I am reading text on physical geodesy. It says, we can not compute the gravity potential directly because we don't have sufficient information of density structure of the Earth. Why is so?
Despite significant advancements in geophysical techniques and technologies, we still do not have sufficient knowledge about the density structure of the entire Earth for several reasons:
Overall, while significant progress has been made in studying the density structure of the Earth, we still have a long way to go before we can fully understand the composition and structure of our planet's interior. We must use new techniques.
Hopefully this help:
The gravity potential is a measure of the strength and direction of gravity at different points on the Earth's surface. It depends on the distribution of mass within the Earth, which in turn is related to the density structure of the Earth.
However, we do not have direct measurements of the density structure of the Earth. We can only infer it from indirect measurements such as seismic waves, gravitational anomalies, and magnetic anomalies. These methods provide information about the Earth's interior but are limited in their resolution and accuracy.
Furthermore, the Earth's density structure is not uniform and varies with depth. This means that even if we have accurate measurements at one depth, we cannot directly extrapolate them to other depths without making assumptions about the Earth's composition and structure.
As a result, it is not possible to compute the gravity potential directly from the density structure of the Earth. Instead, we use mathematical models and techniques such as spherical harmonics and the finite element method to approximate the gravity potential based on available data and assumptions about the Earth's density structure.
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