Earthquakes below the Yellowstone caldera originate at very shallow depths,
about 4 kilometers on average. Below this depth, the rocks are at least
\(400^{\circ} \mathrm{C},\) too hot and weak to store elastic energy. Based on
this data, answer the following questions:
a. What is the minimum geothermal gradient in the first 4 kilometers beneath
the Yellowstone caldera, assuming an average surface temperature of \(0^{\circ}
\mathrm{C}\left(32^{\circ} \mathrm{F}\right) ?\)
b. At about what depth is the groundwater below the Yellowstone caldera hot
enough to "boil" and therefore capable of generating a geyser?