1. The value of the gravitational acceleration on the Earth is roughly 9.81 m/s2
ID: 297570 • Letter: 1
Question
1. The value of the gravitational acceleration on the Earth is roughly 9.81 m/s2 and the mean radius is approximately 6, 371 km. Therefore,
(a) what is the mean density of the Earth and how does this compare with the density of surface materials of the Earth and that of the Earth’s lithosphere?
(b) What are the implications of this result?
2. A horizontal sandstone formation serves as an aquifer. The analysis of samples from the formation indicates that it has a grain density of 2, 650 kg/m3 and an average porosity of 15%. What is the density of the formation
(a) when it is water saturated, and
(b) when it is dry?
(c) What is the minimum thickness of the aquifer, assuming the formation covers an extensive area and is bounded by a shale formation that has a density of 2,200 kg/m3 if a 1.0 mGal gravity anomaly is observed across the margin of the aquifer?
3. Consider the gravity observations (open circles) collected along a profile across the topography depicted in the figure below. The Bouguer gravity anomaly effects of the topography were computed using different values of density. From these results which are shown in the upper portion of the figure below,
(a) what is the density of the topographic feature and why? What do the reduced profiles indicate about the related topographic corrections that are (b) positively, and (c) negatively correlated with the topography?
4. How might borehole gravity observations from 3 or more boreholes be used to locate a subsurface body of anomalous density that has not been intersected by any of the boreholes?
5. Errors which are inherent in geophysical data propagate as various mathematical processes are performed. For a set of 17 observations with the mean value 2.06 and standard deviation 0.32 and another set of 39 observations with a mean of 4.54 and standard deviation of 0.26, calculate the (a) sum, (b) difference, (c) product, and (d) quotient of these data, including (e) their combined standard deviation.
Explanation / Answer
1. a.The average density of the earth is about 5.5 g/ cm3 whereas the average density of the continental crust is about 2.67 g / cm3.
B. It indicates that the spinning of earth materials in early times tends to maintain its angular momentum by displacing light material to the outer and denser to the inner portion.
2. A. saturated water with density 1 g/ cm3 fills all pores.
Then density becomes
= 2.65*0.85 + 1*0.15
= 2.40 g/cm3
B. Dry has no water, then it becomes
2.24g/cm3
3. Figure has not been provided.
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