Principles and Practice of Gravity and Magnetic Methods in Geological Studies

By DC Mishra

Contents
1.    Introduction
2.    Gravity Method
3.    Magnetic Methods
4.    Common Data Processing Methods and Parameter Estimation – Digital Signal Processing

• Language: English
• Publisher: BSP BOOKS
• Release date: Feb 2, 2021
• ISBN: 9789389974249

Book preview

1

Introduction

Geophysics is the study of the earth, based on the principles and laws of physics. The study of the earth, based on the laws of the gravity and the magnetic fields, is known as the gravity and the magnetic methods of geophysical exploration. They are known as the natural methods as they employ the natural fields, namely, the gravity and the magnetic fields of the earth. Contrary to them, there are methods which employ artificial fields created specially for those surveys in an area such as electrical and seismic methods. As the gravity and the magnetic methods employ natural fields of the earth, they are the oldest geophysical methods used for the study of the earth and are easy to operate and cost effective compared to the other geophysical methods. Therefore, they are ideally suited for reconnaissance survey of large areas to limit the areas for detailed investigations. The gravity and the magnetic methods being directly related to the physical properties of the rocks, namely, the density and the susceptibility, respectively they are found to be very useful by field geologists and geophysicists in mapping and identification of various rock types. They are also used for direct detection of minerals with large contrast in density and susceptibility compared to country rock.

The earth has its own gravity and the magnetic fields, which gets modified in the presence of rocks of different properties. The earth's natural field F1 gets modified to F2 near a structure (Fig. 1.1) or anomalous body depending on its shape, size, depth and the physical properties like density or susceptibility in case of gravity and magnetic methods, respectively. The differences between the two fields (F2 - F1) is known as geophysical anomaly, namely, the gravity anomaly or the magnetic anomaly in the two cases. It depends on the configuration of the body, depth and physical properties of the causative sources. These fields are measured with the help of sensitive instruments at the surface of the earth or using different platforms, for example ship, helicopter, aeroplane and satellite depending on the target, their size, desired accuracy of the survey and accessibility to the survey area. The data is processed to obtain the gravity and the magnetic anomalies with respect to the ground position, which, in turn, are related to the surface or subsurface rocks, structures and their physical properties. The two most important characteristics of the anomalies are their spatial size and magnitude, which are popularly referred to as wavelength and amplitude, respectively. Broadly, the geological studies for which the gravity and magnetic methods have shown promise, are as follows:

Fig. 1.1 F1 is the normal earth’s gravity/magnetic fields which get modified to F2 in the vicinity of sub-surface anomalous bodies or heterogeneity. (F2-F1) is known as gravity/magnetic anomaly which depend on shape, size, depth and physical parameters, namely, density/ susceptibility of the anomalous body which can be derived from the observed/ measured anomaly.

1.1 Geological Studies and Gravity and Magnetic Methods

Gravity and magnetic methods are related to variations in density and susceptibility of rocks, respectively and produces complimentary images of structures which are integrated to provide their details. In fact, they are also integrated with all other available data sets to map subsurface structures. Their applications to various geoscientific studies are briefly described below while their detailed applications integrated with other geophysical - geological data sets are discussed and demonstrated in the forthcoming chapters.

1.1.1 Geodynamics and Plate Tectonics

Since 1912, when Alfred Wegener proposed the theory of continental drift that has explained several geological observations in a unified manner, it therefore, formed one of the most important aspects of geodynamics. However, it did not account for the forces responsible for drifting of the continents and was therefore, replaced by plate tectonics during 1960s, which accounted for these forces due to mantle convection (Uyeda, 1978).

Plate tectonics is presently one of the most important aspects of global geodynamics. Gravity and magnetic methods are used to study the different aspects of geodynamics and plate tectonics of a region. Some of their applications in this regard can be briefly described as follows. However, there are several other applications of geophysical methods in general and gravity and magnetic methods, in particular, that are outlined in the forthcoming chapters.

