LIMESTONE POROSITY
5.3 Measuring gravity
5.2 Introduction
The acquisition of gravity data, which is relatively simple in principle, is based on determining the gravity force field acting on a test mass within the instrument. This can be accomplished in a number of different ways, from drop- ping the test mass in free fall, to pendulums, to the down- ward force of the test mass measured by a spring, to elec- tromagnetic accelerometers. The accuracy and horizontal spatial resolution requirements of gravity used in the study of the Earth are high, and thus care must be exercised in selection of survey instrumentation, design of the investi- gation, and the procedures used in data acquisition. Most geological studies require an accuracy of 10−6to 10−8of the surface gravity (1 to 0.01 mGal), while measurements for many shallow-zone investigations and the mapping of time variations in the Earth’s gravity field associated with subsurface migration of fluids and elevation changes seek accuracies at the 10−9(0.001 mGal or 1μGal) level. These sensitivity requirements are among the most stringent encountered in scientific studies, making gravity instru- mentation among the most sensitive mechanical devices humans have produced. As a result of the specialized instrumentation, great care must be employed in making the measurements and adjusting them for use in subsurface interpretation. This is especially true in high-resolution surveys where the station interval is measured in meters or tens of meters, and sensitivities at the microgal level are required.
In addition to the accuracy of measurements, horizontal spatial resolution, which is the minimum separation that permits recognition of adjacent individual sources, is an important consideration because it determines the smallest features that can be identified in a survey. Resolution in gravity data is commonly expressed in terms of the min- imum half-wavelength that can be readily mapped in a survey provided the amplitude of the signal exceeds the accuracy limits of the observations and reductions. Reso- lution is a function of the measurement interval, either real or virtual. In land-based measurements it is specified by the actual data interval which can be adjusted to the objec- tives of the survey. However, for measurements made on a moving platform such as marine vessels, aircraft, and satellites, the resolution is not necessarily determined by the measurement interval, but rather by a virtual interval established by the requirements for filtering over a series of consecutive observations to eliminate undesirable noise components due to motion of the platform. As a result there is a non-linear relationship between accuracy and spatial resolution leading to a decrease in accuracy as the spatial resolution or the minimum observable wavelength
of the survey decreases. Thus, in gravity data acquisition, it is necessary to obtain the accuracy and resolution dic- tated by the objectives of a survey or the converse will be true – that is, the objectives of a study will be determined by the accuracy and resolution of the data acquisition.
The accuracy and spatial resolution of a particular mea- surement system for a specific survey are complicated, especially in dynamic survey systems. The noise envelope of the measurements which affect both accuracy and reso- lution depend not only on the instrumentation, but also on the environment of the measurements including the speed and accelerations of the platform and the non-geologic sources of the gravity force field, and on the schemes for noise rejection and filtering of the observations. How- ever, “best possible” results can be compared based on experience with the individual systems.Fairhead and Odegard (2002) have shown such a comparison with a time-trend plot of “best possible” gravity accuracy ver- sus resolution (Figure 5.1). The arrows show the change in these parameters over time, with the arrowhead being the current estimate at the time of the 2002 publication.
Although somewhat dated, this figure provides order of magnitude results that are generally applicable today. All the systems have improved markedly with time, and that trend continues today. For example, the use of a lighter- than-air airship for the platform of an airborne gradiometry survey has led to improvements in both accuracy and res- olution because of the stability of the airborne system and its relatively low speed (Hatchet al., 2007;Hatchand Pitts, 2010).
5.3 Measuring gravity
The gravity method uses the measurement of spatial and temporal variations in the intensity or gradients of the planetary force field. The actual measurements are made indirectly using observations of parameters such as time, linear or rotational displacement, spring tension, or an electrical component that can be related through funda- mental relationships to the value of planetary gravity or its spatial rate of change. Traditionally in exploration, the spatial and temporal change in gravity or its gradients are measured rather than the absolute value of gravity inten- sity. This is due to the high sensitivity requirement of absolute measurements, which is of the order of 10−8for 0.01 mGal resolution, compared with a significantly lower sensitivity requirement for relative instruments.
