## 1. Introduction

The gravity method is a nondestructive geophysical technique that measures differences in the Earth’s gravitational field between specific locations. It has many applications in engineering and environmental studies such as locating karsts, monitoring aquifer recharge, determining geologic layer thickness and the structure of the basement rocks, estimating the mass and volume changes in geothermal reservoirs, monitoring precursors of volcanic eruptions, and monitoring gas production and carbon sequestration. The gravity method is also used in oil, gas, and mineral exploration.

The gravity method depends mainly on the differences in the density of the Earth materials. The variations of densities of subsurface rocks produce variations in the measured gravity field. There are many numerical and analytical methods to study the variations in gravity and interpret the source of these variations (geometry, depth, and density). A GPS measurement should be associated with gravity measurements in order to know the exact coordinates (longitude and latitude) of the gravity stations and their altitudes. The measured gravity data is then processed by removing all the quantifiable disturbing effects and interpreted using computer programs. The most highly processed data are known as the Bouguer gravity, and anomalies are measured in units of mGal. Recent computer models are capable of creating three-dimensional subsurface density models.

## 2. Gravity method

### 2.1. Definition of the gravity field

The gravity field is defined as follows: a gravitational force or gravity exerted on a unit mass at a point in space or on the surface of the earth or its vicinity [1]. The gravity field is a force or a force field distributed over the region surrounding the generator. A measurement of gravity fields should be made in a region or space in which gravity fields exist.

### 2.2. Gravity method and its applications

Gravity is a geophysical potential field method. Various applications and developments of gravity method in the fields of geology, engineering, geothermal, and volcanology have been demonstrated and developed. Gravity can be used in time-series applications such as geothermal reservoirs and by estimating the underground mass changes [2, 3]. Also, gravimetric studies at active volcanic systems have contributed significantly to the better understanding of pre-, syn-, and post-eruptive processes [4, 5]. With the development of gravimeters with improved accuracy, the measurements have become much easier. Recently, time-variable gravity from satellites has detected the redistribution of mass over large scales and the gravity data are used, for example, in hydrology and oceanography. The gravity method can also detect geological anomalies and contacts (faults) by using gravity gradient interpretation techniques.

### 2.3. Basics of gravity

Gravity surveying is based on Isaac Newton’s universal law of gravitation, described in *Principia Mathematica* in 1687. One of the basic forces of nature is the attraction between all masses. This attraction is called the force of gravity. According to the Newtonian law of gravity, the gravitational force between any two point masses is given by:

where G (universal gravitational constant) = 6.673 × 10^{−11} m^{3} kg^{−1} s^{−2}. M_{1} and M_{2} are the two masses in kg, and r is the distance between the point masses, in meters. *g* is the local value of the Earth’s field, and *m* is a test mass. This force acts in the direction joining the two masses (**Figure 1**). **Figure 2** shows the gravitational attraction of a small mass on the Earth.

#### 2.3.1. Units of gravity

Recent gravity meters are very sensitive and can routinely measure differences in the gravity field to within one part in 10^{9}. The c.g.s unit commonly used in gravity measurement is the milliGal: 1 mGal = 10^{−3} Gal = 10^{−3} cm s^{−2}. In gravity surveys, commonly, mGal is used.

#### 2.3.2. Shape of the Earth

If the Earth was a uniform, homogenous sphere, g would be constant over its surface. However, gravity varies because the density varies within the Earth, and the Earth is not a perfect sphere. One predictable effect on local gravity measurements is earth’s shape. The Earth has the shape of a flattened sphere because of its rotation (**Figures 3**–**5**).

### 2.4. The pendulum

It is possible to find the acceleration of gravity (g) from the period of oscillation of a pendulum (**Figure 6**) swinging with a small amplitude using Eq. (2):

where *f* is the frequency and L is the length.