(i) Plate Tectonics

Plate tectonic theory provides a unified model to explain most of the tectonic processes observed on the surface of the earth and subsurface. It is briefly outlined here to introduce this topic that is essential to discuss gravity and magnetic anomalies due to its certain aspects in Chapters 2 and 3, respectively. Plates may consist of both continental and oceanic parts representing both continental and oceanic lithospheres. It shows some major and some minor plates which are separated by ridges and subduction zones referred to as divergent and convergent plate boundaries where different plates diverge and converge, respectively. Some important mid-oceanic ridge systems are Mid-Atlantic Ridge, Indian Ocean Ridge system, East Pacific Rise etc., named after the oceans they occupy. Collision and subduction zones are found on other side of the plate accompanied by fold belts on continents and trenches in oceans, respectively. Such as besides these two features, the third important element is known as Transform faults, which are similar to strike slip faults along which the two plates slip past each other. San Andreas Transform fault system along west coast of USA. Chamman fault in Pakistan (CH; Fig. 5.13) related to Pakistan Fold Belt between the Indian and the Eurasian plates is an example of transform fault related to the Indian plate.

Mid oceanic ridges are linear features where volcanic rocks wells up from inside the earth and spreads over the ocean bottom forming the ridges, which diverge the plates on either sides and are therefore known as divergent margins (Fig. 1.2). Mid oceanic ridges are, therefore characterized by mafic volcanic rocks and magnetic profiles across them show normal and reverse polarity of rocks located almost symmetric with respect to the ridge. These are known as sea floor spreading magnetic anomalies and their polarity indicate the polarity of earth’s magnetic field at the time of their formation. On the other hand, along convergent margins plates on the surface of the earth converge and collide and in the process, one subducts under the other and is therefore known as subduction zones (Fig. 1.2). As shown in this figure, magma erupts and spreads at Mid Oceanic Ridges and pushes the oceanic lithosphere on either side as indicated by arrows. Once the oceanic lithosphere encounters a continental shelf as shown on either margins of this figure, it subducts below the continental crust as it is comparatively heavier (higher density) than the latter. The contact of the two is characterized by deepest parts of the ocean known as trenches where deep basins are formed. During its movement, it may encounter some localized sources of magma such as plume which may give raise to chains of volcanoes that are known as sea mounts in case of oceans. Once the zig saw puzzle of sea floor spreading magnetic anomalies were sorted out and continents were brought back in time, they appeared to join together. This gave rise to plate tectonic theory, which in most simple form suggests that the earth is made up of several plates, which move and collide with each other and on collision, form the mountain chains and depending on the density of rock types subduct one under the other. They are chanacterized by seismic actiurty due to intense tectonic activities at plate boundaries.

Fig. 1.2 A schematic section of Mid Oceanic Ridge where two plates diverge due to intrusion of magmatic material from asthenosphere forming oceanic crust. During plate motion, they encounter continental shelf where they would subside due to their higher density compared to continental crust. The subducted material melts at the depth giving rise to volcanic arcs. During plate motion, it may encounter plumes giving rise to volcanic chains.

Based on direction of forces in two cases, viz. mid oceanic ridges and subduction zones (Fig. 1.2), the tectonics related to them are termed as extensional and convergence tectonics. The subducted material at certain depth, melts due to frictional heat and high temperature to give rise to magma, which rises through fractures and faults giving rise to volcanic chains known as island arcs or magmatic arcs. However, in case of collision between two continental plates, such as Indian -Eurasian plates, the rocks are deformed as both are of almost same density. In such cases, the upper part of the crust forms the mountain chain through thrusting and folding, while its lower part slips one under the other causing thick crust and several related tectonic activities like earthquakes, volcanoes etc., Due to weight of the overriding plate, the subducting plate flexes and causes bulging of the subducting plate as it happens in case of cantilever beams in civil engineering (Fig. 1.2). This implies that while material is generated at mid oceanic ridges from within the earth, it is consumed at plate boundaries during subduction providing a mass balance in earth’s system. Plate tectonics is important not only for tectonics and geodynamics but is also important for resource exploration. Most of the mineralized sections of base metals, precious metals (gold), chromites etc., occur along fold belts (mountains) that are formed due to collision of two plates as shown in Fig 1.2. In this regard, ancient fold belts of Archean- Proterozoic period (Appendix I) assume special significance. It is also important for hydrocarbon exploration as most of the sedimentary basins are formed along fold belts (Fig 1.2) or along rifted margins that are essential elements of plate tectonics.

