HR outside the cavity, we subtract the moving average $\bar\Psi$. using the procedure described in Sec. \[sec:smoothing0\]. $\bar\Psi$ approximates the dominant, slowly-varying background \[with $k\sim0$ as in Fig. \[fig:exp\](b)\]. We choose the smoothing window $D_s=5.4\ \mu$m, such that it is large enough so that $\bar\Psi\approx0$ between the horizons, yet small enough to capture the slow variations of the background outside the horizon.

The portrait displays an interference pattern between the background supersonic flow and excited modes of $\delta\Psi$. The evolution of the BH is indicated by the diagonal orange (right) line. To clearly display HR upstream of the horizon, we have multiplied $|\delta\Psi|$ there by a factor of 10. At the beginning of the evolution, as the condensate spills over the step, a left-moving flow develops, indicated by the growing light gray area. When this flow reaches the WH, at $t\approx 10$ ms, a standing wave (BCR) is generated. In Fig. \[fig:stimulated\_HR\](b), it is clear by inspection of the dashed red line and solid red (left) line \[which is parallel to diagonal orange (right) line\] that the standing wave has zero frequency in the WH rest frame, but nonzero frequency in the BH rest frame. Since its frequency is nonzero 