LIMESTONE POROSITY
5.4 Gravity surveying
The combined effect of the vertical gradient of gravity
and the attractive effect of the included mass between the elevation datum and the observation site is
gz=4.193σ×10−5 h (5.9)
whereσis the density of the included mass in kg/m3andh is the height of the station in meters. Assuming the density of surface material is of the order of 2,000 kg/m3, the ver- tical gradient of gravity is approximately 84μGal/m. As a result the surface elevation must be known to an accuracy of approximately 1 cm to achieve a 1μGal accuracy.
The effect of the anomalous vertical gradient is not significant considering the elevation accuracy required for most surface surveys. The maximum vertical gradient of gravity inμGal/m caused by an anomalous source in the shape of a sphere is
∂g
∂z
max
5.6×10−2σ R3
z3
, (5.10)
where the variables are the same as given for Equation 5.8. Thus, for the earlier example of an air-filled cavity in limestone with a radius of 5 m at the depth-to-center of 10 m, the maximum anomalous vertical gradient that occurs directly over the center of the sphere is roughly 19μGal/m, which is negligible where the elevation accu- racy is of the order of 1 cm.
Vertical control for gravity surveying can be achieved by measuring differences in atmospheric pressure, deter- mining vertical angles and distances, spirit leveling, and most recently by GPS surveying. The first method is sel- dom used because of potential errors in using aneroid barometers due to difficulties in monitoring local transient atmospheric variations. However, the elevations of many stations in national data bases where the observations were made prior to the availability of GPS are based on baro- metric altimeter elevation. The most accurate methodol- ogy is spirit leveling, but this surveying is slow even with self-leveling instruments and requires line-of-sight access.
GPS methods, especially those employing carrier phase measurements, are being used for essentially all gravity position surveying including marine and airborne surveys.
Elevations determined by GPS are inherently less accu- rate than GPS-determined horizontal positions by a factor of roughly 1.5 (Aiken et al., 1998). As a result, accu- racies of GPS elevations using rapid methods are of the order of a few centimeters. Subcentimeter GPS accuracies currently use static methods which typically require occu- pation times of an hour or more. This long period of time invalidates a major advantage of GPS, its speed, and thus its cost-saving attribute.
Elevations determined with GPS methods are refer- enced to a mathematical model of the Earth’s shape – a smooth reference ellipsoid (World Geodetic System of 1984, WGS84) or local datum – rather than the conven- tional geoid which is what the Earth’s shape really is at sea level. If GPS elevations are to be combined with sea level elevations, a correction must be made to the GPS measure- ments to account for this difference from the mathematical model of the shape of the Earth. This is done by interpo- lating of the geoid height at the observation location from a digital grid of geoid heights and adjusting the observed elevation accordingly. Geoid digital models are included in some GPS receivers so that this can be done automatically.
In regions of great topographic variability such as moun- tains, the local variations in the geoid roughly parallel the gravity observations corrected for the vertical gradient of gravity or the topography. In contrast, in regions of sub- dued topography, the geoid primarily reflects the gravity associated with subsurface density variations.
As a rule of thumb, a 3 mGal gravity variation results in a geoidal variation (N) of approximately 1 cm. Regional geoidal undulations are available on a global basis, but more detailed, higher wavenumber geoidal fluctuations can be readily computed from Bruns’ formula given by Equation 5.13 below (See Section 5.5.2).
5.4 Gravity surveying
Gravity field mapping is implemented by ground, marine, airborne, and satellite surveys. This section considers the design, measurement, and other factors that influence the effectiveness of surface surveys for mapping the gravity field, whereas Section 5.5 below describes gravity survey- ing from space by satellites. General guides to this topic for land surface surveys are available fromSeigel(1995) andMilson(2003) and in instrument manuals.
5.4.1 Survey design
A critical step in gravity surveys, as in all geophysical stud- ies, is the design of the layout of stations to be observed in the study. The factors to be considered include the purpose of the survey, the minimal amplitudes and the areal size and configuration of the anomalies of interest, terrain of and access to the survey area, nature of noise in the gravity field, size of the area, available instrumentation, and the time and financial resources for the survey.
