Ralph R. B. von Frese

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

Abstract To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1°-averaged surface free-air gravity anomalies and POGO satellite magnetometer data for the United States, Mexico and Central America illustrate the capabilities of the method.

Long-wavelength aeromagnetic anomaly map of the conterminous United States

Total intensity magnetic anomaly unflltered and low-pass filtered profile and contour maps of the conterminous United States have been prepared from data provided by the U.S. Naval Oceanographic Office9s Project MAGNET Survey. The maps are useful for regional geological investigations because the anomalies, particularly on the filtered maps that emphasize long-wavelength anomalies, can be correlated with known major geologic features. The most intense positive, long-wavelength anomaly occurs over Precambrian mafic basement rocks in eastern Tennessee and Kentucky. Other examples of prominent positive anomalies occur over the Great Valley of California and the Colorado Plateau and along the Appalachian fold belt. In contrast, prominent negative long-wavelength magnetic anomalies occur over the Cascade Mountains, Mississippi Embayment, and southern Rocky Mountains and marginally to the positive anomaly related to the Mid-continent Rift.

Gravity and Magnetic Exploration: The gravity method

Overview The gravity method of geophysical exploration is based on the measurement of variations in the gravity field caused by horizontal variations of density within the subsurface. It is an important technique for many problems that involve subsurface mapping, and it is the principal method in a number of specific types of geological studies. The method, which has its roots in geodetic studies from the seventeenth to the twentieth centuries, has developed rapidly over the past century as a result of significant technological advances: primarily high-accuracy gravity measuring instruments for use on land, sea, and air, and in space, as well as the increasing computational and graphics power of digital computers. These advances are backed up by continuing improvements in data processing, interpretational schemes, practical experience, and surveying methodologies. Traditionally the gravity method has been used primarily in regional characterization of the Earth for determining the architecture of the crust, identifying potentially favorable regions for resource exploration, and developing conceptual exploration models. This is made possible by the millions of gravity observations now available worldwide in both public and commercial data sets. The accuracy now available in gravity observations and the relative ease of measurement have made the method viable for exploration objectives such as assessing subsurface changes over time and combined interpretation with seismic reflection mapping.

Gravity and Magnetic Exploration: Magnetic anomaly interpretation

Overview Magnetic interpretation, as in gravity interpretation, operates at several levels of complexity. It can range from simple identification and location of anomalous magnetic bodies in the subsurface to three-dimensional modeling leading to complete characterization of anomaly sources. However, there are numerous differences in the interpretation of these two potential fields. For example, magnetic anomalies in most investigations are primarily caused by contrasting crystalline rocks containing variable amounts of the trace mineral magnetite. This limits the range of possible anomaly sources that need to be considered, although as in all potential field interpretations no interpretation is unique. Magnetic interpretation is complicated by the dipolar nature of the magnetic field, resulting in both attractive and repulsive effects from an anomaly source, and by the large range of variables that enter into determining the character of a magnetic anomaly. Anomaly characteristics vary significantly with the location and orientation of the source in the geomagnetic field and may be further complicated by the effects of remanent magnetization and internal demagnetization. Nonetheless, various interpretational techniques have been developed for dealing with these complications and shown to be successful in identifying and characterizing magnetic sources. Magnetic anomalies are particularly sensitive to their depth of origin, so special emphasis is placed on depth determination methods. Although these methods generally involve simplifying assumptions of theoretical formulations, with care errors commonly can be limited to roughly 10%.

