Magnetic Force Fields

Magnetic Force FieldsIntroduction

Aeromagnetic surveys are the most commonly used of all airborne geophysical methods. Over the past 25 years, the equipment and techniques used to acquire, process and interpret data from these surveys have advanced dramatically. In complex geologic provinces, aeromagnetic data can enhance results obtained from detailed, prospect-level interpretations. Precise definitions of magnetic anomalies can result in thorough structural interpretations of basement tectonics and the magnetic effects of some sedimentary rocks.

The concept of magnetic force fields provides a foundation for discussing magnetic survey methods in petroleum exploration.

The magnetic force between two isolated magnetic poles is given by

(1)

where P0 and P are magnetic pole strengths, R is the distance between the magnetic poles, and m is the magnetic permeability of free space.

By convention, the north-seeking pole is positive. The magnetic field strength, H, is the force "felt" by a positive unit magnetic pole, and is derived as shown in Figure 1 ( Magnetic force fields ).

Figure 1

The oersted is a unit used to measure magnetic field strength in the cgs system, but it is too large for the quantities of interest in magnetic prospecting. Most exploration anomalies range from .0001 to .01 oersteds. As a result, the gamma (or recently, nanotesla) is used in exploration:

1 gamma = 1 nano-tesla = 10-5 oersted

Magnetic field strength is the quantity measured by magnetometers. Thus, we can think of a magnetometer sensor as an isolated unit positive pole ( Figure 1 ). Negative poles cause a positive magnetic field due to attraction of the magnetometer sensor. The Earth's main magnetic field strength varies between about 25,000 and 70,000 gamma. Typical crustal-sourced magnetic anomalies measured in petroleum exploration range between one and one thousand gamma. Gravitational and Magnetic Potential (Simplified)

In developing an understanding of magnetic anomaly signatures and filtering of gravity and magnetic data (i.e., upward and downward continuation, reduction-to-magnetic pole, and derivatives), it is useful to introduce some concepts relating to potential energy. Gravitational Potential

The total mechanical energy of a system of particles is the sum of the kinetic energies resulting from particle motions, and the potential energies resulting from particle positions. In gravity and magnetic exploration, geologic sources for anomalies are stationary within the frame of reference of the observation points; thus, the kinetic energy is zero.

(On a subatomic level, electron spins and orbits are related to rock magnetism. In this discussion, however, we are treating rock magnetism strictly on a macroscopic basis. We therefore present the following mathematical treatment so as to account for macroscopic rock properties without having to know the whereabouts of each electron!)

Potential energy arises from the arrangement or position of gravity or magnetic anomaly sources with respect to the observation points. A basic, qualitative understanding of gravity and magnetic potential energy helps make clear the idea of gravity and magnetic force fields.

The gravitational force between two spheres M1 and M2 is

(2)

where G = universal gravitational constant = 6.670 x 10-11 N-m2/kg

M1, M2 = masses 1 and 2, respectively R = distance between center of masses

F = force

The gravitational acceleration a1, on a unit mass is

(3)

We can show that the gravitational potential energy U due to a sphere of mass M2 equals

(4)

The gravitational potential energy acting on a unit mass (such as the gravity meter sensing mass) is defined as gravitational potential and is given by:

(5)

Thus, the gravitational potential of a sphere is inversely proportional to the distance from the center of the sphere to an observation point outside of the sphere. The negative sign convention provides that the maximum gravitational potential occurs when R= G, where Ug=0. Gravitational potentials from R-values closer than R=G are negative, in that energy is needed to move the unit mass away from the sphere out to infinity to reach zero potential energy.

The gravitational attraction, or acceleration, from a sphere equals the change in gravitational potential with a change in the radius to the unit mass, as that change in radius approaches zero.

(6)

Magnetism of Rocks

Introduction

This section, while it does not address the microscopic and atomic aspects of rock magnetism, provides an elementary macroscopic concept to help the explorationist understand magnetic effects of geologic models.

From a macroscopic point of view, most rock-forming minerals are non-magnetic. Only a few minerals, such as magnetite (Fe3O4), ilmenite (FeTiO3), and pyrrhotite (FeS), significantly affect the local magnetic field. Magnetic rocks contain these minerals, usually in small percentages.

There are two components involved in a rock's magnetization: remanent magnetism and induced magnetism. Remanent magnetism is that which remains in a material after removal of the magnetizing force field which exists outside the rock sample. Induced magnetism is related to the ambient Earth's magnetic field by a proportionality constant known as magnetic susceptibility.

The total magnetization vector Mnet of a rock is the sum of the remanent and induced magnetism vectors:

Mnet = kF + MR(1)

where k is the magnetic susceptibility constant,

F is the Earth's magnetic field vector,

MR is the remanent magnetism vector.Most sedimentary rocks contain negligible quantities of magnetic minerals, and are therefore non-magnetic. Most basic igneous rocks, on the other hand, have high magnetic susceptibilities, while acid igneous rocks and metamorphic rocks can have susceptibilities ranging from negligible to extremely high.