Land surface surveys
Land surface surveys performed for regional studies gen- erally involving anomalies derived from sources within the
110 Gravity data acquisition
Earth’s crust or for reconnaissance of the types of anoma- lies that are present in a region typically have stations distributed in as uniform a grid as possible considering the limitations imposed by access, and at station intervals measured in kilometers. In many land areas of the Earth, regional surveys are not required because of the availabil- ity of data from governmental, academic, or commercial data banks. Generally these data are available as discrete stations as well as in gridded formats of anomaly values at an interval appropriate to the spacing of the original data. In contrast, most gravity studies for near-surface and upper crustal mapping purposes require detailed surveys of rather limited areas. Station intervals for these studies are measured in meters to hundreds of meters. These types of data are not available in repositories for most regions, and thus need to be acquired in modern surveys.
Stations are distributed in a regular grid pattern over the entire area of interest where equidimensional anomalies are of interest, but if reconnaissance surveying or geologi- cal information suggest that the anticipated anomalies are much longer in one predictable direction than the other, surveying commonly is performed along straight, paral- lel profiles perpendicular to the longer dimension. The direction of the profiles may be modified somewhat from this idealized situation by terrain and access considera- tions. The distance between profiles is usually kept to a maximum of five times the distance between observations along the profile. Where the only purpose of the survey is to detect anomalies, statistical principles can be used to deter- mine the probability of encountering a specific anomaly size for a particular layout of stations (e.g.Agocs, 1955).
Selection of the size of the area covered by a sur- vey and the length of profiles is based on two primary considerations: (1) the maximum depth of the anticipated sources, and (2) the areal size and amplitude of the regional anomalies in the area. As described in the next chapter, the anomalies of interest in a survey must be isolated from the effects of deeper, broader, so-called regional anoma- lies, which produce gravity gradients that can distort the anomalies of interest. These regional anomalies must be mapped by gravity surveying extending beyond the area of immediate interest or determined from pre-existing gravity data. A common rule of thumb is that the gravity survey- ing should extend a minimum of three times the maximum depth of the sources of interest beyond the limits of the area of interest, as, the anomaly from a concentrated mass will decrease to 10% or less of the maximum amplitude at this distance. The distance derived from the “three times the depth” rule should be considered a minimum, especially where the depth extent of the source exceeds one-tenth of the depth.
In selecting the station spacing it is important to con- sider the trade-offs between numerous factors. Critical concerns include the amplitude and areal size of the anomalies of interest, the objective of the study, the grav- ity noise, surface terrain and access, and the available resources. Given a minimal amplitude and size of anoma- lies of interest, a principal criterion in selection of station spacing is the objective of the survey. Surveys may be used to detect anomalies or map the anomalies for quanti- tative analysis and modeling as well as for calculation of gradients and other short-wavelength components of the gravity field from the observed measurements. The opti- mum station spacing for these different objectives is not the same.
In the simplest of cases for detection of anomalies based on amplitude, it is necessary to have only three stations per anomaly, or, as stated in the Nyquist sam- pling theorem in Appendix A.4.3, the minimum number of equally spaced observations that will define a specified wavelength is three located at a separation equal to one- half the wavelength. If there are not three observations per wavelength, the anomaly will be aliased or folded into observations of longer wavelengths.
Where significant gravity anomaly noise is present, the selection of station spacing may become more complex depending on the wavelength and amplitude of the noise.
In the exreme case, it may be necessary to choose a spac- ing that will map the noise so that it can be identified and extracted from the observations. However, it is commonly difficult to ascertain the full noise characteristics prior to a survey, so it is desirable to minimize sources of noise, such as terrain effects which cannot be precisely estimated, by proper siting of the station locations and other appropri- ate survey procedures. A general guideline for detecting anomalies is that the distance between stations should not exceed the depth to the center of the anticipated concen- trated sources in the region. This assures a minimum of one station within the area in which the anomaly from a concentrated source exceeds 70% of its maximum ampli- tude.
This criterion is inappropriate for mapping anoma- lies and performing other quantitative calculations on the anomaly, including the calculation of gradients from the discrete observations. Detection is based on absolute amplitudes, but, the success of modeling and other quan- titative calculations is very much a function of accurately mapping spatial changes in amplitude, that is their gradi- ents. It is best, then, to map anomalies for interpretation purposes at an interval over which it is possible to approx- imate the gradient with a linear function. A reasonable linear approximation can be achieved for a concentrated
5.4 Gravity surveying 111 source, which has the highest gradient anomaly among
the various idealized anomaly sources, with an interval of one-quarter the depth to the source.