Gravity and Magnetic Exploration: Gravity data processing

Overview Gravity observations include the combined effects of instrumental, surface, terrain, and planetary sources in addition to the subsurface mass variations that are the objective of an exploration gravity survey. To isolate the effects of subsurface sources, extraneous effects which include both temporal and spatial variations are removed from the data using theoretical considerations, geological information, and empirical observations. Some are considered universally, but others only in specific geological, surface, and observational conditions. There is an increasing need to eliminate a broader range of extraneous effects more precisely as the objectives of gravity surveying require higher precision and accuracy and are focused on both long- and short-wavelength anomalies. Unwanted effects are removed by calculating the gravity anomaly, which is the arithmetic difference between the observed vertical acceleration of gravity and the predicted or theoretical acceleration at the observation site. Theoretical gravity is based on a conceptual model of the sources of gravity variations. This model varies depending on the intended use of the gravity anomaly and the conditions of the survey. Three classes of anomalies are recognized. The primary class, planetary anomalies, incorporates only analytically determined planetary considerations in the theoretical model, e.g. the Bouguer gravity anomaly. A second type, geological anomalies, applies additional effects from known or postulated subsurface geological conditions in the model, e.g. the isostatic residual gravity anomaly. The third type, filtered anomalies, is calculated by removal of arbitrary gravity effects caused by unknown sources, empirically or analytically determined by filtering that enhances particular attributes of the spatial pattern of the anomalies, e.g. wavelength-filtered gravity anomalies. The latter type seeks to isolate or enhance those of interest at the expense of other anomalies.

Gravity and Magnetic Exploration: Gravity data acquisition

Overview Although simple in principle, the measurement of gravity for geologic purposes to an accuracy of the order of 10 -8 to 10 -9 of the Earths gravitational field requires highly sophisticated instrumentation and rigorous survey procedures. Fundamentally because of the nature of the measurement, all gravity instrumentation must be mechanical. Most land gravity measurements are made with relative-measuring instruments using the zero-length spring principle to achieve high sensitivity in portable instrumentation. Although extensive governmental and commercial databases containing millions of observations exist, additional gravity surveying continues to achieve greater detail and accuracy in the data. Random errors are minimized in modern instrumentation by performing the observations automatically. However, residual errors remain, owing both to inherent instrumentation problems and non-geologic acceleration components that need to be considered while conducting surveys. Increasingly accurate observations and improved anomaly resolution are being achieved especially in marine and airborne observations of gravity. A variety of instrumentation is used for measurements on mobile platforms, including modified zero-length spring gravimeters and electromagnetic accelerometers mounted on gyrostabilized platforms to minimize short-period horizontal and vertical accelerations due to movements of the ship or aircraft. In addition, highly accurate absolute gravity measurements are being made with stable, portable free-fall instruments, and rotating-disk gravity gradiometers are being used to observe the gravitational tensor components. These improvements are useful not only in mapping components of the gravity field related to variations in subsurface geology, but also in monitoring time-variable processes within the Earth associated with mass changes.

Density of Earth materials

Overview The gravity method measures horizontal spatial changes in the gravitational field that result from mass differentials which in turn are controlled by the volume and contrasting densities of anomalous masses. As a result, an understanding of the density of Earth materials is essential in planning surveys as well as in interpreting gravity anomalies. Density is a function of the mineral composition of Earth materials as well as their void volume and the material filling the voids. As a result, densities of rocks can be estimated by considering their origin and the processes that subsequently have acted upon them. However, it is advisable to measure densities either directly or indirectly wherever possible, preferably in situ , because of the difficulties in obtaining samples that are representative of the actual geological setting. In situ measurements may be obtained from the relationship of gravity anomalies to topography or determined indirectly from correlative measurements such as seismic wave velocity or attenuation of gamma rays. Introduction Knowledge of germane Earth material densities within a study region is required for effective planning and implementation of gravity surveys. Accordingly, as an introduction to the gravity method, the sections below describe the fundamentals of this property and the controls on it, together with methods of determining density. Representative values are presented of the density of a variety of Earth materials including igneous, metamorphic, and sedimentary rocks, sediments, and soils to aid the explorationist in the use of the gravity method.