Magnetic susceptibility is a trace property of rocks, because the percentage of magnetic minerals is usually one percent or less, even in basic igneous rocks. Slight variations in magnetic mineral content can cause large changes in magnetic susceptibility. A rock's magnetic susceptibility is proportional to the volume percent of magnetic minerals it contains. One volume percent of magnetite in a rock, for example, will usually cause a magnetic susceptibility of about 2500 x 10-6 cgs unit, which is considered quite high. Table 1 lists "average" susceptibilities of common rocks, based on laboratory measurements of surface samples and cores (after Peters, 1949); keep in mind, however, that because magnetic susceptibility is a trace property, actual susceptibilities will vary considerably from these listed values.

Rock typeAverage magnetic susceptibility, 10-6 cgsRange of magnetic susceptibilities, 10-6 cgs

Dolomite80 - 75

Limestone232 - 280

Sandstone320 - 1665

Shale525 - 1478

Metamorphic610 - 5824

Acid Igneous6473 - 6527

Basic Igneous7844 - 9711

Table 1: Average magnetic susceptibilities of rocks, based on surface sample and core measurements (after Peters, 1949).

Table 1 makes clear that rocks have a large range of variation in magnetic susceptibility. This range seems especially large compared with the range of rock densities and velocities ( Figure 1 , Velocity-Density relationship in rocks of different lithology ).

Figure 1

In general, basic igneous rocks have high magnetic susceptibilities; and sedimentary rocks have low magnetic susceptibilities. Metamorphic and acid igneous rocks can have susceptibilities ranging from near-zero to very high values. Table 1 does not show salt (halite) which has a very slight (-.5 106 cgs) negative magnetic susceptibility.============

Natural Remanent MagnetismIf we place a magnetic rock in a magnetic field of strength F and gradually increase the field strength, the magnetization induced in the rock, MI, will initially increase linearly by a proportionality constant m, which is the rock's magnetic permeability. But after exceeding a certain F value, the induced magnetism no longer increases linearly. Eventually, the induced magnetism attains a certain saturation point where MI no longer increases with increasing F. If the we turn off the magnetic field F, the rock retains a certain remanent magnetism. This phenomenon is referred to as magnetic hysteresis. Remanent magnetism is present even if no ambient magnetic field exists ( Figure1 ).

Figure 1

Natural remanent magnetism (NRM) can result from many natural causes. It can occur, for example, if a rock cools below its Curie temperature (i.e., the temperature above which a given material cannot be substantially magnetized) in the presence of an external magnetic field. In this case, the magnetic dipoles within the rock tend to line up parallel to the ambient magnetic field. This phenomenon is referred to as thermoremanent magnetism (TRM). Natural remanent magnetism can also occur as a result of lightning strikes, or deposition of sedimentary materials with a preferred orientation due to the ambient magnetic field.Natural remanent magnetism seems to decrease with increasing geologic age. Therefore, remanent magnetism effects tend to be more common in Tertiary volcanics than in Precambrian basement. Since the Earth's magnetic field is believed to have reversed itself many times throughout geologic time, it is common for remanent magnetism to be approximately parallel or anti-parallel with the Earth's present magnetic field, unless the rock mass has been tectonically rotated or relocated after obtaining its remanence. Study of remanent magnetism has provided important evidence for the formulation of plate tectonic theories, especially in the reconstruction of relative plate movement.In practice, remanent magnetism is often detected by the magnetic anomaly signature. If significant remanent magnetism is present, and if the remanent magnetic vector is considerably different from. the direction of the Earth's present field, then the resultant magnetic anomaly will have an abnormal signature compared to that expected for induced magnetism.============

Temperature EffectsMagnetism results when atomic particles of magnetic minerals become preferentially aligned in rocks. Heat tends to cause a random alignment of atomic particles. Above a given material's Curie temperature, significant magnetization cannot occur.

Because subsurface temperatures increase with depth, substantial magnetization can occur only above certain depths. In areas with relatively high geothermal gradients, the maximum depth of magnetization is shallower than it is in areas with lower geothermal gradients. The maximum depth of magnetization, (the Curie depth) is usually around 20 km.

Figure1 illustrates the relative magnetism possible in magnetite as temperatures approach the Curie value.

Figure 1

=============

Physical MeasurementMost modern magnetometers measure the total magnetic field, which is merely the scalar magnitude of the Earth's magnetic field. They do not measure the direction of the magnetic field.Since the Earth's total magnetic field averages about 50,000 gamma and most local (or crustal-sourced) magnetic anomalies measured in petroleum exploration average only a few hundred gamma, the presence of a local magnetic anomaly will not appreciably alter the direction of the Earth's total field. The magnitude of the measured total magnetic field will be altered only by the component of the anomaly which is parallel to the Earth's magnetic field. Thus, if the local anomaly component is in the same direction as the total field, the total field measured locally will be greater than the Earth's normal total field ( Figure1 , Field measured by total field magnetometers ).

