Question

An ocean basin has a depth of \(5.5 \mathrm{~km}\). If it is filled to sea level with sediments of density \(2600 \mathrm{~kg} \mathrm{~m}^{-3}\), what is the maximum depth of the resulting sedimentary basin? Assume \(\rho_{m}=3300 \mathrm{~kg} \mathrm{~m}^{-3}\).

Short answer

The sedimentary basin's maximum depth is 2.115 km.

Step-by-step solution

Understanding the problem

We need to find the maximum depth of a sedimentary basin created when sediments fill an ocean basin. We are given the ocean basin depth as \(5.5 \text{ km}\) and the densities of the sediments \(\rho_{s}=2600 \text{ kg/m}^3\) and the mantle \(\rho_{m}=3300 \text{ kg/m}^3\).

Isostatic equilibrium hint

The depth of the sedimentary basin will reach an equilibrium controlled by their densities, involving the concept of isostasy. This implies the weight per unit area of the column of sediment will equal that of the original column of water it replaced plus the original sediments.

Calculating the original water weight

The water has the same volume as the original ocean basin depth, \(5.5 \text{ km}\), with water having a density \(\rho_w = 1000 \text{ kg/m}^3\). Weight per unit area \(= 5.5 \times 10^3 \times 1000 \text{ kg/m}^2\) because volume is height multiplied by unit area.

Weight equation of sediment

The weight per unit area of the sediment replacing the water will be \(d_s \times \rho_s\) where \(d_s\) is the sediment depth that contributes to isostatic equilibrium.

Equating weights for equilibrium

Set the weight of the sediment equal to the weight of the original column before sediment addition to find depth, \(d_s \): \[d_s \times 2600 = 5.5 \times 1000\]

Solving for sediment depth

Rearrange the equation to solve for \(d_s \): \[d_s = \frac{5.5 \times 1000}{2600} = 2.115 \text{ km}\].

Conclusion

The maximum depth of the sedimentary basin is \(2.115 \text{ km}\).

Key concepts

Isostatic Equilibrium

Isostatic equilibrium is a crucial concept in understanding how the Earth's crust balances itself. Simply put, it refers to the state where the earth's crust remains balanced by floating atop the denser, more fluid-like mantle. Think of it like an iceberg floating on water, where only a part of the iceberg is visible. Just like the iceberg, the crust's light materials float on top of the denser layer.
In the context of ocean and sedimentary basins, this concept helps explain how sediments accumulate and balance out. When sediments fill an ocean basin, they exert a downward force due to gravity. Meanwhile, the underlying mantle exerts an upward buoyant force. When these pressures find a balance, isostatic equilibrium is achieved. This means the basin will stay stable unless something alters this natural balance, such as a change in sediment density or basin topography.
This equilibrium is essential for calculating how much sediment a basin can hold before it reaches its equilibrium point. This understanding helps geologists predict changes and stability in Earth's surface structures.

Density Calculations

Density calculations are vital to determine how different materials interact and settle in geological contexts. In the problem of finding the maximum depth of a sedimentary basin, density plays a key role in understanding isostatic equilibrium.

• Density is defined as mass per unit volume. It's represented by the symbol \(\rho\) and its units are often \(\text{kg/m}^3\).
• In our exercise, sediments and the Earth's mantle have different densities: sediments are \(2600 \text{ kg/m}^3\) and the mantle is denser at \(3300 \text{ kg/m}^3\).

The calculation uses density to equate the weight of the sediment column with the original weight of the water column replaced by sediments. This ensures that the basin remains in isostatic equilibrium. For calculating the sediment depth \(d_s\), we set these weights equal to each other, which helps us discern the new sedimentary basin depth based on known densities. Precise density calculations allow us to accurately model these natural processes.

Ocean Basin Geology

Ocean basin geology is an intriguing field, focused on understanding how these massive structures form and evolve. An ocean basin is essentially a vast depression on the Earth's surface that contains large bodies of salt water.
Geologists study these basins to understand the process of sedimentation, where materials like sand, silt, and organic matter settle at the bottom. This sedimentation creates sedimentary basins, shaping the geology beneath the oceans. When ocean basins fill with sediments, they transform over time due to processes like tectonic shifts and erosion.
Studying the geology of ocean basins involves examining how these sediments compress and integrate into layers within the basin. Over geological time, these layers can become compacted and eventually turn into sedimentary rock. This process and the resulting formations help us understand the Earth's history, including plate tectonics and ancient climates. Ultimately, ocean basin geology provides a critical insight into how Earth has changed and continues to change over millions of years.