### 2.5. Modern gravimeters

There are two main types of modern gravimeters. The first type, which uses a pendulum arrangement or a dropping weight, records the actual acceleration of gravity wherever it is placed. The second type uses levers and springs to measure the difference in gravity between two stations. Since the springs are not calibrated, these readings are all relative to a base station.

Gravimeters, essentially a mass suspended from a sophisticated spring balance, have been used to measure relative gravity since 1930s. As weight of mass (mass x gravity) increases, the spring is stretched (**Figure 7**).

#### 2.5.1. Relative modern gravimeter

### 2.5.1.1. CG-3M relative gravimeter

The Scintrex CG-3M gravimeter is a very sensitive mechanical balance that detects gravity field changes as small as one part in a million. CG-3M (**Figure 8**) has a resolution of 1 μGal and automated corrections for tide, instrument tilt, temperature, and rejection of noisy data. **Figures 9** and **10** show the CG-3M gravimeter in the field with GPS measurement. Please check **Table A1** for gravity data sheet information.

### 2.5.1.2. CG-6 relative gravimeter

The CG-6 Autograv (Scintrex) is the newest generation of land gravity meter. **Figure 11** shows CG-6 acquired by United Arab Emirates University in March 2017. **Figure 12** shows the gravity stations observed in Al Ain city. **Figure 13** shows the three-dimensional inversion of the Bouguer gravity data for geological investigations.

#### 2.5.2. Absolute modern gravimeter

The A-10 (**Figure 14**) is a portable absolute gravimeter recently developed by Micro-g LaCoste, Inc. (MGL) that is designed for use in the field to measure the vertical acceleration of gravity (*g*). A test mass is dropped numerous times in a vacuum, and its position is measured with a laser interferometer as a function of time with an atomic clock. The vertical acceleration of gravity is calculated by fitting the equation of motion to the measured trajectory of the test mass. The drops are combined into a “set” which typically consists of 100–200 drops. Multiple sets are collected, and the average of the sets provides a value of *g*. The specifications of the A-10 are: a precision of 100 μGal at a quiet site, a repeatability of 10 μGal on a high-quality pier, and an accuracy of 10 μGal [8]. **Table 1** and **Figure 15** show the absolute gravity data recorded in Kyushu University [7]. Please check **Table B1** for gravity data sheet information.

Setup height | 2.20 cm |

Transfer height | 100.00 cm |

Actual height | 74.00 cm |

Gradient | −3.086 μGal/cm |

Nominal air pressure | 1004.27 mBar |

Polar motion coord.^{**} | −0.1049 “0.2862” |

Measurement precision | 0.94 μGal |

Number of sets | 10 |

Number of drops | 100 |

Gravity | 979634789.69 μGal |

Measurement of absolute gravity at base station is very important in calculating absolute gravity values at other stations as follows:

### 2.6. Corrections to gravity observations

#### 2.6.1. Instrumental drift

Gravimeters are very sensitive instruments. Temperature changes and elastic creep in springs cause meter readings to change gradually with time even if the meter is never moved. Drift is monitored by taking repeated readings at the same station over the course of the day, perhaps every 1–2 h, to produce a drift curve (**Figure 16**). Instrument drift correction for each station can be estimated from drift curve.

#### 2.6.2. Variation with elevation

### 2.6.2.1. Free-air effect

Height correction is important in a microgravity survey. The measured gravity is corrected by using free-air gradient of −308.6 μGal/m (**Figure 17**).

Free-air correction is the difference between gravity measured at sea level and at an elevation, h, as if there was no rock in between.

### 2.6.2.2. Bouguer effect

Free-air correction does not take into account the mass of rock between measurement station and sea level. The Bouguer correction, Δg_{B}, accounts for effect of the rock mass by calculating extra gravitational pull exerted by rock slab of thickness *h* and mean density ρ (**Figure 18**).