Figure 1

==============

Superposition of Potentials

The superposition principle applies to both gravitational force fields and potential fields. In the case of gravitational potential fields, as more bodies are added to a system, the total potential decreases, because all bodies mutually attract each other and it takes more energy to remove all of the bodies from the system.

Potential is a scalar quantity, the potential from a particle varies only with that particle's distance from the observation point, not with the direction. For a three-body system, a statement of the superposition principle would be:

Ug = UBody1 + UBody2 + UBody3(1)

Potentials due to complex bodies from any observation point are determined by integration.

Figure 1 is a simple diagrammatic example of superposition of gravitational potentials for two identical spherical orebodies.

Figure 1

Note that the negative potentials add together, and the equipotential surfaces and lines of force are approximately as shown. If Earth did not exert a gravity field, a particle's gravity acceleration would be in the direction of the lines of force (i.e., normal to the equipotential lines directed toward lower potentials). But in fact, the Earth's vertical gravity force field dominates the local gravity anomalies measured from local geologic features. Thus, the gravity anomaly measured by the gravity meter is the slope of the gravitational potential in a vertical direction, as shown on Figure 1 .

The gravity acceleration of any body is

(2)

where the minus sign gives positive attractions at increasing z values with increasing depths.

Figure 2 qualitatively introduces the concept of magnetic potential.

Figure 2

It shows a polarized dipole, with pole locations the same as the sphere centers shown in Figure 1. The negative pole, which is shown at the shallower depth, generates negative equipotential lines (which attract the magnetometer sensor, defined as an isolated positive unit pole). These lines are superimposed with positive equipotential lines from the positive pole. Thus, because of superposition, the effects from the positive pole cancel out the effects from the negative pole. This cancellation produces a configuration of equipotential lines entirely different from that of Figure 1 , which shows two positive poles of exactly the same pole strength and geometry as the positive-negative dipole shown in Figure 2 . Figure 2 shows the lines of magnetic force that we would observe at ground level with a positive pole magnetometer sensor in the absence of an external field. Older land magnetometers typically measured the vertical or various horizontal components of magnetic attraction. These components are determined in a way analogous to determining the gravitational attraction from a gravitational potential:

Vertical Component:

; z increases with depth(3)

Horizontal Component:

(4)

where Um = magnetic potentialMost modern ground and aeromagnetic data are measured by total field magnetometers, which essentially measure the component of the magnetic attraction in the direction of the Earth's magnetic field. The component of the magnetic attraction in the direction of the Earth's magnetic field is given by

(5)

where /f is the directional derivative in the direction of the Earth's magnetic field.

Some T components of the magnetic attraction lines of force are shown on Figure 2 (expanded view "A") for local magnetic anomalies that project in the same direction as the Earth's field and cause positive T and Figure 2 (expanded view "B") for local magnetic anomalies that project in the opposite direction as the Earth's field and cause negative T.

Compare the gravity and magnetic equipotential line configurations, the configuration of the lines of force, and typically measured gravity and magnetic components, shown on Figure 1 and Figure 2 . The differences in the potential configuration, for what is essentially an identical subsurface feature, illustrate why a subsurface body causes different gravity and magnetic anomaly signatures.=====================================================Gravity and Magnetic Potentials

The following generalized equations are true for complex distributed bodies (refer to Figure 1 [Diagram for potential field equations, complex bodies] for symbols).

Figure 1

Gravitational Potential at Observation Point:

(1)

where (V) is the density of the body as a function of where each volume element is located, and where R(v) is the distance from each volume element to the observation point, and where ? is the volume integral carried out over the entire body.

Magnetic Potential at Observation Point:

(2)

where M(V) is the magnetic moment, or magnetization, as a function of position for each volume element within the body, and where

is the directional derivative of 1/R(v).in the direction of polarization of the body (assumed constant for this case). R(v) is the distance from each volume element to the observation point.

The expression for the magnetic potential of a magnetic dipole, which is the quantity inside of the volume integral in Equation 2, was developed by Poisson in 1826.====================================================Gravitational and Magnetic Attractions

Gravitational Attraction at Observation Point (Vertical Component) Figure 1 (Diagram for potential field equations,

Figure 1

complex bodies ):

; (z positive downward)(1)

Magnetic Attraction at Observation Point (Vertical Component):

: (z positive downward)(2)

Magnetic Attraction at Observation Point (Horizontal Component):

(3)

Magnetic Attraction at Observation Point (component in the direction of the Earth's magnetic field):

(4)

where is the directional derivative in the direction of the Earth's field.

From Equations 1 through 4, we can derive further simplified expressions for special cases. For this discussion, we are assuming that the density contrast, along with the magnetic moment contrast and magnetic moment direction, are constant.

