1.What is gravity measurement?

Gravity is the combination of earth attraction force and the earth self-rotation centrifuge force (as shown below). In the gravity measurement field, cm/sec2is defined as Gal, in memory of the Physicist Galilei. But, in gravity measurement, Gal could not satisfy the precision requirement. Therefore, the 1/1000 of gal us used as unit, that is mGal. The unit conversion calculation is as follows:

1Gal = 1cm / sec2

10-3Gal ( 0.001Gal ) = 1cmGal

10-6mGal ( 0.001mGal ) = 1µGal

In short, the gravity measurement is the measurement of the gravity. Generally, it is divided into absolute gravity measurement and relative gravity measurement two surveying methods.

2.The principle of absolute gravity measurement

The so-called absolute gravity measurement is to use absolute gravity instrument to measure the gravity value at each point.

The earlier absolute gravity measurement principle uses the relationship between the pendulum periodic movement and the length of the line. This is so called pendulum principle. The general mathematic pendulum equation is as follows:

T = 2PI x (l/g)1/2

Where T is the swing period, l is the pendulum length, and g is the gravity force. Or, use variable pendulum line length to measure the swing period for different length. It may be derived from the above equation: where, the pendulum lengths are l1 and l2, the measured pendulum periods are T1, and T2, and g is the gravity force. The T1 and T2 are half period, that is the time required for the pendulum swing from the vertical position to the one side and then return to the vertical position.

Before the 21st century, the measurement of gravity force requires much effort but the rate of success is not large. The main reasons are the requirement of measurement of the line length and the period at the same time. Especially, there are difficulties to measure the length of the line. It is difficult to achieve the required precision. With the use of laser and superconductivity technology to improve the instrument, the nGal class precision absolute gravity instrument (as shown in diagram, the SG type instrument), may achieve the high precision absolute gravity measurement.

The so-called relative gravity measurement is to use the relative gravity instrument to measure the differences between any testing points in relationship to the gravity base point readings.

In the past, the principle of relative gravity measurement is rather simple. Use a pendulum with fixed length, swing at different positions. Then, use the gravity value and the square root of the period as inversed ratio to calculate the relative gravity. For example, the gravity value of point A is known. Then the gravity ratio value of B may be determined.

TA = PI x (1/gA)1/2 ` TB = PI x (1/gB)1/2 => gB = gA x T2A / T2B

For the present, the relative gravity measurement uses the relative gravity instrument (as shown in diagram, EG type instrument) to measure the differences between any testing points in relationship to the gravity base point readings. Then, the difference in reading is multiplied by the constant marked on the instrument. The gravity difference /\g between the testing point and the gravity force base is then calculated. From the absolute gravity value gAof the gravity force base and use the following equation to calculate the absolute gravity values gBfor all testing points. The equation is as follows:

gB = gA + /\g

The gravity force at any points on the earth will change with time. The environmental factors cause the change includes the tidal

attraction¡@and attraction of ocean tide of each day and each month, atmospheric pressure change, polar motion, change in underground water level, the change in soil moisture, etc. Most of the relationship and models are described in references, such as Torge(1989), Vanicek and Krakiwsky (1986), Moritz and Mueller (1987), Melchoir (1983), in addition to the consideration of the above-mentioned corrections, the system errors caused by the relative gravity instrument, such as Calibration Function, and Drift Function, may apply the gravity net horizontal difference, and use the extra measurement method to calculate its parameters relationship. The absolute gravity force may then be calculated for any points in the gravity net.