1. Chapter I: The gravity field of Earth
Wan Yongge

2. Earth’s Free Air Gravity:

3. Chapter I: The gravity field of Earth
1. Basic theory
2. Normal gravity and anomaly
3. Gravity measurement

4. 1. Basic theory

5. What is gravity?
The branch of geophysics dealing with the earth’s gravity field is called gravimetry, sometimes the simple term gravity field is used.
Gravity is a force of attraction only between bodies that have mass.
The word “gravity” comes from the Latin word “gravis”, meaning “weight” or “heavy”.

6. In other word
Gravity not only must measure gravity, but also solve many problem of the processing and interpretation of gravity data theoretically and practically.
The strength and direction of gravity varies according to position and time.

7. the shape and size of the earth, estimate underground construction,
By measuring the distribution of gravity and its change with time it is possible to know:
the shape and size of the earth,
estimate underground construction,
study the seismic and volcanic activities
investigate the viscosity and elasticity of the earth.

8. Gravity: Fundamentals
Newton's Law describes the force of attraction between two point masses, M1 and M2 separated by r:
The force per unit mass, F/ M2 defines the gravity field which is the gravitational acceleration, g, when M1 is the Earth (Me) and r is the radius of the Earth, Re. So
The gravitational constant G is:
x m3 kg-1 s-2 ( SI units ), or
x 10-8 cm3 g-1 s-2
第一部分公式

9. UNITS USED Results are presented in c.g.s units rather than SI units.
SI unit for g: m/s2
In c.g.s the unit acceleration, 1.0 cm s-2, is called the gal (short for Gallileo).
A convenient subunit for surveys is the milligal, mgal, 10-3cm s-2.
Another unit that has been used is the gravity unit, gu, which is defined as 10-6 m s-2 or 0.1 mgal.)

10. Gravitational Acceleration
Acceleration is defined as the time rate of change of the speed of a body.
Speed, sometimes incorrectly referred to as velocity, is the distancean object travels divided by the time it took to travel that distance (i.e., meters per second (m/s)).
Thus, we can measure the speed of an object by observing the time it takes to travel a known distance.

11. Positive acceleration Negative acceleration
If the speed of the object changes as it travels, then this change in speed with respect to time is referred to as acceleration
Positive acceleration
Negative acceleration
means the object is moving faster with time
means the object is moving slower with time

12. Acceleration can be measured by determining the speed of an object at two different times and dividing the speed by the time difference between the two observations. Therefore, the units associated with acceleration is speed divided by time; or distance per time per time, or distance per time squared.

13. Units of acceleration “Gals” “millGals”
The Earth's gravitational acceleration is approximately 980 Gals.
The Gal is named after Galileo Galilei and is defined as a centimeter per second squared
The milliGal (mgal) is one thousandth of a Gal.
In milliGals, the Earth's gravitational acceleration is approximately 980,000.
The SI unit which is becoming more widely cited is the micrometre per second squared, which is one- tenth of a mGal

14. How is the Gravitational Acceleration, g, Related to Geology
How is the Gravitational Acceleration, g, Related to Geology? Density is defined as mass per unit volume.
For example, if we were to calculate the density of a room filled with people, the density would be given by the average number of people per unit space (e.g., per cubic foot) and would have the units of people per cubic foot. The higher the number, the more closely spaced are the people.
Thus, we would say the room is more densely packed with people. The units typically used to describe density of substances are grams per centimeter cubed (gm/cm3); mass per unit volume.

16. Consider a simple geologic example of an ore body buried in soil
Consider a simple geologic example of an ore body buried in soil. We would expect the density of the ore body, d2, to be greater than the density of the surrounding soil, d1.
Thus, to represent a high-density ore body, we need more point masses per unit volume than we would for the lower density soil*.

17. Now, let's qualitatively describe g by a ball as it is dropped from a ladder. This can be calculated by measuring the time rate of change of the speed of the ball as it falls. The size of the acceleration the ball undergoes will be proportional to the number of close point masses that are directly below it.
We're concerned with the close point masses because the magnitude of the gravitational acceleration varies as one over the distance between the ball and the point mass squared. The more close point masses there are directly below the ball, the larger its acceleration will be.

