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Gravity acceleration on the Earth is produced by the gravitational attraction of the mass of the Earth and the centrifugal acceleration due to the rotation of the Earth. In most cases of gravity measurements, gravimeters determine the magnitude of the gravity acceleration along the local plumb line at each gravity station. There are two mechanisms employed in modern gravimeters: the free‐fall method and the spring method. The former is based on measuring the absolute acceleration of a test mass falling in a vacuum chamber, in which the air drag is reduced. The FG5 absolute gravimeters produced by Micro‐g Lacoste Inc. have become the de facto standard of absolute measurements (Niebauer et al., 1995). As a test mass, the use of laser‐cooled atoms has been proposed and recently commercialized (Ménoret et al., 2018). These instruments are costly and require delicate handling of vacuums, lasers, atomic clocks, electronics, etc. The absolute measurement, therefore, has been performed mostly indoors where benchmarks can be maintained. The other spring‐type gravimeters are widely used outdoors (Fig. 3.1). The principle of the spring‐type gravimeters is easily understood by imagining a test mass attached to the end of a spring; a tiny gravity change, Δg, is amplified and observed as a displacement of a spring, Δx, via well‐known Hooke’s law, mΔg=kΔx, where k stands for a spring constant. The stability of the spring constant is precisely controlled by thermostats. Highly stable gravimeters are available, such as Scintrex CG series, Lacoste & Romberg gravimeters, etc. (Seigel et al., 1993). The users of spring‐type gravimeters begin the measurement at reference stations, where the absolute gravity acceleration is known beforehand, and determine the gravity acceleration of outdoor stations by cumulating the gravity differences.

A typical value of gravity acceleration on the Earth is known as g = 9.8 m/s². It varies depending primarily on the latitude and elevation of the observer; the gravity is maximum at the north and south poles (g _pole = 9.83 m/s²) and it is minimum on the equator (g _equator = 9.78 m/s²). This variation is explained by the oblate spheroidal shape of the Earth and the fact that the centrifugal force is proportional to the distance to the rotational axis (Fig. 3.2). Since the gravity variation is very small (just 0.5% of g), it is convenient to employ smaller units for discussing the gravity variation. One common such unit is Gal = cm/s², the name of which is taken from Galileo Galilei (1564–1642). Under this unit, the typical gravity acceleration becomes g= 980 Gal. The observation errors of absolute and relative gravimeters are approximately 1 and 10 μGal in best cases, respectively.

The main focus of this chapter is to extract the gravitational effect of mass in the near‐surface. It can be done by removing the global trend of the gravity field of the Earth, referred to as the normal gravity field. The normal gravity field is defined by the equatorial radius of the Earth, the geocentric gravitational constant of the Earth, the dynamical form factor of the Earth, and the angular velocity of Earth rotation (Torge & Müller, 2012). According to Torge & Müller, 2012, the normal gravity is expressed as a function of geographic latitude ϕ

Figure 3.2 (a) Geometrical relationship between the gravitational, centrifugal, and gravity acceleration on the Earth. (b) Normal gravity field of the Earth γ as a function of the latitude (equation 3.1).

(3.1)

which is accurate to 1 μms⁻². The change of the normal gravity with height is given as

(3.2)

where h is defined as height (in km) from the surface of the reference ellipsoid. Since the latitude dependence and the quadratic term of h in equation 3.2 are small, a constant gradient is often employed (free‐air gradient):

(3.3)

The negative sign in equation 3.3 shows that the gravity acceleration decreases as the observer gets away from the center of the Earth. Gravity anomaly is then defined as a deviation of the observed gravity acceleration from the reference given by normal gravity. Specifically, the free‐air gravity anomaly is defined as

(3.4)

where g ^obs is the observed gravity and H is the station height above the geoid surface. The height h is taken from the surface of the reference ellipsoid in equation 3.2 and H is taken from the geoid surface (equipotential surface approximating the sea surface) in equation 3.4. This confusion originates from the traditional definition of gravity anomaly, equation 3.4. Before the global navigation satellite system became available at the end of 20th century, H could be directly measured by level surveys but h could not be measured. Replacing H with h in equation 3.4 leads to the definition of the gravity disturbance, which is often used when discussing the satellite gravimetry data. As long as the objective is just to correct the effect of different elevations on the observed gravity in a narrow region, the choice of height definition does not cause severe differences.

Figure 3.3 The free‐air gravity anomaly can be decomposed into the three terms: the gravitational contribution of the target volume (Δg ^target), that of the topographic mass (Δg ^terrain) and the regional trend (Δg ^trend).

The free‐air gravity anomaly can be decomposed into the following three components (see Fig. 3.3):

(3.5)

The first term, Δg ^target, is the gravitational effect of the masses within the target volume of the survey, whose density distribution we wish to solve by inversion analysis. The second term, Δg ^terrain, is the effect of topographic mass outside the target volume and above the geoid surface. This term can be evaluated by assigning the optimal density to the topographic material and integrating the gravitational effect (see Supplemental Information). The third term, Δg ^trend, is a so‐called regional trend, which originates from the deeper parts of the Earth, such as lithology, tectonics, and mantle dynamics. The latter two terms must be properly understood and removed to extract the first term, the gravitational effect of interest.