For a body of constant density, the gravitational potential is

(5)

and the gravitational attraction is

(6)

For a body polarized in the direction of the Earth's magnetic field, the magnetic potential is:

(7)

The magnetic attraction from this body in the direction of the Earth's magnetic field (as measured by a total field magnetometer) is

(8)

If the Earth's magnetic field is vertical, but the body is polarized in a direction p, the vertical magnetic attraction is

(9)

By substituting Equation 6, we can express Equation 9 as

(10)

For the special case of vertical magnetic polarization in a vertical Earth's magnetic field, the vertical magnetic attraction is

(11)

and substituting from the gravitational attraction from a constant density body, the vertical magnetic intensity is given by;

(12)

This last equation, for the special case of the Earth's essentially vertical gravity field (Garland, 1951), shows that the magnetic anomaly (at the magnetic pole, where the body is polarized vertically) is a constant times the first vertical derivative of the gravity anomaly. Thus, for uniform density contrast and uniform polarization of a body, we can theoretically calculate the magnetic anomaly from the gravity anomaly. Furthermore, the magnetic anomaly can cause steeper gradient anomalies, since it is a derivative of the gravity anomaly. The higher mathematical "order" of the magnetic anomaly gives rise to signatures that can vary more dramatically than gravity signals caused by the same source body. Equation 12 is often called Poisson's Relation.=======================================

Principles Arising from Potential Analysis

A review of basic concepts shows that we can compute gravity and magnetic force fields (and therefore, gravity and magnetic attractions) from gravity or magnetic potentials. A more detailed analysis, which is beyond the scope of this discussion, would show the following:

If we know the gravity or magnetic field everywhere at a given elevation, we can calculate the gravity or magnetic field at a higher or lower elevation, as long as we do not continue into the source bodies. (In practice, the accuracy of the downward continuation process is inherently limited due to noise amplification).

We can fit any gravity or magnetic field by a shallow layer or surface of variable density or variable magnetization. From a practical point of view, however, the magnitude of the required density or susceptibility contrast could be geologically absurd.

If we observe a magnetic field at latitudes other than the magnetic poles (with vertical polarization), we can recalculate the magnetic field as if it were measured at the magnetic poles. This process is known as reduction-to-pole, and is subject to certain accuracy limitations. For example, reduction-to-pole for data acquired near the equator can be difficult and may yield unsatisfactory results.

If the gravity or magnetic field is known everywhere on a surface, then we may calculate any degree of derivative. This is subject to certain accuracy limitations due to noise amplification.

For a uniformly dense and uniformly magnetized body, if we know or can calculate the gravity field, we can also calculate the magnetic field if we know the direction of the body's magnetic polarization.The study of potentials also shows numerous additional interesting relationships, which are beyond the scope of this manual. Refer to Kellogg (1929) or Ramsey (1964).

Earths Magnetic FieldTo a first order of approximation, Earth's magnetic field is similar to that of a bar magnet, with the Earth's magnetic poles corresponding to the magnets poles. ( Figure1 , Earth's magnetic field like a giant bar magnet ). Strictly speaking, what we refer to as the Earths north magnetic pole (because the north-seeking end of a compass needle points in that direction) is actually a south pole.

Figure 1

Like that of a bar magnet, the Earth's magnetic field strength is about twice as great at the magnetic poles as at the magnetic equator. Figure2 ( Earth's magnetic lines of force [simplified] ) (after Nettleton) is a simplified diagram of the lines of magnetic force on the Earth.

Figure 2

Figure3 ( Earth's magnetic field total magnetic intensity ) shows the variation in total intensity of the Earth's magnetic field.

Figure 3

Note that the dip of magnetic field lines with respect to the Earth's surface is vertical at the poles and horizontal at the equator. This dip is referred to as inclination, while the angle between geographic north and local magnetic north is called declination. The local magnetic inclination, declination, and average value of the total field are often referred to as local magnetic elements or magnetic field parameters. Local magnetic elements affect the amplitude and shape of local magnetic anomalies caused by magnetic rocks. The magnetic anomaly signature over a basement high block, having a positive magnetic susceptibility, varies from a magnetic high in polar regions to a magnetic low in equatorial regions. Anomalies from intermediate latitudes are asymmetric with the magnetic high shifted toward the equatorial side of the basement high. Keep in mind that this dipole behavior of anomalies, varying with respect to their position in the Earths field, is unique to magnetics. We do not observe this behavior for gravity.

Local magnetic elements vary with time, both in short-term diurnal variations (i.e., those occurring from day to day) and long-term secular changes (i.e., those occurring over periods ranging from years to thousands of years). The secular variation is due to the rotation and internal motion within the Earth's molten outer core, which is believed to play a major role in generating the Earth's main magnetic field.

For example, the Earth's field reflects a solar effect known as the solar daily variation, a cycle of pulsations which is not simultaneous for all longitudes, but where each phase of the cycle in turn traverses the globe from east to west. The daily effects are called diurnal variations, and are due to variations in the Earth's external magnetic field. These perturbations often vary as a function of solar activity and daily global heating.