They are characterized by specific features which produce typical gravity and magnetic anomalies as discussed in sections 2.9 and 3.8 respectively. Gravity and magnetic methods used for various applications in plate tectonics are briefly as follows:

(a) Reconstruction of continents and their movement during different geological periods based on direction of magnetization and seafloor spreading magnetic anomalies.

(b) Crustal structures and physical properties of rocks (density and susceptibility) with depth.

(c) Continuation of large-scale structures from one continent to the other before their breakup based on their gravity and magnetic signatures.

(d) Mantle dynamics related to plate tectonics based on satellite gravity anomalies.

(ii) Crustal Structures

The top most layer of the earth is known as crust. Its structure and composition plays a vital role in geodynamics of a region. Gravity and magnetic methods are extremely useful for crustal studies, which can be summarized as follows:

(a) Delineation of deep seated structures in the upper mantle and the crust and their physical properties, viz density and susceptibility.

(b) Variation in the crustal thickness (depth to Moho) based on gravity anomalies.

(c) Curie point geotherm based on magnetic data, which is defined as the temperature beyond which magnetization in rocks cannot exist. It is equivalent to the Curie point of magnetite equal to 570o C. In some sections, it may coincide with Moho or may be deeper or shallower depending on heat flow in the region.

(d) Compensation of surface load and rheological properties of the crust and the lithosphere based on isostasy such as elastic thickness, flexural rigidity etc., based on gravity anomalies and topography which is described in Chapter 4.

(iii) Plume Tectonics

Plumes are large bodies of gaseous and fluids, which rise from inside the earth (Fig. 1.2) and give rise to large scale volcanic provinces in different parts of the world such as Deccan trap and Rajmahal trap in India, Karoo volcanics in Africa, Columbia flood basalt in USA and islands of Reunion, Kerguelen etc. Due to their high density and high susceptibility, gravity and magnetic methods are widely used for their studies, which are as follows:

(a) Delineation and demarcation of plume affected surface/subsurface regions

(b) Assessment of their physical properties like bulk density and bulk susceptibility and based on them identification of rock types.

2

Gravity Method

2.1 Introduction

Gravity method of the geophysical exploration depends on Newton’s laws of gravitational force, which states that two masses attract each other depending on their mass and distance between them. The earth itself being a body of large mass, attracts all other bodies, which depends on their mass and the mass of the earth. The attraction due to the earth is called the gravity field of the earth and is one of the primary forces in nature. Depending on the latitude, every point on the surface of the earth is characterized by a normal value of the gravity field. The deviation of the earth’s gravity field from its normal value is known as gravity anomaly at that place which is related to the rock mass surrounding it and in turn is related to the density of the rocks. In actual practice, instead of measuring absolute value of the earth's gravity field, which is a cumbersome process, the variation in the gravity field from one point to the other is measured, which is known as gravity anomaly. The variations in the gravity field of the earth are related to the variations in the density of the surface/subsurface rocks, which can be derived through application of this method.

2.2 Basic Principles

2.2.1 Forces of Gravity

Gravity is defined as the mutual attractive force between two masses. According to Newton’s law of gravitation, the force of attraction between two masses m1 and m2 separated by distance r is given by (Fig. 2.1):

Fig. 2.1 m1 and m2 are two masses separated by a distance r.

