Gravity exploration
2.4 History of the gravity method
these determinations is of the order of several milligals, but
the anomalies must have a wavelength exceeding roughly 15 km to be mapped by the satellite.
In addition, accurate tracking of satellites carrying GPS receivers allows the satellite orbits to be compared to stan- dard Earth orbits to identify orbital deviations that can be analyzed for the Earth’s gravity field variations. Radars on two or more satellites measuring the distances between them as they orbit the Earth yield range rate data that also translate into gravity field variations. Most recently, accelerometers have been deployed in orbit to measure the full gravity tensor. The accuracy of these various satellite systems is on the order of several milligals, but the anomaly resolution is limited by the orbital altitudes above ground surface which typically range between 300 and 550 km.
These measurements are very useful, however, for map- ping large-scale features of the lithosphere that are difficult to study by airborne and shipborne surveying.
Relative gravity observations have been made over much of the accessible land surface of the Earth with gravimeters and over vast areas of the oceans with a combi- nation of satellite-derived measurements and gravimeters mounted in surface ships. Many of these data are available from a wide variety of geophysical data centers. However, for the most part the station interval of the data in these centers limits their use to studies of anomalies covering several kilometers or more. Additional details concerning the measurement of gravity observations are described in Chapter 5.
2.4 History of the gravity method
The effects of gravity have been recognized for millennia and began to be formalized in the third century before the common era with Aristotle’s incorrect assertion that heav- ier objects fall faster than lighter objects. However, he did correctly deduce the basic spherical shape of the Earth from lunar eclipses and other data. In the second century before the common era, the Librarian of Alexandria and father of geodesy, Eratosthenes, accurately measured the Earth’s circumference, and hence its radius and the volume necessary for deducing the density of the Earth from grav- ity observations. The validity of Aristotle’s assertion was questioned by the experiments of John Philoponus in the fifth century of the common era and conclusively rejected by Galileo Galilei’s investigations in the late sixteenth cen- tury. Since the Renaissance there has been an accelerating understanding of gravity and expanded application of it to the study of the interior of the Earth.
The classical history of the gravity method in imag- ing the Earth can be divided into four broad and overlap-
ping periods that largely were initiated by technological developments. The first period (Table 2.2) extended from the beginning of the seventeenth century, near the end of the Renaissance, until the beginning of the twentieth century. During these three centuries, studies of gravity were related to geodetic investigations of the size, shape, mass, and density of the Earth using the newly invented pendulum for measuring gravity. It was during this period that much of the basic theory of gravity and the terrestrial gravity field was described.
At the beginning of the twentieth century, a new period (Table 2.3) of gravity studies was initiated with recognition of the potential of gravity for mapping of the subsurface, especially oil- and gas-bearing structures. The incentive for geophysical exploration of oil and gas drove the devel- opment of high-accuracy, portable instruments for mea- suring relative gravity into the 1950s. Many of the basic concepts of geological mapping with gravity and related interpretational methods were founded in this period.
The third period (Table 2.4), extending from the 1950s through the 1980s, was marked by the rapid increase in computational power and speed available in digital computers, and the improved processing and modeling methodologies made possible by this increased comput- ing power. Also during this period, advances were made in instrumentation for marine and drillhole measurements of gravity capable of an accuracy useful for geologic studies. Since the 1990s and continuing to the present (Table 2.5), the development of accurate surveying and observation of gravity by satellites especially in marine regions, the availability of exploration-grade airborne gravity measurements, and improved methods of conduct- ing independent and joint inversion with other geophysical data of gravity measurements have led to the recent renais- sance in gravity methods.
Numerous publications have described the history of the gravity method of exploring the Earth (e.g.
Eckhardt, 1948; Jakosky, 1950; Sazhina and Grushinsky, 1971;Torge, 1989). A particularly com- prehensive review of its modern development is presented by Nabighian et al. (2005a). The description of the gravity method given below from the Renaissance period to the present and detailed in Tables 2.2, 2.3, 2.4 and 2.5 is largely derived from these references and serves to place the method in a historical context.
