A seismic refraction survey is conducted to find the depth to solid bedrock for a new building foundation. The data reveals a two-layer system: a top layer of loose soil and a bottom layer of hard rock. The velocity of the P-wave in the upper soil layer ($V_1$) is $400 \text{ m/s}$. The velocity of the refracted P-wave traveling along the top of the bedrock ($V_2$) is $2,500 \text{ m/s}$. The "crossover distance" ($x_c$)—the distance from the source where the refracted wave overtakes the direct wave—is measured at $30 \text{ m}$. Calculate the depth ($z$) to the bedrock.

A highway contractor is bidding on a large earthmoving project that requires excavating a $15 \text{ m}$ deep road cut through a hillside. To determine if they can use standard heavy excavators and bulldozers (ripping) or if they must use expensive explosives (drilling and blasting), they hire a geophysicist to perform a seismic refraction survey. The survey determines the P-wave velocity ($V_p$) of the rock mass is $3,200 \text{ m/s}$. Based on standard rippability charts (e.g., Caterpillar tables), how should the contractor classify this rock?

During a seismic refraction survey, an engineer plots a time-distance graph from the first arrival times recorded by a line of geophones. The first straight-line segment on the graph (representing the direct wave through the topsoil, Layer 1) passes through the origin $(0 \text{ m}, 0 \text{ ms})$ and the point $(20 \text{ m}, 40 \text{ ms})$. The second straight-line segment (representing the refracted wave along bedrock, Layer 2) passes through the point $(30 \text{ m}, 50 \text{ ms})$ and $(80 \text{ m}, 60 \text{ ms})$. Calculate the seismic velocities of Layer 1 ($V_1$) and Layer 2 ($V_2$) in $\text{m/s}$.

A major telecommunications company plans to forcefully dig a $2 \text{ m}$ deep trench perfectly straight down the middle of a busy, historic downtown street to lay a massive bundle of new fiber-optic cables. The city's utility maps date back over a century and are notoriously inaccurate.

A massive, heavy concrete nuclear power plant is proposed to be constructed in a region underlain entirely by a very thick, flat formation of highly soluble limestone (Karst topography). The surface of the ground is completely flat and covered in a thick layer of dense clay, showing no visible signs of danger.