Micropulsations and magnetic storms are transient variations in the external magnetic field. These phenomena are superimposed upon the diurnals, and are random in behavior. They result from various geomagnetic phenomena (i.e., solar flares) and pulsations of the Earth's internal and external magnetic currents. Refer to Figure 6 ,

Figure 6

Figure 7 ,

Figure 7

and Figure 8 , respectively, for typical depictions of diurnal variations, micropulsations, and magnetic storms.

Figure 8

Explorationists must correct for the time-varying component of the magnetic field. Magnetic base station monitoring equipment can detect magnetic storms while survey operations are underway. Except for magnetic surveying connected with marine seismic operations, magnetic operations should be shut down during magnetic storms.It is sometimes possible to correct for diurnal variations by subtracting the variations observed at the base from the variations observed on the aircraft or survey vessel. However, the diurnal variations at the base station may be dissimilar to those on the survey vehicle. Adaptive filtering techniques have been developed to improve the effectiveness of such diurnal subtraction. Typically, in aeromagnetic surveying, where the airplane covers large distances during diurnal events, the survey line mistie analysis and adjustment can remove some of the diurnal component. =-=============

Problem:

A spherical massive sulfide orebody has a density contrast of 1.0 g/cm3 with the "country rocks," and a diameter of 100m. Plot the gravitational potential as a function of distance from the center of the orebody. Draw equipotential lines of -10, -8, -6, -4, and -2 ( 10-5 joule/kg) and gravitational "lines of force." What is the gravitational attraction at a point 150m above the orebody? Show that the same gravitational attraction can be estimated by calculating potentials at R=145m and R=155m and using the relationship

Solution:

a. Determine the anomalous mass of the sphere:

b. Calculate and plot potentials (refer to Figure 1 ).

Figure 1

R, metersUg, joule/kg

0

3000-1.16 10-5

2500-1.40 10-5

2000-1.75 10-5

1500-2.33 10-5

1000-3.49 10-5

500-6.98 10-5

20017.4 10-5

155-22.51 10-5

145-24.06 10-5

100-34.90 10-5

c. Draw equipotential lines. Extrapolate the radius to equipotential lines as shown in Figure 2 .

Figure 2

Ug, joule/kgR, meters

-10 10-5349

-8 10-5430

-6 10-5560

-4 10-5850

-2 10-51700

Notice that the equipotential lines in Figure 2 are contoured on a 2 10-5 joule/kg contour interval. Since the gravitational attraction is given by

it is apparent that the faster that Ug changes with respect to R, the greater the attraction will be. Since the equipotential contours are closer together nearer to the sphere, it is apparent that the gravitational attraction becomes greater as the sphere is approached.

Gravitational "lines of force", which are lines along which an unrestrained particle would accelerate in the absence of any other gravitational field, are perpendicular to the equipotential lines.

d. The gravitational attraction 150m above the orebody center, assuming the Earth's gravity field is vertical, is given by:

= 0.155 mGale. To approximate the gravity attraction by using the difference in potentials, we have

; if R is small

As the observation point moves further from the sphere, where the rate of change of Ug with respect to R is less ( refer to Figure 1 and Figure 2 ) , that the gravitational attraction is also less.=====================

Magnetic Instruments and Field Surveys

IntroductionAeromagnetic surveying is the most common and, for most exploration applications, the most effective way of making magnetic measurements. Before World War II, ground-based magnetic instruments had a long development history. Since then, optically pumped and proton precession magnetometers have virtually replaced these devices. The fluxgate magnetometer was developed during World War II and used for finding submarines. After the war, fluxgate magnetometers were used all over the world in petroleum exploration. The data acquired with these magnetometers is of very good quality and still in use, although the instruments themselves are obsolete. There are other applications of the fluxgate sensor (e.g., susceptibility measurements), but fluxgates are no longer used for surveying. Today, commercial aeromagnetic survey contractors use either optically pumped Cesium-vapor magnetometers or some type of proton precession magnetometer.

Aeromagnetic data acquisition has a number of advantages over land and marine-based surveys. Rapid speed of acquisition, an advantage in itself, is a help in dealing with the time-variations of the magnetic field. Time changes in the magnetic field are usually slow compared to the time for an aircraft to traverse a geologically caused anomaly. The survey height of an airplane has the advantage of moving the measurement point away from the influence of near-surface magnetic disturbances that are usually not of exploration interest. Survey height can be chosen to avoid aliasing.

Marine magnetic data are commonly acquired during gravity or seismic surveys. The incremental cost of adding a magnetometer to a fully outfitted survey vessel is small. Land-based magnetic surveys are common for mining, engineering and environmental applications, but less common in petroleum exploration.