As outlined in Table 2.2, current knowledge of gravity began with the work of Galileo Galilei who in roughly 1590 showed that the speed of objects falling in the Earth’s gravitational field are independent of their mass, that they accelerate the longer they fall, and that the distance an object falls is proportional to the square of the elapsed time.
30 The gravity method
TABLE 2.2 Classical gravity milestones I. Development of gravitational theory and geodetic measurements from the seventeenth to early twentieth centuries.
Date Event
1590 Galileo Galileiestablishes the basic principles of the gravity field
1605 J. Keplerdeduces the laws of movement of the planets around the sun based onBrahe’s observations of planetary orbital motion 1657 C. Huygensdevelops pendulum clock and
mathematical theory of the pendulum which showed that gravity acceleration is related to the pendulum’s period
1672 J. Richerdeduces that the change in period of pendulum clock in different places is due to variation in gravity
1687 I. Newtonformulates the universal law of gravitation and that the source of gravity of the Earth is the result of the Earth’s mass and rotation
1735–1743 The first relative measurements of gravity;
P. Bouguerdevelops the gravity correction for the height of an observation relative to sea level
1743 A. C. Clairautpublishes a theorem that permits the determination of geometric parameters of the Earth’s figure from gravity data and vice versa
1797 H. Cavendishmeasures the gravitational constant “bigG” with high accuracy 1775–1850 J. L. Lagrange, P. S. Laplace, A. M.
Legendre, C. F. Gauss, S. D. Poisson, and G.Greendevelop the classical theory of potential fields
1854 G. Stokesdescribes a theorem that shows there is no unique solution to the inverse problem of potential fields and the geoid can be determined from global gravity 1855 G. B. AiryandJ. H. Prattgive geological
models for how regional terres- trial topographic features are in hydrostatic equilibrium in accordance withG. Everest’s measurements of the deflection of the vertical in India in the 1850s
1889 C. E. Duttoncoins the termisostasyto describe the hydrostatic equilib- rium condition of mountains, basins, and other crustal features with considerable relief
Although his observations are often related to experiments conducted from the famed leaning tower of Pisa, Italy, they were actually made from observing the movement of objects sliding on an inclined plane, which permitted greater accuracy in the measurement of time than in a free fall. He used the pulse rate of his heart and those of his assistants to establish the travel-times of moving objects in his experiments. Galilei also discovered that the period of a pendulum is a function only of its length and probably made the first measurement of gravity.
Building on Galilei’s work and Johannes Kepler’s observations of the movements of the planets around the Sun, Isaac Newton in the latter part of the seventeenth cen- tury formulated the law of universal gravitation, the famed inverse square law. Newton described his studies in a 1687 publication which showed that gravity is produced by the attraction of the Earth’s mass and the centrifugal force due to the Earth’s rotation, and that weight is the effect resulting from gravity. His theory is applicable across the universe at all scales. He also suggested that the equatorial bulge due to the Earth’s rotation accounted for latitudi- nal differences in gravity as measured by pendulums and that gravity increases from the equator to the poles as the square of the sine of latitude.
A fundamental aspect of Newton’s formulation is that the force of attraction between masses, such as the Sun and its planets, is a function of a proportionality constant, the gravitational constant. Although Newton had to approxi- mate this value, Henry Cavendish roughly a century later (around 1797) used torsion balance measurements to deter- mine the constant to within 1% of the currently accepted value. With bigGdetermined, gravity measurements or littlegcould be evaluated for the mass of the Earth via the extension of Newton’s Second Law in Equation 2.5.
Dividing the Earth’s mass by its volume as obtained from Eratosthenes’ observations showed that the mean density of the Earth is about 5500 kg/m3, which is roughly twice the average density of the rocks at the surface. Thus, the density clearly must increase with depth, which is also consistent with a mass-differentiated Earth involving crustal, mantle, and core components of increasing densi- ties (Figure 1.1).
Building upon Galilei’s studies, Christian Huygens in the seventeenth century developed the mathematical the- ory of the pendulum and built the first pendulum clock which led to the discovery that gravity varies over the Earth’s surface. Jean Richer in the 1670s, upon moving a pendulum clock from Paris, France to French Guinea in South America, found that the clock had lost about 2.5 minutes per day. Richer correctly deduced that this change was due to variation in gravity as predicted by the
2.4 History of the gravity method 31 pendulum law of Galilei and resulted from the change in
latitude from Paris to near the equator.
