt}
=\frac{\partial f}{\partial t}
+\dot{\mathbf x}\cdot\nabla f.
$$
= Total derivative along a ray
Along a ray $\mathbf x(t)$, the derivative of a field $f(\mathbf x,t)$ is
$$
\frac{df}{dt}
=\frac{\partial f}{\partial t}
+\dot{\mathbf x}\cdot\nabla f.
$$