### 2.6.2.3. Elevation effect

### 2.6.2.4. Terrain effect

Bouguer correction assumes subdued topography. Additional terrain corrections must be applied where measurements are near to mountains or valleys (**Figures 19**–**21**). If the station is next to mountain, there is an upward force on the gravimeter from mountain that reduces the reading. This effect was first noticed in topographic surveys run near the Himalayan Mountains.

If gravity station is next to valley, there is an absence of the downward force on gravimeter assumed in Bouguer correction, which reduces free-air anomaly.

In both cases, terrain correction is added to Bouguer anomaly.

#### 2.6.3. Variation with time

### 2.6.3.1. Earth and ocean tides

The solid Earth responds to the pull of the Sun and the Moon just like the oceans, but movements are much smaller. The Sun and the Moon also pull on the gravimeter and its parts. These effects are large enough to affect gravity readings (**Figure 22**). Changes in observed gravity due to “tides” occur with periods of 12 h or so. Earth tide effects can be controlled by repeated readings at same station in same way as instrument drift.

Precipitation and atmospheric pressure: These effects can be significant in a microgravity survey. It is recommended to measure gravity in a stable weather condition (on the same day, for example).

### 2.7. Bouguer anomaly

The Bouguer anomaly (D*g _{B}*) is the difference between the observed value (

*g*), properly corrected, and a value at a given base station (

_{obs}*g*), such that:

_{base}with

where the subscripts refer to the following corrections: *L*: latitude; *F*: free-air; *B*: Bouguer; *TC*: terrain correction; and *D*: drift (including the Earth tides).

**Figure 23** shows the different steps for gravity data processing.

## 3. Applications of gravity method in geosciences with case studies

Gravity can be used for: (1) regional surveys and (2) local surveys. These two cases depend on the scale of the geologic target under the study. For fault and regional geological surveys, we use a regional gravity survey with a large grid size. However, for local geological studies such as cavity investigations, active fault detection or local geological features, we use more dense gravity surveys with a small grid size and small spacing between gravity stations.

### 3.1. Geology and structural geology

Gravity data can give us much information about the subsurface geological structures such as faults, rock intrusions, dykes, and sills. We can also study basin structure, grabens, horts, and salt intrusion all of which are very important in oil and gas exploration. The most important physical property is rock density, and density contrast between the different rocks will create gravity anomalies which are easy to detect if the measured gravity data are good enough (**Figure 24**). Gravity measurements are very sensitive to noises such as cars and human activities including walking vibrations from machinery or nearby seismic operations and even earthquakes. The geophysicist and/or user must pay close attention during field measurement in order to get good gravity data.

Bouguer anomaly maps contain both regional and residual (local) anomalies (**Figure 25**). Regional anomalies have long wavelengths and are usually due to deep crustal features. A residual (local) anomaly will have a short wavelength and is due to shallower structures.

There are many filtering techniques that can help us to separate the residual and the regional gravity anomalies such as band-pass filters. Power spectrum analysis techniques are also useful in determining the number of geological layers and their depths and can also be used to remove noise from the data.

#### 3.1.1. Forward modeling

**Figure 26** shows an example of forward modeling of gravity data from Aynak-Logar Valley (Afghanistan) for studying the local geology.

#### 3.1.2. Three-dimensional gravity inversion, case study: Tindouf Basin (Algeria)

The gravity effect of the three-dimensional (3D) density model for Tindouf basin has been computed using GRABLOX-1.7 and BLOXER-1.5 software developed by M. Pirttijärvi, University of Oulu, Finland [11].

The model of study area covers an area of 42,501 km^{2} and was oriented in a north–south direction, extending 269 km in the east–west direction and 157 km in a north–south direction (**Figure 27**). The spatial discretization was 83 grid blocks in the east–west direction (“i” index) and 39 blocks in the north–south direction (“j” index). In the Z-direction (“k” index), the model contains three blocks. The model is based on two-layer case: sedimentary layer represented by clays with a density of 2.2 g/cm^{3} and a dolerite layer with a density of 2.9 g/cm^{3}. **Figures 28**–**32** show the 3D gravity inversion results.