Magnetic borehole measurements, although not yet common, have seen a variety of applications. One interesting application that is under development is to use the decay rate of proton precession signals as a measure of both porosity and fluid type (Vail, 1987). Magnetic logging has also been used for aiding stratigraphic correlations (Bouisset and Augustin, 1993).

Recent advances in magnetometer design and GPS surveying have led to "high resolution" surveying techniques. These surveys are commonly flown at 200 flight line spacing, much tighter than basement-mapping surveys. The high resolution surveys are often used to map intrasedimentary anomalies.

Magnetic Survey DesignFor petroleum exploration surveys, Nettleton (1976) recommended that surveys be flown with a primary line spacing of about one-half the depth from the airplane to the magnetic basement. Survey grids of 2 by 10 km are typical for basement mapping, and a tie-line spacing ratio of about 5 times the primary line spacing is normally an efficient choice for surveys of any scale. For applications involving quantitative analysis, such as basement mapping or modeling, it is desirable to design the survey to be flown at a constant elevation, usually about 300 m above ground level. For all but the highest magnetic latitudes, the most effective primary survey line direction is magnetic north. At high latitudes, a primary line direction perpendicular to geologic strike may give the best definition of the field.

Reid (1980) examines the problem of aliasing in terms of the average height above magnetic sources and concludes that the survey line spacing should be between one-half and twice this height depending on the intended use of the data. A magnetic map over a similar, nearby area, is a good source of survey design information. The map can serve as a model so that line spacing and orientation can be chosen for optimal definition of the field while economizing on total survey traverse kilometers.

Closer line spacing with tie lines nearly as close as primary lines is often a good choice, and an effective use of funds. Shallow anomaly sources are often superimposed on the response of target structure; this is common in Nevada, for example. In such cases, inadequate sampling of the local magnetic field will lead to a distorted view of the target, and a geologic picture from the magnetic survey that is not as useful as what could be achieved with a more detailed survey.

Another means of economizing on total survey kilometers is band or triplet flying. Band flying has been used for reconnaissance surveys over very large areas. The bands usually consist of three primary lines spaced at about 2 km; the bands themselves are spaced about 25 km apart. The magnetic field can be contoured within the bands so that azimuth corrections can be established for the magnetic depth estimates.

Drape flown surveys are typical for mining exploration in rugged terrain, where maximum definition of shallow detail is an objective. The main purpose of such surveys is to locate strongly magnetic shallow sources that may be associated with mineralization. Flight heights for drape flown surveys are 100 meters or less above the topography. In very rugged terrain, helicopters can fly lower than fixed wing aircraft and so are often used in spite of their greater cost. Although draped surveys can be quite effective for locating shallow magnetic features, the draped data are more difficult to map consistently or quantitatively interpret, especially for depth estimation.

Time Variations in the Magnetic FieldFor any magnetic survey, we need some means of monitoring time variations in the Earth's magnetic field. Techniques range from frequent returns to a base station for small-scale, land-based surveys to establishing one or more base station observatories in or near the survey area. Government-run magnetic observatories may also prove helpful. The quality of data available from these observatories varies; some is quite good and available in digital form. A magnetic observatory farther than a few hundred kilometers from the survey area is of little help in reconstructing the diurnal field in the survey area for quantitative removal. In fact, base stations only 50 km apart often show responses that are quite different in amplitude and phase. This typically occurs where the magnetic character of the rock underlying each of the base stations is different.

Ideally, base station monitors determine when acceptable survey data may be acquired and when survey operations should be suspended. The specification for unacceptable flying conditions depends on the survey objectives. The best magnetic data are acquired when the time varying magnetic field is quiet. When the amplitude and wavelength of the time variations approach that of anomalies of interest, the survey should be suspended. Economic considerations often dictate that magnetic data be acquired from the beginning of the survey period to the end, as in the case of a marine seismic or gravity survey, where magnetic data are being acquired at the same time. High-quality magnetic base station data can often be quite effective in removing some time variations with little distortion of the geologic signal, although magnetic data acquired during magnetic storms is normally uncorrectable and useless for exploration. Magnetic base stations should be placed far from cultural magnetic activity such as passing cars, power lines or large amounts of magnetic metal. Digital recording and accurate timing of samples are important. A sampling interval of about 1 minute is normally adequate, because shorter period variations in the field can't be reliably correlated for removal. This is because we can only correlate shorter period time variations in the magnetic field over relatively short distances compared to the typical distance from a base station to a survey magnetometer.

Magnetometers

The optically pumped Cesium-vapor magnetometer is now the most widely used instrument for aeromagnetic surveys. Before these devices came into common use, proton-precession magnetometers were the instruments of choice; and before that, fluxgates had been used. Proton-precession magnetometers are still widely used on marine surveys and as land-based instruments.