The first relative gravity measurements were made dur- ing the French expedition to Peru from 1735 to 1743 to determine the shape of the Earth. It was this study together with the results of a complementary expedition to Lapland that showed a degree of latitude decreases in length from the equator to the poles, proving that the shape is that of an oblate spheroid, that is, the equatorial radius of the Earth is roughly 21 km greater than the polar radius. It was during this expedition that Pierre Bouguer developed the gravity correction for the mass effect of the ground defined by the height of the observation relative to sea level.
Continuing gravity observations were made into the nineteenth century primarily for the purposes of deter- mining the gravitational constant and the mass and mean density of the Earth. The reversible pendulum for making relatively accurate gravity measurements was developed by H. Kater in 1819, and it was improved with the devel- opment of the invariable pendulum which measures the relative gravity change from a base station. The pendulum with various modifications to minimize errors and improve the timing of the pendulum swings was used for relative gravity measurements until around 1930 and for absolute measurements until the 1970s when free-fall instrumenta- tion displaced it.
In the mid-eighteenth century, A. C. Clairaut published his now widely used theorem that permits the determina- tion of geometric parameters of the Earth’s figure from gravity data and vice versa. During the latter part of the eighteenth and into the early nineteenth century, classical mathematical studies on potential fields by J. L. Lagrange, P. S. Laplace, A. M. Legendre, S. D. Poisson, C. F. Gauss, and G. Green led to the theoretical foundations of both the gravity and magnetic methods. In the mid-nineteenth century, G. Stokes showed that there was no unique solu- tion to the inverse problem of potential fields, and that the flattening of the Earth’s ellipsoid and the deviation of the best fitting equipotential surface, the geoid, can be deter- mined from the global gravity. His theorem, which relates the shape of the Earth and gravity, led to campaigns to measure gravity over the Earth’s surface.
In the railroad surveys of India, G. Everest observed increasing closure errors as the surveys approached the Himalaya Mountains. He deduced that the mountains involved mass deficits which affected the plumb bobs in the surveying instruments to cause the erroneous deflections of the vertical. This confirmed the speculation by Leonardo da Vinci that terrestrial topographic features tend to be in hydrostatic equilibrium. C. F. Dutton in 1889 coined the term isostasy for this effect that describes the hydro-
static equilibrium of the Earth at some level by changes in subsurface masses despite the variation in the eleva- tion of the Earth’s surface. G. B. Airy and J. H. Pratt in 1855 described quite different, but equally plausible explanations for this phenomenon. Airy proposed that the mountains were of constant density but had roots. Pratt proposed that the mountains were less dense the higher they were. This prompted a variety of geophysical stud- ies to determine which theory was valid. During the early part of the twentieth century, J. F. Hayford, W. Bowie and others made extensive gravity observations to investigate the relationship between surface topography and the iso- static state of the Earth. This initiated the use of gravity for geological purposes.
Despite the continued use of pendulums for measuring gravity through the nineteenth century, increasing atten- tion was devoted to develop more efficient, portable, and accurate methods of measuring gravity in the latter part of the nineteenth century and into the twentieth century (Table 2.3). The work of R. von E¨otv¨os at the turn of the century in developing the portable double-beam torsion balance which measures gradients of gravity is notable.
Studies in the first decade of the twentieth century showed that gravity measurements could be used to study subsur- face features. In 1915, J. Fekete and D. P´ekar conducted the first practical torsion balance survey over the Egbell oilfield in Czechoslovakia and in 1917, H. V. Boeckh explained why geological structures such as salt domes and anticlines have associated gravity anomalies. At the end of World War I, H. Shweydar performed a torsion bal- ance survey in petroleum exploration at the site of a salt dome in northern Germany. He also developed schemes for calculating and removing topographic effects from gravity observations. These surveys continued in north- ern Germany. As part of post World War I reparations, in 1922 Everett Lee De Golyer brought the torsion bal- ance to the Gulf Coast region of the United States where a positive anomaly was found associated with the cap rock of the Spindletop dome in Texas. Drilling in 1924 on an anomaly mapped by the torsion balance that is associated with the Nash dome in Texas discovered the first petroleum in America by geophysical methods. The torsion balance led to several other discoveries, but by 1940 it was entirely replaced by gravimeters.