Where r1 is a unit vector directed from m1 to m2 and - sign indicates that it is always attracted.

In C.G.S. units, F is in dynes, m in grams and r in centimeters. G is known as the gravitational constant and is given by G = 6.67 × 10-9 CGS units (dyne - cm²/g²) which is the force in dyne exerted between two masses of 1 gm each with their centers one cm apart.

In a simple form, equation (2.1) can be rewritten as:

2.2.2 Gravitational Potential and Laplace Equation

Potential is defined as the work done in moving a unit mass from infinity to its present position at distance r from the reference point. Therefore, the gravitational potential u is given by:

Substituting for F from equation (2.2) for m1 = m and m2 = 1. As per convention potential is always positive and therefore:

Similarly a force is defined as the derivative of potential with respect to distance. Therefore, as u is the gravitational potential, the gravitational force F is given by

Substituting for u in equation (2.5)

This is similar to equation (2.2) which suggest that potential and field are interchangeable. Gravity field of the earth being vertical in nature, it can be referred as:

where p is the gravitational potential and z is the vertical direction directed downwards. The components of the gravitational attraction in horizontal directions x and y is given by:

These three components of gravitational field satisfy a unique relationship as:

where ρ is the density of the body. This is known as Poisson’s equation which reduces to Laplace equation for ρ = 0, in a source free space. Therefore,

Laplace equation is therefore, a special case of Poisson’s equation in source free space where ρ = 0.

Magnetic field and magnetic potential discussed in Chapter 3 also satisfy the Laplace equation and hence gravity and magnetic fields are known as potential fields. In simplified 2-dimensional form equation (2.10) can be written as:

Solving equation (2.11) for a particular solution of type:

Substituting for u in equation (2.11)

where                         

Equation (2.13) can be written as:

This suggest a pair of solution as

where k is a constant which may be real, imaginary or complex.

The two solutions (2.15) and (2.16) can be combined as:

A more general solution can be written as sum of all possible constants as:

Equation (2.18) is the basis of representing potential field data as exponential functions which is the basis to apply modern signal processing techniques (Spectral method) as discussed in Chapter 4.

2.2.3 Gravitational Acceleration (g)

The force exerted on a mass at the earth's surface due to the attraction of the earth is known as the earth’s gravitational force (F). Therefore, if the mass of a body is m and that of the earth is me and R is the radius of the earth, the force of attraction between them is given by equation (2.2) as:

This force will produce an acceleration, g and according to Newton's second law of motion, force is the product of mass and acceleration. Therefore,

where g is gravitational acceleration or acceleration due to the gravity field of the earth. From equations (2.19) and (2.20)

g is force per unit mass which is equivalent to acceleration and is therefore, expressed as cm/s². In geophysical literature, it is called Gal after the famous physicist Galileo who first provided the value of g. The value of g at the surface of the earth has been measured and the worldwide average is found to be 980 Gal. Due to variations in the radius of the earth and its rotation, the gravity field changes at the surface of the earth with latitude, the maximum being at the pole and minimum at the Equator with a difference of approximately 5 Gal. The value at the Equator is 978.0318 Gal. Its variation measured from one place to other due to the variation in the density of rocks is very small and therefore, further smaller units as milliGal (mGal) = 10-3 Gal and micro Gal (μ Gal) = 10-6 Gal are used in geophysical prospecting. An intermediate unit as gravity unit (gu) equal to 10-4 gal is also used at some places.

Based on the numerical values of g and G, the mass of the earth (me) can be obtained for an average value of R = 6.37 × 10⁸ cm = 6.37 × 10³ km.