Although a wide variety of gravimeters (gravity meters) has been developed for measuring relative gravity and used since the first one was developed early in the nineteenth century (Chapin, 1998), most are spring-type in which
92 Gravity data acquisition
Land and seabed
Ship
Satellite
Airborne
Gradiometer
H FW 101
100
10-1
10-1 100 101 102
10-2
Shortest half-wavelength (km)
Accuracy (milligal)
Satellite
FIGURE 5.1 Relative accuracies and wavelength resolution of gravity surveying methodologies. The log–log time-trend plot gives inferred optimal gravity resolutions of survey systems where the arrow points represent current claims. Here FW=fixed wing and H=helicopter aircraft. In addition, drillhole gravimeters have an accuracy of a few microgals and a resolution of approximately 10 m, and absolute gravity measurements have an accuracy of
approximately one microgal. Adapted fromF a i r h e a dand O d e g a r d(2002).
the relative gravity is measured by the change of strain (length) of a spring which accompanies a change ing (Figure 5.2). This is the same principle used in a sen- sitive weighing device. A critical problem in this type of gravimeter is to achieve sufficient amplification of the change in length associated with the required sensitiv- ity. Without amplification a spring would have to have an absurdly long length of tens of meters or have an extremely heavy test mass to achieve a sensitivity equivalent to mod- ern gravimeters.
Several methods of optical and electrical amplification have been employed in gravimeters, but the most success- ful and most widely used is mechanical magnification.
This is achieved through astaticization in which by con- struction a mechanical force reinforces the gravity force and opposes the restoring force of the spring. In this man- ner, a small change in gravity produces a large, measur- able displacement of the test mass. Astaticization causes the system to operate very near a point of instability. In this position, the period of oscillation becomes very long because of the near equivalence of the restoring force and the gravitational force. The sensitivity is proportional to the square of the period of oscillation of a system. To avoid undesirable non-linear response of an astaticized system, the measurement of gravity in land meters is made by bringing the system to a reference position by a force from a calibrated nulling screw. The null position is placed near the horizontal to minimize effects of misleveling.
M
Spring
Fulcrum
g + δg δs
FIGURE 5.2 Principle of the gravimeter showing how a change in gravity,g, causes a displacement of the lever arm,δs, which can be used to measure the change in gravity.
Several principles other than spring-type balances are the basis for construction of gravimeters (e.g.Chapin, 1998). One of these that is useful in studies requiring very high sensitivity is the so-called superconducting gravime- ter in which the vertical position of a niobium sphere sus- pended between superconducting coils is electrically mon- itored (e.g.Crossley, 1994;Goodkind, 1999). This instrument is purported to have sensitivities of the order of 1 part in 1012of the Earth’s surface gravity, sufficient to detect a change in elevation equal to the thickness of a piece of writing paper, opening up new opportunities for studying internal changes within the Earth as well as Earth dynamics and rotation with temporal variations in gravity using continuous gravity observations.
Specialized gravimeters have been constructed and placed on gyroscopically controlled stable platforms for making measurements on moving ships and aircraft (LaCoste, 1967). These measurements have lower sen- sitivity and resolution than land surface measurements, and therefore are generally not suitable for detailed sur- veys requiring an accuracy higher than 0.1 mGal. How- ever, the development of highly accurate airborne gravity gradiometers has broadened the use of airborne measure- ments for exploration purposes, even for mineral resource exploration where the targets are small and the amplitudes of the anomalies limited.
Advances continue to be made in the operational sys- tem of gravimeters utilizing new technology to increase their accuracy by minimizing environmental and human effects, and to increase the efficiency of the meters by making them more automatic. Chapin et al. (1999) have found, in considering the accuracy, convenience, and speed of measurement of several different static gravime- ters in surveying stations separated by several tens of meters, that all of the gravimeters have relative advantages
5.3 Measuring gravity 93 and limitations. Their conclusions reinforce the need for
careful selection of a specific gravimeter based on its design and operational characteristics, and on the objec- tives and nature of the survey. Recent advances in gravime- try for exploration purposes are focused primarily on improving the accuracy and resolution of measurements obtained from mobile platforms and space satellites, and notable progress has been made in the past decade (e.g.
FairheadandOdegard, 2002;HerringandHall, 2006;Lane, 2010). Significant advances have also been made in absolute gravity measurements (e.g.Niebauer et al., 1995) that are finding new uses in gravity explo- ration especially related to temporal variations and in the use of the Global Positioning System (GPS) to improve the accuracy of airborne, marine, and land gravity positioning, and thus the processing of observations to anomalies.
5.3.1 Land surface measurements
Most land surface gravity observations are made with the gravimeter placed on a tripod set firmly on the ground sur- face. Virtually all modern exploration gravimeters used in this mode are based on the zero-length spring principle originally developed byLaCoste(1934) for increasing the sensitivity of vertical long-period seismographs. The zero-length spring is wound in a pre-stressed condition like the spring of an ordinary screen door. A specific force is required to open the spring so that if it were capa- ble of collapsing to zero length, the force would be zero.