Breiner (1981) reviewed the types of magnetometers used for geophysical applications, and provides a good source for more detail. Mechanical instruments that saw use in mining for centuries are virtually no longer used in exploration. Induction coil magnetometers are useful only in measuring changing magnetic fields, and they are used in exploration with some types of magnetotelluric systems. They are not useful for exploration magnetic surveys. Another type of magnetometer that many have tried to develop into an exploration instrument is the SQUID (Super conducting Quantum Interference Device) magnetometer. SQUID magnetometers are capable of measuring changes in the magnetic field of 10-5 gamma. They are used in some magnetotelluric systems, but they have not been used in magnetic exploration because of their cost and the difficulty of effectively using their very high resolution.

Optically pumped and proton-precession magnetometers measure the scalar value for the Earth's total magnetic field. Both the fluxgate and the SQUID measure the vector component of the field aligned with the sensor. In these vector magnetometers, the three orthogonal sensors are needed to compute the value of the total field. The promise of the SQUID is that it will measure magnetic gradient to a high degree of accuracy, which could be very useful if the problem of magnetic variation in the survey vehicle must be overcome.

Proton-Precession Magnetometer

The proton-precession magnetometer gives the most accurate measure of the absolute value of the Earth's magnetic field, although it is not the most sensitive instrument to small changes. Its absolute accuracy is about 0.1 gamma and the maximum sensitivity is about 0.01 gamma.

We can use a "spinning top" analogy to demonstrate the principle of the proton-precession magnetometer ( Figure 1 , Proton precession and the spinning top analogy ).

Figure 1

The strong DC magnetic field of a polarizing coil momentarily aligns the magnetic spin axes of all the hydrogen-atom protons in a bottle of kerosene or water so that they are all parallel to the coil. In Figure 1 , all the spin axes would point to the right while the polarizing current is on. As soon as the polarizing current is shut off, the protons will begin to precess around the Earth's magnetic field vector, just as a top precesses around the vertical. As the protons precess they induce a weak AC signal into the coil. The frequency of the signal is proportional to the strength of the magnetic field. The precession frequency, w, is known as the Larmor frequency.

= F(1)

gp is the gyromagnetic ratio of the proton, a precisely known constant. At 50,000 gamma, the Larmor frequency is about 2130 Hz?23.4874 gamma/Hz.

The frequency of the AC field induced into the coil after the polarizing current is shut off is thus a measure of the magnetic field. The polarization decays after a few seconds, so the fluid in the bottle must be repeatedly re-polarized after each measurement. The polarization interval varies from less than a second to about ten seconds or more in the case of manual readings.

Marine magnetometers must operate in a relatively noisy environment, so longer polarization times are required to get accurate measurements. The typical polarization rate for most marine magnetometers is 6 to 10 seconds. Proton magnetometers in aircraft typically read once per second and can be up to ten times per second.

A sensor for a land instrument is just what it appears to be: a pint-size bottle of fluid with a cable attached, usually mounted on an aluminum pole. They are smaller than marine sensors, which are about 60 cm long and 18 cm in diameter. The electronics package for the land instrument weighs about 6 pounds, and is normally carried in a chest pack around the operator's neck. Most land and marine proton magnetometers used in exploration are manufactured by GeoMetrics, Inc. in California.

The Overhauser magnetometer is a variation on the proton magnetometer, in which a free radical is introduced into an organic fluid so that a radio-frequency excitation signal can be used to maintain continuous precession of the protons and a continuous measurement of the field becomes possible. An additional advantage of the Overhauser magnetometer is its lower power requirement. Its sensitivity is about 0.01 gamma, the same as an ordinary proton magnetometer, although the absolute accuracy is said to be slightly less. Overhauser magnetometers are manufactured by GEM Systems, Inc. of Canada.

Optically Pumped Magnetometer

Optically pumped magnetometers are not used on land or on ships, but they provide the greatest sensitivity and resolution at high sample rates for aeromagnetic surveys. When they were first introduced, they were billed as ?high-sensitivity? instruments, and are referred to as such in some literature and old aeromagnetic survey reports. The operating principle of the optically pumped magnetometers is well explained in a classic article from Scientific American (Bloom, 1958). Breiner (1981) gives the following succinct explanation (refer to Figure 2 , Alkali-vapor optical sensor Dobrin et al., 1988.

Figure 2

): "The optically pumped magnetometer was first used for geophysical measurements in 1957. This magnetometer takes advantage of optical pumping to cause atomic or electron spin precession in very much the same way as the principles of nuclear magnetic resonance are applied to take advantage of proton precession. The optically pumped magnetometer utilizes a population of electrons in alkali vapor gas such as rubidium or cesium (sometimes potassium or sodium) or in metastable helium to obtain a continuous measurement of the scalar field intensity at sensitivities better than 10-3 nT. The typical optically pumped magnetometer utilizes a lamp containing the alkali metal or helium whose light is passed through a glass cell containing the vapor of the same element and focused on a photo detector on the other side of the vapor cell. The output of the photo detector is connected through an amplifier to a coil surrounding the vapor cell. This electro-optic system, through resonance absorption and re-radiation of energy, constitutes an oscillator whose frequency is directly proportional to the scalar magnetic field intensity in much the same way as the proton precession magnetometer. The optically pumped magnetometer, however, operates with a continuous signal at frequencies considerably higher, on the order of several hundred kHz for the alkali metals and two MHz for helium."The most popular optically pumped instrument is a Cesium-vapor magnetometer manufactured by Scintrex in Canada. GeoMetrics offers a Helium magnetometer that is also in exploration use.