2.2.4 Density of Rocks

Density (ρ) is an intrinsic property of materials, which is defined as mass per unit volume. Therefore, if m is mass and v is the volume:

Its unit is g/cc or g/cm³. A smaller unit of kg/m³ equal to 10-3 g/cm³ is used to describe fine variations in density. Different rocks have different densities, which is the basis of the gravity survey. The most commonly found rock on surface of the earth is granite and gnisses with a density of 2.652.70 g/cm3 (2650-2700 kg∕m³) with an average density of 2.67 g/cm3 (2670 kg/m³). It is considered as the main constituent of the upper crust. The addition of mafic/ultramafic minerals increases the density. In brief, density of sedimentary rocks is less compared to igneous and metamorphic rocks. Table 2.1 presents the average density of important rock units generally found in the field.

A simple way of measuring density is based on Archimedes principle using a special balance. One such balance is known as Walker’s Steel Yard balance. Rock samples are weighed in air (Wa) and water (Ww) which provides density (ρ) as:

Due to heterogeneity present in rocks, their density varies considerably from sample to sample. Therefore, an average representative value for a particular rock type is obtained by measuring densities of several samples from that unit. This is referred to as bulk density of that rock type.

Table 2.1 The densities of some important rock types compiled from different sources:

2.2.5 Variation of Density with Depth

The mass of earth as inferred in equation (2.22) is

If d is the average density of the earth.

where v is the average volume equal to 4/3 π.R³. Substituting for me, v and ρ in equation (2.26)

This is the average density of the earth, which is almost twice the average density (2.70 g/cm³) of rocks exposed at the surface suggesting a general increase in the density of the rocks with depth inside the earth. The density inside the earth cannot be determined directly. It can only be inferred indirectly based on seismic velocities and composition of rocks derived from it at different depths.

Based on the velocities of waves inferred from earthquakes at different depths inside the earth, provided general composition of rocks and structures inside the earth and their densities dividing it into three major parts namely crust, mantle and core, which are further divided into two subdivisions each as lower and upper parts (Fig. 2.2). The differences in the thickness of continental (36-40 km) and oceanic crusts (6-8 km) and respective lithosphere may be noted. This figure shows the Lithosphere-Asthenosphere Boundary (LAB) at a depth of about 150-200 km under continents and about 10-100 km under Oceans, which represent the average depth world over. This is an important boundary for geodynamics defined by 1200-1300oC isotherm as it represents transition from rigid lithosphere to partially molten asthenosphere and therefore convection in the latter drives the lithospheric plates, which is primarily responsible for plate tectonics. Another important aspect of earth’s interior is semi solid mantle, followed by fluid outer core and solid inner core.

Fig. 2.2 Simplified layered structure of earth’s interior under continents and oceans. Thick crust under continents (36 - 38 km) and thin crust under oceans (6- 8 km) are indicated by Mohorovicic discontinuity (MOHO). LAB- Lithosphere-Asthenosphere Boundary separate rigid lithosphere at the top of a partially molten asthenosphere below at a depth of 150-200 km under continents and 80-100 km under oceans.

Based on seismic velocities and inferred composition, density model with depth has been provided by several workers. One such model showing variations in density with depth based on Preliminary Reference Earth Model is reproduced in Fig. 2.3(a) (PREM; Dziewonski and Anderson, 1981). It shows a consistent increase in the density of the rocks from 2.7 g/cm³ at the surface to approximately 3.3 g/cm³ in the upper mantle below the Moho at a depth of about 40 km and small jumps at various discontinuities (200, 400, 670 km, Fig. 2.3(a)). It further increases to 5.9 g/cm³ at the base of the mantle at a depth of 2900 km where it shows a sudden jump of approximately 10.0 g/cm³ in the outer core increasing further downwards to approximately 12.0 g/cm³ at the base of the outer core, beyond which it remained almost constant up to the center of the earth (Fig. 2.3(b)). In fact these discontinuities inside the earth represent changes in seismic velocity, density and composition across them, which have been primarily used to define them. However while dealing with gravity anomalies recorded in gravity surveys the most important section of the earth is the crust and upper mantle, which represent the outer shell of the earth up to Mohoravicic discontinuity referred to as Moho and immediately below it. The Moho lies at an average depth of approximately 36-40 km under continents in relatively plane areas. The crust is generally divided in two equal parts namely upper and lower crust with bulk average densities of 2.7 g/cm³ and 2.9 g/cm³ respectively, which primarily represent felsic (granite and gneisses) and mafic (basalt) compositions, respectively. In fact, the variation of density in crust is continuous and therefore, crust can be divided even in three equal parts for modeling of gravity anomalies with bulk densities of 2.7, 2.8 and 2.9 g/cm³ as the upper, the middle and the lower crusts, respectively. The oceanic crust is primarily mafic in composition and can also be divided in two groups of basalt and sediments upper crust (2-3 km) and mafic/ultramafic (gabbros) lower crust (4-5 km) with bulk average density of 2.7-2.8 and 2.9-3.0 g/cm³, respectively. These are the average values on a worldwide basis, which may differ locally depending on local conditions.