### 3.2. Geothermal

Time-lapse gravity surveys at geothermal fields have been going on for at least four decades. The movement of fluids and mass redistribution in geothermal reservoirs are essential for geothermal energy development and its sustainability (**Figure 33**). [12] explained many possible causes of gravity change at Wairakei geothermal field. Recently, geothermal reservoirs have been monitored with a high-precision hybrid technique (absolute/relative gravity-measurement) [13, 14]. **Figure 34** shows the gravity changes in Obama geothermal field (southwestern Japan).

### 3.3. Hydrogeology

Hydrogeology is perhaps the most complex use of intermediate scale (hour–year) variations in gravity [15]. In the case of horizontal layer (Bouguer slab) of aquifer of thickness h and porosity *ϕ*, we get a gravity perturbation [16],

The groundwater level change is calculated after rearranging Eq. (7) as follows:

Where Δg: gravity change (μGal = 10^{−8} m/s^{2}), G: universal gravitational constant = 6.673 × 10^{−11} m^{3} kg^{−1} s^{−2}, ρ_{water}: density of groundwater, *ϕ*: porosity of aquifer, and h: water-level change (m). We assume that the groundwater level variations stem from a shallow aquifer (**Figure 35**); however, there is no bound on aquifer depth in this approximation [5].

**Figure 36** shows the evaluation of the required groundwater level changes at the shallow subsurface of Unzen volcano (southwestern Japan) calculated using Eq. (8). The maximum values of water-level change are in the range of several meters.

### 3.4. Active faults

Gravity method can detect fault zones especially if there is vertical displacement and there is density contrast between the geological layers as shown in **Figure 37**.

### 3.5. Volcanology

Gravity surveys are very important in monitoring volcanic activity and studying hydrothermal activity beneath volcanoes [5]. **Figure 38** shows the two-may measurements of microgravity in volcanic regions.**Figure 39** explains the different corrections necessary to calculate the residual gravity.

For gravity surveys in volcanic areas, it is recommended to:

Use gravity residuals for plotting the gravity changes at a volcano/geothermal field.

Add the 1-σ error residuals in the same plot of the gravity residuals.

Use Student’s

*t*-test to derive indications of statistical relevance of the residual data (to check significant changes at stations).Measure gravity in stable weather conditions (i.e., on the same day).

Minimize operator errors as much as possible by taking the readings in a good way.

#### 3.5.1. Residual gravity calculation

The Residual Gravity at *Station 1* (t_{1}-t_{2}) = [(measured gravity at *Station 1* t_{2}: measured gravity at *Base Station* t_{2}): (measured gravity at *Station 1* t_{1}: measured gravity at *Base Station* t_{1})].

#### 3.5.2. Error datum (1−σ error) calculation

The error for the datum t_{1} is as follows:

Error *Station 1* t_{1} = sqrt [(error at *Station 1* t_{1})^{2} + (error at *Base Station* t_{1})^{2}]

For the datum t_{2}:

Error *Station 1* t_{2} = sqrt [(error at *Station 1* t_{2})^{2} + (error at *Base Station* t_{2})^{2}].

error at Station = sqrt [(drift corrected gravity)go: (drift corrected gravity)back]^2.

#### 3.5.3. Calculation of errors in case of ground deformation

The error of the residual gravity changes (1−σ error residuals) is calculated via:

Residual error *Station 1* t_{2} = sqrt [(error *Station 1* t_{1})^{2} + (error *Station 1* t_{2})^{2} + (X μGal)^{2}].

Residual error *Station 1* t_{3} = sqrt [(error *Station 1* t_{1})^{2} + (error *Station 1* t_{3})^{2} + (2*X μGal)^{2}].

Residual error *Station 1* t_{n} = sqrt [(error *Station 1* t_{1})^{2} + (error *Station 1* t_{n})^{2} + (*(n*−*1)**X μGal)^{2}].