The advantage of the zero-length spring concept is that it involves a key principle in measuring the gravity effect on the displacement of the test mass. That principle is that the spring behaves in a known, reliable way. Prior to zero-length springs, spring gravimeters underwent exten- sive laboratory testing to determine the property of the spring in each gravimeter, resulting in gravimeters of the same model behaving either reliably or erratically over different ranges of measurement. With the zero-length spring, the only calibration needed within the gravimeter was the mechanism to stretch the spring (commonly with a micrometer screw). Gravimeters based on the principle of a zero-length spring are commonly classified as either metal or quartz zero-length spring meters. An inventory of gravimeters found that about 4,000 instruments based on the zero-length principle had been constructed up to 1998 with roughly 3,000 of them made in equal num- bers with metal springs by LaCoste & Romberg Grav- ity Meters, Inc., and with quartz springs by the Worden Gravity Meter Co. (Chapin, 1998). Today, the only man- ufacturer of new relative gravity meters is LaCoste &
Romberg-Scintrex (LRS), Inc., which makes an automated
zero-length spring quartz instrument (currently the CG-5).
Nevertheless, many older gravity instruments, if properly maintained, are satisfactory for most surveying purposes.
Indeed, some professionals prefer the older instruments because most of the post-manufacture instrument drift is no longer present.
These gravimeters normally are employed in a static mode on land and in underground workings where the instrument is mounted on a tripod and leveled to align the sensor sensitivity axis in the local vertical direction.
However, they have been modified to include automatic leveling, nulling, and readouts for use in specialized hous- ings in drill holes and underwater, or when deployed on the surface from hovering helicopters, or simply to min- imize human errors in land observations. Typically sea- bottom surveys have been limited to depths of a few hun- dred meters with deployment and observations made by cables reaching from the remotely operated instrument to a surface vessel. However, recent interest in monitoring sub-sea petroleum reservoirs with time-lapse gravity mea- surements has led to development of remotely operated vehicle-deployed deep ocean systems (Sasagawaet al., 2003;Zumberge et al., 2008). The measurements are made automatically and remotely using a standard quartz zero-length spring gravimeter in a waterproof housing which is deployed by a remotely operated vehicle onto the ocean bottom. Recent systems are reported to have a repeatability of 3μGal in gravity and 5 mm in station depth (Zumbergeet al., 2008). This measurement accu- racy is desirable because of the small size (generally less than 100μGal) of the variations anticipated in time-lapse gravity to monitor petroleum of the reservoirs.
Zero-length spring concept
A critical breakthrough in modern-day gravimeters occurred whenLaCoste(1934) described a method of achieving great sensitivity in a vertical seismograph which measured the acceleration of the ground motions of the Earth upon the passage of a seismic wave. This type of instrument, including both metal and quartz spring meters, is capable of measuring the change ing when seismic vibrations are not prominent. Astaticization, and thus high sensitivity, is achieved through the principle of the zero- length spring without a long spring. For example, a 10 cm spring will experience a 10−7m change with a 10μGal variation in gravity (Chapin, 1998). This change in length is readily measured with current technology. As a result, gravimeters based on the zero-length spring concept can be made relatively small for ease of portability and the required consistency of the environment within the sensor housing.
94 Gravity data acquisition
a
b
Mg α θ
β
M
d s
r
FIGURE 5.3 Diagram of an inclined zero-length spring assembly used in modern gravimeters showing the parameters that describe the location of a reference massMin the Earth’s gravity field on a lever attached to the spring. Courtesy of LaCoste &
Romberg-Scintrex (LRS), Inc.
The zero-length spring, which counteracts the force of gravity on a test mass in the gravimeter, is constructed so that if the mass were removed, the force would be zero and the spring would have zero length. This condition is attained by pre-stressing the spring while it is being wound so that it will be in compression before its coils are sepa- rated by stretching. In quartz instruments, this is achieved by constructing the quartz spring so that the spring coils spiral inward such that it would literally become a nested flat zero-length spring if allowed to be free of the mechanism.
Figure 5.3 from LaCoste and Romberg (2004) illustrates the principle of the zero-length spring gravime- ter, whereby the restoring force of the helical spring coun- teracts the force of gravity acting on the test massM, bringing the mass arm to a neutral, equilibrium position.
A change ingcauses the mass arm to deflect to a new position, raising it for a decrease in gravity and lowering it for an increase in gravity.
