Instead of quoting the 503-rule directly, derive it from the physics of EM diffusion and then solve.
Step 1: Skin depth from Maxwell's equations.
For a plane wave diffusing into a conductor, \(\delta = \sqrt{\dfrac{2\rho}{\omega \mu_0}}\), with \(\omega = 2\pi f\) and \(\mu_0 = 4\pi\times10^{-7}\) H/m (Earth materials are essentially non-magnetic, \(\mu_r \approx 1\)).
Step 2: Simplify.
\(\delta = \sqrt{\dfrac{2\rho}{2\pi f \times 4\pi\times10^{-7}}} = \sqrt{\dfrac{\rho \times 10^{7}}{4\pi^2 f}} = \dfrac{1}{2\pi}\sqrt{10^7}\sqrt{\rho/f} \approx 503\sqrt{\rho/f}\), recovering the same rule-of-thumb constant used above.
Step 3: Solve numerically.
\(400 = 503\sqrt{\rho/1000} \Rightarrow \rho = 1000\times(400/503)^2 \approx 632\ \Omega\text{m}\), consistent with the accepted range \(\boxed{630\ \text{to}\ 640\ \Omega\text{m}}\).