Gravity and Magnetic Exploration: Magnetic data acquisition

Overview The acquisition of magnetic data is relatively simple, rapid, and less complex than are the observations of data of most geophysical methods. Significant improvements continue to be made in magnetic instrumentation which facilitate accurate observation of the geomagnetic field on the Earths surface as well as on a variety of airborne platforms, and from satellites of the Earth, Moon, and planets of the solar system. Most observations are made of the scalar, total intensity of the field, with alkali-vapor (resonance) magnetometers which readily achieve a sensitivity of better than a nanotesla with rates of several observations per second from a moving platform. These measurements are supplemented for special purposes by measurements of gradients, vectors, and tensors. Vector and tensor measurements are made with flux-gate magnetometers and increasingly with the highly sensitive superconducting quantum interference device magnetometers. Surface or near-surface surveys are conducted on grids or parallel lines to map with high resolution the near-surface, local magnetic anomalies associated with a variety of archaeological, engineering, and environmental problems, but most magnetic surveys are conducted from a wide variety of airborne platforms. Although helicopter surveys may use outboard sensors placed in an aerodynamically stable housing at the end of a cable towed by the helicopter to place the sensor close to the surface to achieve the highest possible resolution, most airborne surveys use inboard sensors which require that extraneous magnetic effects of the aircraft are compensated by passive and active systems.

Gravity and Magnetic Exploration: Gravity anomaly interpretation

Overview Raw gravity observations are reduced for their non-geologic effects to one of a variety of anomalies which in turn are processed by isolation and enhancement procedures into residual anomalies that map the gravity effects of interest in interpretation. Anomaly interpretation, which models the gravity anomalies for the nature and processes of the subsurface, is a relatively straightforward process compared with the measurement, reduction, and residual-regional separation phases of the gravity method. However, anomaly interpretation is never unique, owing to the ubiquitous presence of data errors and the inherent source ambiguity of the gravity potential. Thus, ancillary geological, geophysical, and other constraints on the subsurface are essential to help limit the ambiguity. Gravity interpretations can be qualitative where the analysis objectives are satisfied by the mere presence or absence of an anomaly. Interpretation also can be highly quantitative with comprehensive modeling of the geometric and physical properties of the anomaly sources. Effective interpretation requires knowledge of the key geological variables that influence the anomalys amplitude and geometry. It also requires an understanding of the key geophysical variables that control the inverse problem of estimating source parameters from the anomaly. Gravity interpretation generally is initiated using simplified techniques to estimate preliminary source depths, depth extents, margins, density contrast, and mass. These estimates are often enhanced by more comprehensive analyses that include forward modeling using trial-and-error inversion methods if only a few unknown modeling parameters are involved. For more unknowns or where they must be estimated by least squares or some other error norm, inverse modeling is commonly implemented by matrix inversion. Both inversion methods compare the predicted anomaly from an assumed forward model with the observed gravity anomaly.

Gravity and Magnetic Exploration: Data systems processing

Overview Gravity and magnetic anomaly data are commonly expressed in standard formats for electronic analysis and archiving in digital data bases. A voluminous literature full of application-specialized jargon describes numerous analytical procedures for processing and interpreting anomaly data. However, when considered from the electronic computing perspective, these procedures simplify into the core problem of manipulating a digital forward model of the data to achieve the data analysis objectives. The forward model consists of a set of coefficients specified by the investigator and a set of unknown coefficients that must be determined by inversion from the input data set and the specified forward model coefficients. The inversion typically establishes a least-squares solution, as well as errors on the estimated coefficients and predictions of the solution in terms of the data and specified model coefficients. The inversion solution is never unique because of the errors in the data and specified model coefficients, the truncated calculation errors, and the source ambiguity of potential fields. Thus, a sensitivity analysis is commonly required to establish an “optimal” set or range of solutions that conforms to the error constraints. Sensitivity analysis assesses solution performance in achieving data analysis objectives including the determination of the range of geologically reasonable parameters that satisfy the observed data.