During the 1920s, there was intense interest in improv- ing the accuracy and ease of gravity measurements, driven by the potential of the gravity method in petroleum explo- ration. This led to the development and greatly expanded use of gravimeters of a variety of designs, but generally based on variation in the length of a spring. It was also during this time that the gal was first used in Germany as
32 The gravity method
TABLE 2.3 Classical gravity milestones II. Development of gravity for mapping the subsurface from the early twentieth century into the 1950s.
Date Event
1900 Development of gravimeters for measuring gravity field commences
1902 R. von E¨otv¨osdevelops the double-beam torsion balance for measuring gravity gradients and conducts first survey in Hungary
1915 J. FeketeandD. P´ekarconduct torsion balance survey over Egbell oilfield
1917 H. V. Boeckhexplains why
geological structures in sedimentary basins have associated gravity anomalies
1922 H. Schweydarperforms torsion balance survey over a salt dome and develops schemes for removing topographic effects from gravity observations
1922 Torsion balance brought to USA where a positive gravity anomaly is map- ped, associated with the cap rock of the Spindletop dome in Texas
1920–1930s Intense interest in improving the ease and accuracy of gravity measurements leading to development and greatly expanded use of gravi meters based on various designs, but generally on the measurement of the length of a spring holding a constant mass.
Gravimeters replace torsion balances for measuring gravity by 1940
1920s F. A. Vening Meineszmodifies the pendulum for obtaining geologically usable gravity observations at sea 1924 Drilling on an anomaly mapped by the
torsion balance associated with the Nash Dome in Texas produces probably the first petroleum in the USA discovered by geophysical methods
1928 First use of gal for the CGS-unit of gravity acceleration, with international acceptance of unit in 1930. Standard data reductions for pendulum and gravimeter data discussed byM. K. HubbertandF. A.
Melton, and expanded byS. Hammer, L. L. Nettleton, and others
1930–1935 Portable pendulum used in exploration for measuring relative gravity
TABLE 2.3 (cont.)
Date Event
1934 L. J. B. LaCostedevelops the zero-length spring principle which obtains the highest accuracy measurements in any relative gravimeters
1940s S. Wordenincorporates universal temperature compensation into quartz spring gravimeters which achieve high accuracy without external power supply 1940–1950s Gravimeter in wide use in oil and gas
exploration and introduced in mineral exploration
1949 L. L. Peterspublishes methodology for enhancing potential field data useful in interpretation
a unit of gravity acceleration and subsequently accepted internationally (1930). Standard data reduction procedures for pendulum and gravimeter observations were discussed by M. K. Hubbert and F. A. Melton in 1928 and were expanded upon by S. Hammer, L. L. Nettleton, and oth- ers. It was also during the 1920s that F. A. Vening Meinesz modified the pendulum to achieve geologically usable gravity observations at sea, although O. Hecker had made a few hundred gravity observations in the major oceans prior to this, during the period from 1901 to 1909, that showed the oceans to be in isostatic equilibrium except for deep-sea trenches of the Pacific Ocean.
In 1934, L. J. B. LaCoste developed the principle of the zero-length spring which opened the way for greater accuracy in relative gravity measurements. Subsequent development of gravimeters based on this principle has led to the majority of gravimeters used today for land, sea, and air observations. L. M. and F. W. Mott-Smith were among the first to take advantage of the excellent mechanical and thermal properties of quartz in building a gravimeter. By 1945, gravity was being used extensively in petroleum exploration as evidenced by the peak of 170 crews observing gravity in the USA alone. The use of quartz elements in gravimeters was expanded after World War II by S. Worden to include temperature compensation which permitted high-accuracy measurements without an external power supply. The resulting meter and its deriva- tives are very portable, and thus widely used in many gravity applications today. G. P. Woollard showed that this meter could be used for making accurate observations over a wide range of values, and thus could be used for
2.4 History of the gravity method 33 geodetic as well as exploration purposes. Additionally,
these meters and gravimeters capable of 0.001 mGal accu- racy have found significant uses in mineral exploration, engineering, and environmental studies. Woollard also was responsible for popularizing gravity as a useful method of studying regional geological features during and after World War II. L. J. Peters in 1949 described methods of enhancing magnetic anomaly data in the space domain which can also be used for gravity anomaly data.
