D.5 Synthesis, Evaluation, and Skills

The primary hazard is the earthquake itself. For a tsunami to be generated, the critical link is vertical displacement of the seafloor, which pushes the overlying water column upward, setting long-wavelength waves in motion.

Tsunamigenic earthquakes require a magnitude of roughly M 7.0+, a dip-slip (vertical) fault motion, and a shallow epicentre beneath or near the ocean. Strike-slip faults displace rock horizontally and rarely generate significant tsunamis.

In deep water the waves travel at high speed ($v=\sqrt{gd}$) with low amplitude; as they enter shallow coastal water, speed decreases and wave height amplifies dramatically, causing coastal inundation.

The correct sequence moves from ground shaking → vertical seafloor displacement → tsunami radiating across the ocean → coastal inundation and destruction of infrastructure, exactly matching the subduction-zone mechanism described.

The question asks for the physically accurate cascade sequence following a subduction-zone megathrust earthquake, requiring knowledge of which type of fault motion generates a tsunami.

'Ground shaking → strike-slip horizontal fault motion → tsunami' is incorrect because strike-slip motion displaces rock horizontally, not vertically, so it does not displace the water column and rarely generates a significant tsunami.

'Ground shaking → volcanic eruption → lahar' is incorrect because an earthquake does not directly trigger a volcanic eruption as the immediate next step in a tsunami cascade; this conflates two separate hazard chains.

'Ground shaking → soil liquefaction → submarine landslide → storm surge' confuses a storm surge (a meteorological phenomenon) with a tsunami; a submarine landslide can trigger a tsunami but the chain as stated is physically inaccurate in labelling the final wave.

'Ground shaking → vertical seafloor displacement → tsunami → coastal inundation and infrastructure destruction' is the only sequence that correctly identifies vertical dip-slip displacement as the mechanism linking the earthquake to tsunami generation.

Wave speed $v\approx 700$ km/h. Converting: $v=700\times 0.278\approx 194.6$ m/s. The formula is $v=\sqrt{gd}$, where $g=9.8$ m/s².

Squaring both sides: $v^2=gd$, so $d=\frac{v^2}{g}=\frac{(194.6{)}^2}{9.8}=\frac{37,849}{9.8}\approx 3,862$ m.

A depth of approximately 3,800 m is consistent with average open-ocean depth in the Pacific, confirming that tsunami waves travel at very high speeds in deep water and slow dramatically as $d$ decreases near the coast.

The calculated depth of ~3,800 m matches the answer 'Approximately 3,800 m', which aligns with typical Pacific abyssal plain depths.

We need $d=v^2/g$ with $v\approx 195$ m/s and $g=9.8$ m/s², giving approximately $195^2/9.8\approx 3,880$ m.

At 1,200 m depth: $v=\sqrt{9.8\times 1200}=\sqrt{11760}\approx 108$ m/s $\approx 390$ km/h — far slower than 700 km/h, so this depth is too shallow.

At 7,500 m: $v=\sqrt{9.8\times 7500}=\sqrt{73500}\approx 271$ m/s $\approx 975$ km/h — faster than 700 km/h, so this depth is too great.

At 500 m: $v=\sqrt{9.8\times 500}=\sqrt{4900}=70$ m/s $\approx 252$ km/h — far too slow, ruling this out.

Only approximately 3,800 m produces a wave speed consistent with 700 km/h, matching the deep-ocean conditions in which the Tōhoku tsunami travelled.