18. We could, therefore, drop the ball from a number of different locations, and, because the number of point masses below the ball varies with the location at which it is dropped, map out differences in the size of the gravitational acceleration experienced by the ball caused by variations in the underlying geology.
A plot of the gravitational acceleration versus location is commonly referred to as a gravity profile.

19. Importance of Gravity 1. Measuring gravity field of the earth.
2. Solving many gravimetric problems
Theoretically:
Determination of the correct constants in the formula derived theoretically for the normal distribution of the acceleration of gravity over the earth’s body.
Practically :
Explanation of the anomalies of the actual gravity field of the earth with respect to the theoretical field

20. 3. Applying gravity in surveying and investigating deposits of useful minerals, and raw materials such as ores, coal, oil, salt, and sulfides deposits.
4. Applying gravity during hydrogeologic and engineering investigations to:
map regional geologic structure.
map basement topography and sediment thickness.
map basement faults.
locate underground caverns.

21. 2. Normal Gravity and anomaly

25. Bouguer Gravity

26. Bouguer
Topography

27. U.S. Bouguer Gravity Anomaly

28. 3. Gravity measurement

29. Measuring gravity In summary,
Relative
Absolute
Hooke’s law
F=m(dg)=k(ds)
dg=ds*k/m
S=VT
g=a=dv/dt=-(S*t-2)
In summary,
The measured parameter is the force on a mass, m, due to the presence of another mass, M.
The recorded parameter is acceleration, with units of milliGals (compared to m/s2).
The interpreted parameter is usually density of causative buried materials and structures.

30. What is actually measured?

31. Gravity measurements: sensors and platforms
Space-borne gravimetry: GRACE (K-band ranging), GOCE (gradiometer), CHAMP and COSMIC (GPS), LAGEOS (SLR), satellite altimetry (sea only)
Airborne gravimetry
Shipborne gravimetry
Relative gravimetry
Superconducting gravimetry
Absolute gravimetry

32. Satellite gravimetry: GRACE and COSMIC
The joint Taiwan-US mission FORMOSAT-3/COSMIC (FM/COSMIC) was launched on April 17, 2006, deploying six micro-satellites at altitudes ranging from 750 to 800 km and at an inclination of 72 degree in the final mission phase. The expected lifetime is 5 years.
Two single-patch antennas, mounted on the upper part of the main body, are for precise orbit determination (POD)
Combining COCMIC GPS and GRACE KBR for gravity determination

33. Kinematic orbits as 3-D tracking data
In the kinematic POD based on zero-differenced phase measurements, satellite coordinates are estimated together with one GPS receiver clock parameter every epoch
In the NCTU kinematic orbit determination for the COSMIC mission, we first produce a 30-h orbit arc (from -3 h of a GPS day to +3 h), which is then truncated to a 24-h arc (0 to 24 h of a GPS day) for further applications, especially for gravity recovery.

34. Combined COSMIC-GRACE gravity solution
Geoid variation to spherical harmonic degree 25 from the combined COSMIC and GRACE solution

35. Airborne and shipborne gravimetry

36. Airborne and shipborne gravimeter: L&R Air-Sea Gravity System II
resolution
0.01 mGal
accuracy
<1.00 mGal
size
71 x 56 x 84 cm
weight
116 kg
power
240 watts (avg), 450 watts (max)
frequency
1 Hz

37. Shipborne gravimetry

38. Applications of gravity in natural and engineering sciences
Geodesy: geoid modeling, vertical datum, orbit determination, GPS leveling etc
Geophysics: density distribution, isostasy, crustal-mantle structure, seafloor topography
Metrology: pressure, work and power are gravity-dependent
Gravitational constant, G
Terrestrial navigation
Deposit exploration
Geodynamics: tectonics, earthquake etc
Climate change
Hydrology
Oceanography
New applications are yet to be exploited