Gravity Anomaly Analysis for Landmass Characteristics

This problem requires calculating the thickness of an elevated landmass and determining whether it is undergoing subsidence or upliftment, using given gravity anomaly values and density.

Calculating Landmass Thickness

The relationship between the Free-air anomaly ($F$), Bouguer anomaly ($B$), density ($\rho$), and thickness ($h$) of an anomalous mass is given by:

$ F \approx B + 2\pi \text{G} \rho h $

We are given:

• Density, $\rho = 2.7$ gm/cc
• Bouguer anomaly, $B = -96$ mgals
• Free-air anomaly, $F = 63$ mgals
• Constant, $2\pi\text{G} = 42\ \text{mgal/km/gm/cc}$

Rearranging the formula to solve for the gravity effect of the slab ($2\pi \text{G} \rho h$):

$ 2\pi \text{G} \rho h = F - B $

Substitute the given values:

$ 2\pi \text{G} \rho h = 63 \text{ mgals} - (-96 \text{ mgals}) = 63 + 96 = 159 \text{ mgals} $

Now, substitute the constant $2\pi\text{G}$ and density $\rho$ to find the thickness $h$:

$ (42\ \text{mgal/km/gm/cc}) \times (2.7 \text{ gm/cc}) \times h = 159 \text{ mgals} $

$ 113.4 \times h = 159 $

$ h = \frac{159}{113.4} \approx 1.402 \text{ km} $

The calculated thickness is approximately 1.4 km.

Determining Geological Process (Subsidence vs. Upliftment)

An elevated landmass with a negative Bouguer anomaly typically indicates a significant density deficiency beneath the surface, relative to the surrounding crust. While the landmass is topographically elevated (contributing positively to the Free-air anomaly), the strong negative Bouguer anomaly suggests that this elevation is not supported by a dense root and is likely gravitationally unstable.

Such a configuration, where elevation is associated with an underlying mass deficiency, is characteristic of a system tending towards isostatic equilibrium. This implies the elevated region is likely to sink or undergo subsidence.

Conclusion

Based on the calculations and interpretation:

• The landmass thickness is approximately 1.4 km.
• The association of elevation with a negative Bouguer anomaly suggests the process of subsidence.

Therefore, the landmass is 1.4 km thick and is undergoing subsidence.