The correct answer is $\frac{{3{\text{H}}}}{{4\pi }}$ below the water surface.
The hydrodynamic pressure due to an earthquake is caused by the sudden movement of the earth’s crust. This movement causes the water in the ocean to move, creating waves. The height of the waves depends on the magnitude of the earthquake and the distance from the epicenter.
The hydrodynamic pressure is greatest at the surface of the water and decreases with depth. The pressure is also greatest at the epicenter of the earthquake and decreases with distance from the epicenter.
The equation for the hydrodynamic pressure due to an earthquake is:
$$P = \frac{{3{\text{H}}}}{{4\pi }}g\sin \theta$$
where:
- $P$ is the hydrodynamic pressure
- $H$ is the depth of water
- $g$ is the acceleration due to gravity
- $\theta$ is the angle between the water surface and the direction of the earthquake
The hydrodynamic pressure acts at a height of $\frac{{3{\text{H}}}}{{4\pi }}$ below the water surface. This is because the pressure is greatest at the surface of the water and decreases with depth.
The other options are incorrect because they do not take into account the depth of water.