Although gravity measurements were made at sea after World War II using modified land gravimeters set on the sea floor or on surface vessels using a variety of specially designed instruments, it was the introduction during the 1960s of the gyrostabilized platform that led to extensive measurements at sea. Modified land gravimeters are placed on this platform, which eliminates longer-wavelength (period) accelerations associated with the movement of the meter from gravity observations. Similar instruments were successfully used from the early 1980s in aircraft for exploration purposes. The availability of the Global Posi- tioning System for positioning of gravity measurements on land, sea, and air since the 1990s has greatly improved the accuracy and efficiency of gravity measurements.
The ready availability of digital computers and their continuing improvements since the 1950s have led to many computational improvements in the processing and inter- pretation of gravity anomaly data and, during roughly the past decade, in the presentation of anomaly data (Table 2.4). Use of the Fourier transform in potential field analysis byDean (1958) and others, the compu- tation of gravity effects from arbitrarily shaped two- and three-dimensional sources by Talwani et al. (1959), TalwaniandEwing(1960), andParker(1974), and inversion techniques of interpretation by Bott (1960), Corbato(1965), Oldenburg (1974), Li and Old- enburg (1998a) and others brought notable improve- ments in gravity data applications. In addition, druing this period the development of Geographic Information Sys- tems (GIS) enabled interpreters to view and analyze mul- tiple data sets in a synergistic manner.
The global coverage of gravity measurements has markedly increased with the use of artificial Earth satellites (Table 2.5). The observation and analysis of satellite orbits as early as 1958 were used to establish long-wavelength components of the Earth’s field to a greater accuracy than given by surface observations. The number and sophisti- cation of satellites, some designed especially for potential field studies, increased the accuracy of the results and the spectrum of gravity anomalies that can be mapped from satellites. Of particular note are the satellite altimetry stud- ies of the ocean surface beginning in the late 1990s by
TABLE 2.4 Classical gravity milestones III. Development of improved computer data processing and modeling capabilities from the 1950s through the 1980s.
Date Event
1958 W. C. Deanpublishes filter theory for potential fields in frequency domain
1959 M. Talwaniand others develop algorithms for calculating the gravity effect of 2D bodies of arbitrary shape and in 1960M. Talwani and M. Ewingpublish modeling algorithms for the gravity effects of 3Dbodies of arbitrary shape 1960 M. H. P. Bottpublishes a method for
interpretation of gravity data by inversion 1960s Development of the gyrostablized gravity meter
make possible explora- tion grade gravity measurements from a moving platform 1965 C. E. Corbat´opublishes a method of linearizing
nonlinear inversion of 2D bodies of arbitrary shape
1970s Geographic information system (GIS) technology applied to potential field analysis 1972 R. W. Parkeruses Fourier transforms to
calculate gravity anomalies from complex bodies
1972 First gravity measurements on the surface of the Moon
1974 D. W. OldenburgmodifiesParker’sFourier transform method of forward modeling to inversion of gravity data
1977 Airborne gravity measurements used in oil and gas exploration
1978 Free-air gravity anomalies of the global oceans mapped from Seasat and subsequent satellite altimetry missions
Sandwell andSmith(1997) with observations from the Geosat and ERS-1 and ERS-2 satellites that are capable of mapping marine gravity anomalies greater than roughly 15 km in minimum dimension. The GRACE satellite is particularly noteworthy in measuring temporal variations in gravity such as those caused by changes in the water stored in surface water basins and ice in the great ice sheets of Greenland and Antarctica.
Further significant developments in gravity over the past decade are the use of inertial accelerometers for mea- suring the gravity tensor which is finding increased use in gravity interpretation. Airborne gravity gradiometers are being used routinely in exploration, and the GOCE