The principle can be appreciated by considering the clockwise torqueτcacting on the lever armbin Figure 5.3 due to the forceMg, which is
τc=(Mgd) sinθ=(Mgd) cosα. (5.1) The counterclockwise torqueτccdue to the restoring force of the spring, on the other hand, is
τcc=kSr (5.2)
because the spring with spring constantk is constructed (i.e. prestressed) so that its lengthSis zero when no force is applied to it. Furthermore,
S=(b)cosα
sinβ and r=asinβ, (5.3)
so that
τcc=(kba) cosα. (5.4)
At equlibriumτc=τccwhere (Mgd) cosα=(kba) cosα or
Mgd=kba. (5.5)
Therefore, the gravimeter is insensitive to the anglesθ, α, andβ. It will be in equilibrium over a small range of angles and there is no restoring force if displaced from an equilibrium point by only a small amount. There is a basic relationship between a system’s free-period of oscillation and its sensitivity: that is, the sensitivity is proportional to the square of the period. Thus, theoretically the zero- length spring instrument can be constructed to have an infinite natural period and an infinite sensitivity. The only limitation is the quality and length of the micrometer screw that nulls it. In modern instruments, the action of nulling the spring using the micrometer screw is achieved through an electronic nulling system. In modern gravimeters, the full range of the instrument can be nulled in this manner, eliminating the screw altogether. In metal spring devices, large ranges can be achieved electronically, and the screw is only used to re-range the device so that electronic nulling is possible.
Zero-length gravimeters became commercially avail- able immediately after World War II with several man- ufacturers producing instruments based on this princi- ple. In theory, these instruments should be capable of achieving sensitivities of less than 1μGal, but in practice most gravimeters are built with a sensitivity of 10μGal.
Gravimeters built for microgravity surveys and measure- ment of time variations in gravity at a site typically have sensitivities approaching 1μGal, but have limited grav- ity ranges without resetting of the instrument’s mass arm.
Both LaCoste & Romberg type gravimeters using a metal, inclined zero-length spring and the Worden type using a quartz vertical spring are manufactured in models that automatically measure and record the observations cor- rected for tidal effects and take successive observations to achieve greater precision through averaging. These fully portable instruments automatically level themselves and have sensor-housing heaters powered by internal batter- ies. They are easier and faster to use than previous meters and potentially more accurate because of elimination of
5.3 Measuring gravity 95
M Lever
Lever
Measuring screw
Meter box
Weight (Mg) Connecting
links Beam
Zero length spring
Shock eliminating spring
FIGURE 5.4 Simplified diagram of the LaCoste & Romberg gravimeter using the inclined zero-length spring. Courtesy of LaCoste &
Romberg-Scintrex (LRS), Inc.
the possibility of human errors. A special model has a reported sensitivity of 0.1μGal for microgravity studies.
Specialized zero-length meters of somewhat less accuracy which incorporate automatic leveling and reading have been designed for operation on ice and underwater, using increased damping of the sensor element and filtering to remove short-period oscillations.
Metal zero-length spring gravimeters
The LaCoste & Romberg type gravimeter measures the change in gravity between observation sites utilizing a metal zero-length spring to achieve high sensitivity. The major components of the instrument are shown in the sim- plified diagram of Figure 5.4. The sensor itself is roughly a 5 cm cube. The test mass located at the extremity of the pivoted beam is held in place by a metal, inclined zero- length spring. To achieve the necessary sensitivity the mass is relatively large, and is made of dense tungsten in some models and gold in others. As a result, the beam must be arrested when the meter is moved to avoid the possi- bility of mechanical damage to the sensor. Metal is used for the spring because of its strength and the low coef- ficient of thermal expansion that is attained by selected metallic alloys. To achieve constant thermal behavior of the sensor, the instrument is heated to a constant temperature.
When the sensor experiences a change in gravity, the pivoted beam moves to a new equilibrium position. The position of the beam is monitored either optically or elec-
trically, and the meter is returned to a reference null posi- tion by changing the torque on a screw system that modi- fies the position of the upper connection of the zero-length spring. The movement of the beam is linear near the null point, allowing a large range over which precise measure- ments can be made. The torque is calibrated in units of gravity so that the change in gravity causing the displace- ment of the beam can be determined. Calibration is per- formed in the laboratory by placing a standardized weight on the test mass and measuring the displacement of the beam with the nulling screw. Alternatively calibration can be achieved by tilting the meter by a known angle and comparing the observation against the calculated change in gravity due to the tilt. These methods are backed up by checking the calibration in the field with observations between sites of known gravity values.
The LaCoste & Romberg type gravimeters consist of two basic models for land surface measurements. The com- mon variety is the Model G meter which has a worldwide range (7,000 mGal), a repeatability of 0.01 mGal and an accuracy better than 0.04 mGal. With very careful obser- vations and field procedures, some investigators claim a precision of the order of 0.005 mGal for this model. The Model D meter is similar to the Model G, but has two nulling screws, one for the worldwide range of gravity and the other for the limited measuring range (slightly more than 200 mGal). This model has a sensitivity of 0.001 mGal (1μGal) over its fine-adjustment measuring screw, making it useful for microgravity surveys.