Question

There is observational evidence from the continents that the sea level in the Cretaceous was \(200 \mathrm{~m}\) higher than today. After a few thousand years, however, the seawater is in isostatic equilibrium with the ocean basins. What was the corresponding increase in the depth of the ocean basins? Take \(\rho_{w}=1000 \mathrm{~kg} \mathrm{~m}^{-3}\) and the density of the displaced mantle to be \(\rho_{m}=\) \(3300 \mathrm{~kg} \mathrm{~m}^{-3}\)

Short answer

The increase in the ocean basin depth was approximately 60.61 meters.

Step-by-step solution

Understanding Isostatic Equilibrium

Isostatic equilibrium refers to the gravitational balance between the Earth's crust and mantle. When ice melts or seawater volume increases, the extra weight deforms the oceanic crust until it settles into a new equilibrium.

Determine Water Weight Increase

Given that the sea level rose by 200 meters, determine the additional weight of water per unit area: \[ W = h \times \rho_w \], where \( h = 200 \mathrm{~m} \) and \( \rho_w = 1000 \mathrm{~kg} \mathrm{~m}^{-3}\). So, \( W = 200 \times 1000 = 200,000 \mathrm{~kg} \mathrm{~m}^{-2}\).

Calculating Displacement of Mantle

To achieve isostatic equilibrium, the weight of the displaced mantle must equal the additional water weight. Let the increase in depth of the ocean basins be \( d \). Thus, \( \rho_m \times d = 200,000 \).

Solve for the Increased Basin Depth

Using the equation from Step 3, substitute \( \rho_m = 3300 \mathrm{~kg} \mathrm{~m}^{-3}\) to find the depth increase:\[ 3300 \times d = 200,000 \] Solving for \( d \), we find: \[ d = \frac{200,000}{3300} \approx 60.61 \mathrm{~m} \]

Key concepts

Sea Level Changes

Understanding sea level changes involves recognizing how the height of the sea surface fluctuates over time. During the Cretaceous period, for example, a significant rise in sea level was observed. This rise, quantified at around 200 meters higher than present day, was caused by various factors, such as the melting of polar ice caps or thermal expansion of seawater.

Sea level changes can profoundly affect coastal ecosystems and human settlements. They can lead to:

• Flooding of low-lying areas
• Changes in ocean currents and temperatures
• Alterations in marine biodiversity

By understanding historical sea level changes, scientists can better predict future trends and their potential impacts on our planet.

Ocean Basin Depth

The depth of ocean basins plays a crucial role in regulating sea levels and their changes. Ocean basins are the deep underwater regions of the Earth that hold the vast majority of its water. During periods of significant sea level rise, such as the Cretaceous, the increased volume of seawater results in adjustments in ocean basin depth.

In simple terms, when more water enters the ocean basins, they need to compensate for this extra weight. This leads to the concept of isostatic equilibrium, where the weight of the water and the underlying rock must balance. This balancing act causes the oceanic crust to flex and adjust, leading to changes in basin depth, often evidenced by displaced mantle material relocating to accommodate the new equilibrium.

Mantle Displacement

Mantle displacement occurs as a response to the pressure exerted by increased water volume in the oceans or other surface loads. Acting like a slow-moving fluid, the Earth's mantle adjusts to accommodate changes in pressure from above.

When sea levels rise by several meters, say during the peak of the Cretaceous period, the ocean crust pushes downwards on the mantle to restore balance. The mantle then displaces its material elsewhere, likely upward, to equalize this pressure.

• It is similar to placing additional weight on a floating object, causing it to sink deeper while displacing water.
• This equilibrium is vital for understanding how Earth's geology can adapt to changing conditions over geological time scales.

Cretaceous Period

The Cretaceous period, extending from about 145 to 66 million years ago, was a pivotal time in Earth's history, known for warm climates and high sea levels. During this era, sea levels were approximately 200 meters higher than today, significantly reshaping coastlines and ecosystems.

Above-average volcanic activity and the breakup of supercontinents contributed to deep seas and varied marine life. The warm climate meant reduced ice caps, leading to further rise in sea levels.

• It's a period marked by significant evolutionary developments, including the dominance of dinosaurs.
• Important for understanding climatic and biological trends, this period holds clues for today's climate change and ecological shifts.

Understanding the Cretaceous period gives insight into how Earth's systems interact over millennia.