Marine surveys
Most marine gravity surveys are conducted as an add-on to seismic reflection surveys. This minimizes the cost of the surveys and generally allows the use of larger vessels with greater stability for the gravity measurements along a grid of survey lines. In this situation the survey spec- ifications are largely dictated by the requirements of the seismic study. This was not always the case, because prior to the 1980s many marine gravity surveys operated from small dedicated ships with survey specifications designed specifically for the objectives of the survey or employed underwater surveys where the gravimeters were placed on the sea bottom for observations. Stand-alone marine grav- ity surveys are still performed for specific purposes. For such surveys, a stable and easily steered survey vessel is desirable, enhancing the accuracy of the gravity observa- tions. The tracks of these surveys are supplemented by orthogonal tie lines to provide data on intersection mis- ties that are used in leveling of the survey observations.
The surveys should always include onboard data quality control processing for near real-time quality evaluation.
Prior to 1984 when the first commercial, surface marine gravity survey was conducted, navigation was a primary limitation on the accuracy of marine surveys because of the E¨otv¨os effect. Thus, significant attention was directed toward accurately determining the location of the ship, but this changed with the global availability of highly accurate positioning using GPS. The position accuracies, and thus the velocities of the ship, obtained with GPS are especially important in surveys conducted on seismic survey ships.
This is because the heavy cable towed by the seismic survey ship results in frequent course and velocity changes that affect the E¨otv¨os correction (Herring andHall, 2006).
Marine gravity observations that are made continu- ously are determined by averaging the values over a period of time, commonly 30 to 60 seconds to minimize short- period accelerations of the ship that cannot be eliminated by data processing or instrument construction. As a result there is a trade-off between virtual station interval and accuracy of the observations – the longer the averaging of observations, the greater the accuracy, but the lower the resolution or the greater the effective data interval.
Thus, marine surveys require decisions on the averaging period that is commensurate with the objectives of the survey, the velocity of the ship, and the noise parameters of the observations. In addition, water depth is an impor-
tant parameter in the processing of the gravity data, and thus high-resolution bathymetry is a standard component of marine surveys. However, errors in bathymetry may be as large as 10% of the water depth.
Airborne surveys
In contrast to marine gravity surveys, essentially all air- borne surveys are designed and conducted based on the anticipated gravity anomalies of the study area and the objectives of the survey. These are dedicated surveys opti- mized for gravity measurement. Selection of the appropri- ate aircraft is an important initial decision based on the survey objectives, terrain of the study region, and access to the region from air terminals with appropriate mainte- nance facilities. Generally, the aircraft is either a single- or twin-engine aircraft capable of relative slow speeds (∼50 to 100 m/s) to achieve the desired accuracy to reso- lution ratio. In regions of steep topography, cultural fea- tures, and continuous cloud cover, safety considerations may suggest that the fixed-winged aircraft be replaced with a helicopter. Topography and access determine the specifications of the aircraft with regard to rate of climb, descent, and range. Commonly, onboard magnetic sensors and recording equipment supplement the gravity measure- ments, but specifications are dictated by the gravity mea- surements.
Gravity observations are usually made along parallel lines perpendicular to the anticipated strike-direction of the gravity anomalies with orthogonal tie lines at a spac- ing of 5 to 10 times the line spacing. These tie lines are used for quality control of the survey and as an aid in data processing. The basic flight line spacing is dictated by the accuracy and resolution required for the objectives of the survey. Higher accuracy and shorter resolutions require closer line spacings. Thus, in high-resolution surveys for near-surface source mapping, a closer line spacing is used.
Closer line spacing also significantly improves digital ele- vation models that are mapped by altimeters on the aircraft and can be used in calculating terrain effects. Flight line spacings are between 50 and 3,000 m or more for most regional objectives. Generally, line spacing is oversam- pled for the purposes of the survey to minimize noise and is less than the length of the filter applied to the measured data to eliminate short-period inertial accelerations caused by aircraft motions.
Closely associated with the selection of the line spacing is the decision on flight height or altitude above the ground.
