Ocean bottom seismometer observations at 5000 m depth during the long-range ocean acoustic propagation experiment in the North Pacific in 2004 show robust, coherent, late arrivals that are not readily explained by ocean acoustic propagation models. These "deep seafloor" arrivals are the largest amplitude arrivals on the vertical particle velocity channel for ranges from 500 to 3200 km. The travel times for six (of 16 observed) deep seafloor arrivals correspond to the sea surface reflection of an out-of-plane diffraction from a seamount that protrudes to about 4100 m depth and is about 18 km from the receivers. This out-of-plane bottom-diffracted surface-reflected energy is observed on the deep vertical line array about 35 dB below the peak amplitude arrivals and was previously misinterpreted as in-plane bottom-reflected surface-reflected energy. The structure of these arrivals from 500 to 3200 km range is remarkably robust. The bottom-diffracted surface-reflected mechanism provides a means for acoustic signals and noise from distant sources to appear with significant strength on the deep seafloor.