Final answer:
A submarine slide at a continental shelf can create a tsunami primarily through the sudden vertical displacement of water caused by either the upward movement (option B) or the sudden drop (option C) of the seafloor at the shelf's edge.
Step-by-step explanation:
A submarine slide at the edge of a continental shelf can create a tsunami due to a combination of actions. To clarify the points listed, option A suggests that water is displaced into a bulge by the advancing debris, which could push water mass in a wave-like manner, but this by itself is unlikely to cause a large tsunami unless accompanied by significant vertical displacement. Option B refers to the upward shifting of earth's material at the shelf's edge, which can displace water and generate a tsunami. Option C considers the sudden drop of the seafloor when material breaks away from the continental shelf, displacing water above and triggering a tsunami. Option D involves deeper regions where the settling of the ocean floor under the weight of incoming sediment could contribute to a tsunami, depending on the scale and suddenness of the event. Lastly, option E implies that the shelf rebounds when mass is released from its edge, potentially displacing water to initiate a tsunami.
Given the information and the understanding that tsunamis are often caused by sudden, significant vertical displacements of the ocean floor, the most likely scenarios in which a submarine slide could generate a tsunami would be options B, 'the upward displacement of the edge of the continental shelf', and C, 'the sudden drop of the seafloor as the mass of material breaks off the continental shelf'. Both of these actions would result in the abrupt vertical displacement of water needed to produce a tsunami.