To enhance resolution and increase the perceptibility of the anomalies the flight height should be as low as possible taking into account aircraft safety, governmental regula- tions, and near-surface turbulence which may decrease
112 Gravity data acquisition
the accuracy of the gravity measurements. Consideration must be made of longer filters applied to the data to achieve necessary accuracy in the survey resolution for identify- ing individual anomalies. Typically, survey altitudes are a few hundred meters. Surveys are, flown at a constant altitude, but in regions of marked topographic variations, it is desirable to drape the survey over the terrain, taking into account safe climb and descent rates of the aircraft, to avoid poor anomaly resolution in lower elevation regions.
The position of the drape may be established from regional elevation models and aircraft characteristics and entered directly in the onboard GPS for controlling the flight path of the aircraft. Draped surveys more closely mimic land gravity surveys (which follow the topography). Thus, in attempting to merge airborne surveys with ground surveys it may be desirable to drape the airborne survey.
Decisions on the anomaly accuracy and resolution based on the objectives of the survey and anticipated anomalies must be considered with the allowable errors in altitude and position of the aircraft that will not inter- fere with anomaly accuracy. These allowable errors dictate navigational requirements of the survey. As in the case of other gravity surveys, real-time quality control of the data acquisition and processing is important to achieving the goals of the survey.
5.4.2 Survey procedures
Successful acquisition of gravity data for exploration pur- poses depends on the selection of instrumentation, survey design, and measurement procedures appropriate for the objectives of the study, as well as the methodology that will be used for reduction and interpretation. To insure that the process meets the intended goals requires a comprehen- sive quality control procedure at each stage in the process and a thorough knowledge of the principles of gravity and their application to exploration. Most gravity surveys other than land surveys are conducted by industrial contractors, research institutions, and governmental agencies which generally have defined procedures for the acquisition of data for specific objectives. Thus, this section is largely devoted to survey procedures for land surveying, but some of the procedural considerations described are applica- ble to other survey types. Where standardized procedures are used by contract crews, it is advisable for the user of the data to be well acquainted with these and restrictions they may place on the data.
Gravimeter considerations
The efficient measurement of gravity to one part in 108or better equires instrumentation that is subject to numerous
potential errors. It is necessary to select the most appro- priate gravimeter, to maintain it in the optimum working condition, and to fully understand the characteristics of the particular gravimeter under the survey conditions. In marine and airborne surveys, significant criteria are the range and accuracy of the instrument’s measurements on a moving platform. Depending on the objectives of the survey, a meter that measures either gravity or its vector or tensor components may be the best choice. For land sur- face surveys, critical attributes are the sensitivity and range of the instrument and its portability. Both the LaCoste &
Romberg and Worden type gravimeters are constructed in highly portable versions with a large range and a sensitiv- ity of approximately 0.01 mGal or, in specialized meters, 1μGal.
It is advisable to use the microgal meter only where the precision is required, because of increased meter costs and reading time and the more limited operational range of these meters without reset. Resetting requires time and may induce tares in the observations. Where portability is of concern, it is desirable to use instruments that require a minimum battery supply to keep the meter at a con- stant temperature. Batteries add to the weight and require recharging, which can be a problem where observations are made over many hours in remote locations where elec- trical power is unavailable for recharging.
Gravimeters that are kept at a constant temperature, which is the norm today, should be brought to the speci- fied temperature a few days or at least several hours prior to the start of the survey to remove temperature gradients within the meter, and the meter temperatures should be kept constant throughout the survey including overnight periods. The meter temperature should be set well above the anticipated maximum ambient temperature and low enough to minimize the power requirements in cold envi- ronments.
Worden-type meters that are not temperature- controlled are highly portable, but subject to generally high drift rates following a rapid, large change in temper- ature. As a result these gravimeters should be protected from temperature transients while maintaining as constant an ambient temperature as possible. All meters should be kept out of direct sunlight because of possible thermal effects as well as differential thermal expansion which may alter the level of the instrument.
Gravimeters that have a limited operational range should be reset only when absolutely necessary because of possible tares in the observations that may accompany readjustment of the coarse spring which keeps the lever arm carrying the mass within observational range. Adjust- ment of the meter to an appropriate operational range