Fig. 2.3 Variation of density in side the earth with depth showing changes at various discontinuities based on Preliminary Reference Earth Model (PREM model, Dziewonski and Anderson, 1981). a) Density changes from surface up to 1000 km showing small changes at crustal and mantle discontinuities. b) Density variation from surface up to core of the earth showing continuous increase with depth with major jumps at mantle- core-inner core boundaries.

2.2.6 Thermal Structure of Lithosphere

Lithosphere and its thermal structure plays an important role in formation of surface tectonics. Further, it is also important to model the observed gravity and magnetic fields at the surface as both these physical properties, viz. density and susceptibility are controlled by temperature distribution. The average picture world over differ considerably from one part to the other depending on the thermal gradient due to heat sources such as plumes, volcanoes, radioactive minerals, etc., In general, the thermal gradient under shield is less (10 o-15 o C/km) while it is more under oceanic crust and recent orogenic belts (20-30 o C/km). It also decreases with depth due to presence of radioactive element in the upper part of the continental crust. Temperature distribution in crust and upper mantle is also important to understand the magnetization distribution depending on Curie point geothern (Section 3.2.2) that is important to model magnetic anomalies (Chapter 3).

2.2.7 Density - Velocity Relationship

Propagation of seismic waves in rocks depends on the their physical properties including density and therefore, based on laboratory measurements of seismic velocities and densities of different rock types, several workers have provided empirical relationships between them, which can be used to infer density of rocks in case seismic velocities are known. Barton (1986) provided the relationship between the two parameters as given in Fig. 2.4, which shows a considerable scatter. However, the average values provided by solid line can be safely taken as representing the variation in bulk density with velocity. In general, the seismic velocity increases with depth inside the earth and thereby density also increases with depth. However, in certain sections in crust and upper mantle, the seismic velocities may decrease with depth and will be lower compared to the average value at those depths. Such zones are known as low velocity zones (LVZ) and correspondingly density also decreases in those sections, which have special significance for composition and geodynamics of those regions. Similarly, in certain parts of crust, the velocity and the density may be more compared to the worldwide average value, which are known as High Velocity Zones (HVZ) as is the case with volcanic provinces.

Fig. 2.4 Empirical relation between P-wave velocity (V) and density of rocks (Barton, 1986) which increases as velocity increases.

2.2.8 Variation of Earth’s Gravity Field with Depth

The gravity field inside the earth is function of both density and pressure. The variation of gravity field and pressure inside the earth is given in Fig. 2.5. The gravity field remains almost constant up to the base of the lower mantle and then decreases fast to zero at the centre of the earth while pressure increases from surface downwards up to the centre of the earth where it is maximum (Dziewonski and Anderson, 1981). The decrease in the earth's gravity field in the earth’s core is attributed to the high pressure.

Fig. 2.5 Variation of gravity and pressure in side the earth with depth. Due to large pressure, gravity decreases with depth in core (PREM model; Dziewonski and Anderson, 1981).

