It's believed that vertical motion is needed to trigger tsunamis - a sudden vertical displacement of the sea floor caused by an earthquake or a landslide. In fact, since most of the faults along coastal California have rock strata that move horizontally with respect to each other, earthquakes that occur there rarely generate tsunamis. By the way, tsunamis consist of a series of waves that have varying wave heights and not just one huge mass of water. Damage from tsunamis is usually greatest where the continental slopes are steepest. Their wave height drastically increases when they move onto shore, and if the slope is closer to the shore, the wave will be larger.
Tsunamis can travel thousands of miles with little loss of energy.
For tsunamis produced by earthquakes, the depth of the water and the steepness of the offshore slope is more of a factor in influencing the tsunamis's magnitude than is the distance of the epicenter to the coast. A major concern with tsunamis caused by landslides is that there's very little warning. In 1998, a tsunami thought to be caused by a landslide killed over 2,000 people in Papua, New Guinea. Water from such a wave could also push up the Chesapeake Bay, inundating low-lying areas. A pretty scary proposition, but surfers would have it made.