X μGal is Propagated Error Uncertainty (i.e., deformation effect).

## 4. Interpretation techniques

In general, we have three categories of interpretation techniques of gravity data: (1) gradient interpretation techniques based on the derivatives of the gravity field, (2) forward modeling of gravity data, and (3) inversion techniques of gravity data in 2D and 3D.

There are many gravity gradient methods developed for detecting fault structures, intrusive high-density bodies, and geological boundaries. Each technique has some advantages for specific geological investigations. In **Table 2**, we summarized these methods, which are very powerful for investigating geological structures as applied to real gravity field data [18, 19, 20, 21, 22].

Method | Equation | Reference | Advantages |
---|---|---|---|

Analytic signal | [27] | ||

Tilt derivative | [28] | Useful in enhancing and sharpening the potential field anomalies. The zero contour line located on or close to a contact. | |

Horizontal gradient | [29] | Least susceptible to noise in the data because it requires only the calculation of the two first-order horizontal derivatives of the field. The method is also robust in delineating both shallow and deep sources. | |

Euler deconvolution | [30] | Assign structural index (0 for fault, 1 for contact, and 2 for a sphere) Help us in detecting linear fault structures and their depths |

For 2D and 3D modeling and inversion techniques using gravity data, there are many available computer codes and also computer software developed by commercial companies. For more details about these inversion methods and computer codes, you can check these publications [23, 24, 25, 26].

## 5. Gravity gradiometry

In the last decade, there has been a new way of measuring gravity developed, not only one component as previous conventional gravity field in the vertical direction g_{z,} but also full tensor gravity gradiometry for all components of the gravity as shown in **Figure 40**. This feature makes the gravity gradient anomaly more localized to the geological source than the gravity anomaly.

## 6. Gravity data and software

There are many computer programs and codes (**Table 3**) developed by commercial companies or university researchers for gravity data analysis (data filters, data preprocessing, 2D/3D modeling, and 2D/3D inversion).

Software/Code | Link (website) | Capability |
---|---|---|

PyGMI | http://patrick-cole.github.io/pygmi/index.html# | 3D gravity modeling |

International Gravimetric Bureau | http://bgi.omp.obs-mip.fr/data-products/Gravity-Databases/Land-Gravity-data | Land and marine gravity data |

Fatiando a terra | http://www.fatiando.org/dev/index.html | Modeling and inversion of gravity data |

UBC Geophysical Inversion Facility | https://gif.eos.ubc.ca/software/main_programs | Modeling and inversion of gravity data |

Geosoft Oasis Montaj | http://www.geosoft.com/products/oasis-montaj | Modeling and inversion of gravity data |

Petrel, Gravity Magnetic Modeling and Inversion plug-in (Schlumberger) | https://www.ocean.slb.com/en/plug-ins/plugindetails?ProductId=PGDM-B1 | Modeling and inversion of gravity data |

## 7. Conclusions

This chapter summarizes in general from the basics of gravity to instruments used for gravity measurement, gravity corrections, and applications of the gravity method in geosciences. As we stated, gravity is used in many fields of geosciences (geology, structural geology, natural resource exploration, mineral resources, volcanology, geothermal, hydrogeology, CO_{2} sequestration, ground cavities, and so).

With the recent development of new gravimeters and availability of satellite gravity data (such as GRACE), the gravity method will be applied in many other new fields for monitoring and estimation of mass changes underground at regional scales (e.g., regional intercontinental aquifers). Also integration and coupling of gravity with other geophysical methods such as magnetics, electromagnetics, seismic and satellite radar such as InSAR will help us increase the accuracy of our geological models and decrease uncertainties in seismic and to help us construct robust geomechanical model for underground oil and gas reservoirs.

Finally, the development of computers and application of robust numerical techniques will certainly help geoscientists to construct near-real geological models.