2.2.9 Earth’s Shape and Geoid

The earth’s surface is approximated by an ellipsoid described by equation (2.35). It is a mathematical surface, which fits best with the earth’s surface with out any undulations. It is therefore, an imaginary surface over oceans and under continents, which earth will assume if all oceans are filled and elevated lands are removed (Fig. 2.6(a)). It is a close approximation to an equipotential surface such that the earth's gravity field is normal to this surface and plumb line is vertical at every point. However, it is far from existing situation and the earth surface is undulating along with the surface/subsurface mass in homogeneity. Therefore, another equipotential surface, geoid is defined as an average sea surface over the oceans and under the continents, which is an equipotential surface and warped due to mass deficiency (water column) under the ocean and excess of mass (mountains etc.,) over the continent as shown in Fig. 2.6(a). It is referred to as reference geoid. It is further affected by local subsurface mass in homogeneity in a region (Fig. 2.6(b)). As shown in Fig. 2.6(b), due to subsurface positive mass, the geoid plane will pop up showing a positive anomaly while in case of negative mass, it will sink indicating a negative anomaly. The difference between the mathematical ellipsoid, which approximates the earth surface and the geoid as equipotential surface at a place is known as geoid undulation or geoid anomaly. It has acquired importance in recent years as geoid undulations can be obtained from satellite tracking data and used to infer deep seated density in homogeneity in lithosphere as described in section 2.6.

Fig. 2.6(a) Ellipsoid and geoid with latter being warped up due to surface mass caused by the presence of mountains and oceans. This changes the position of perpendicular line (plumb line) requiring corrections for any geodetic survey.

Fig. 2.6(b) Warping up of geoid due to local buried mass and its effect on local gravity field. Due to the effect of local mass, measured local geoid is different from regional/ reference geoid.

2.3 Instruments and Data Acquisition

2.3.1 Instruments - Gravimeters and Gradiometers

The earliest instrument used for gravity prospecting was the Torsion balance (Heiland, 1946) which was used to measure the horizontal and vertical gradients of the earth’s gravity field. However, it was a cumbersome equipment and required almost 1-2 hours for one measurement compared to 5-10 minutes for a measurement using present day modern gravimeters. Therefore, with time, they became obsolete and presently only modern day gravimeters are used for gravity surveys. There are basically two kinds of gravimeters used for the measurement of the earth’s gravity field, viz (i) Absolute gravimeters and (ii) Variometers. The former measures the absolute value of the earth’s gravity field at a particular place while latter measures the variation in the gravity field from one place to the other, known as gravity anomaly. In geophysical exploration, we are generally interested in gravity anomalies and therefore, the variometers popularly known as gravimeters are primarily used for exploration purposes. The order of variation in-geophysical exploration is measured to an accuracy of 0.01 mGal to 0.001 mGal (one microGal), which require highly sensitive instruments.

(i) Absolute Gravimeters

These instruments are used to obtain the absolute value of the earth’s gravity field at a particular place. There are basically two kinds of absolute gravimeters viz pendulums and free fall method. Pendulums based on a weight suspended from a thin fibre are the oldest instruments used for this purpose. It is based on the time taken by a pendulum for a full swing, which is described in any text book on physics for graduate students. The method of free fall is presently used to design modern gravimeters for measurement of absolute value of the gravity field. It has been lately modified to make several free falls of the weight wherein weight is automatically lifted to its original position and allowed to fall and the average time of several falls are used to obtain the gravity filed at that place. This modified version is known as rise and fall method.

(a) Rise and Fall Method

It measures the time taken by a mass to fall for a known distance in a sealed vacuum tube. In such a case the distance d traveled by mass in time t is given by Newton’s law as:

where u is the initial velocity. In case of free fall u = 0

Based on this principle, instruments were designed in which the falling object is again raised to initial position and allowed to fall. In this manner, time taken by object to fall several times are measured and averaged to obtain better accuracy. A Schematic diagram in Fig. 2.7(a) explains its principles (Lowrie, 1997). There are two levels of measurement using a laser source and a detector. The distance