Gradiometers

In practice, magnetic gradiometers are actually differential magnetometers: that is, they consist of two or more identical sensors configured to measure the difference in the magnetic field at each sensor. The distance between sensors is small compared to the depth to sources of interest. In aircraft, the choice of sensor configuration is more flexible than in marine environments. Marine gradiometers measure horizontal gradient using two sensors, with one trailing the other by about 150 meters. Cesium and proton magnetometers installed in the wing tips, nose and tail of an aircraft can measure both longitudinal and transverse horizontal gradients. Vertical gradient configurations, where one cesium sensor is towed below another, are common in mining applications requiring shallow source definition and enhancement.

The benefits of gradient measurement depend on the application. In marine work, the longitudinal gradiometer serves as a time filter to reconstruct and remove time variations in the magnetic field. These variations have distant sources. Therefore, time variations in the field should be exactly the same at each sensor, and distance integration of the longitudinal gradients along the line will result in a diurnal-free total field measurement. Equivalently, a time integration of the sensor measurement as the second sensor passes over the initial measuring point will result in a reconstruction of the time-varying field. The effectiveness of either approach relies on high-quality data that are often difficult to acquire in the marine environment. Where the typical application of airborne vertical gradient measurements is to enhance shallow sources, airborne horizontal gradient measurements can enhance the mapping of complex magnetic fields.==========

Aeromagnetic Survey SystemsA magnetic survey data set must include time, location (including elevation) and the magnetic field value. The undisturbed vertical gradient is about 0.02 gamma/m; the horizontal north-south gradient is about 0.004 gamma/m. Anomalous gradients can be ten or more times these values (Breiner, 1981). Horizontal and vertical survey control becomes more critical as the survey objectives increase in detail.

Stable flight path for the sensor is a concern, especially for sensors mounted in towed birds. The advantage of towed birds is that the sensor is in a magnetically quieter place than on board the aircraft. For some surveys, it is also an advantage for the bird to pass closer to the ground than the aircraft. Stabilization of the bird is a concern that has generally been overcome by proper design. Operationally, the towed bird configuration is not as convenient as a sensor mounted in a stinger in the tail of the aircraft.

Stinger mounts are the most common aircraft survey configuration, although wing tip mounts are also used. Compensation systems are usually installed along with stinger or wing tip mounts to correct for the changing magnetic field of the aircraft as a function of its attitude. Compensation for the magnetic field of the aircraft is accomplished in two ways. The oldest technique is to install permanent magnetic strips of varying sizes in various locations on the aircraft so that the field of the aircraft is canceled at the sensor location. Another system is to measure the field of the aircraft for a range of attitudes (heading, bank and pitch), record the effects and use a computer system to add corrections based on aircraft attitude during the survey. The effectiveness of both types of compensation system is verified by flying a figure of merit over an area where the magnetic field is known to be relatively flat. The figure of merit is a pattern of four flight lines crossing a single point where the course of each line is one of the four cardinal directions. The corrected measured field at the intersection point should be equal for each of the lines.

GPS (the satellite-based Global Positioning System discussed in Section 6.2.4) has recently come into use for aeromagnetic surveys. However it is still common to rely on a combination of barometric and radar altimetry for elevation and photographic control for horizontal position. Flight path recovery is the common term for recovering aircraft position during a magnetic survey. Flight path recovery cameras record time on the film or video camera image so that the position can be correlated with the separately recorded time and magnetic field value. Cameras are helpful for recognizing and removing magnetic effects of such cultural features as buildings, railroad tracks and power lines.

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Marine Magnetic SurveysThe marine environment is a noisier place for magnetic survey measurements than an aircraft. The towed marine magnetic sensor has a long lead-in cable from the towed fish to the instrument recording console. Ships are electrically noisy places, and the largest source of noise is induced electric noise that varies depending on the ship and the routing of the cable. Induced electric noise can also come from seismic streamer cables and other electrical cables deployed behind seismic survey vessels. Two other sources of measurement error, each amounting to as much as several tenths of a gamma in high sea states, are Doppler-precession error and the magnetic field perturbation generated by conducting sea water moving through the Earth's magnetic field (Breiner, 1981). Careful installation is important in achieving the highest quality data. Usually, trial-and-error will result in a cable routing with the least electrical noise, and some configuration of stabilizing fins and drag chutes to help stabilize the fish and reduce noise at the sensor.

Marine magnetic data are usually recorded on a digital data acquisition system that simultaneously records time, location from a radio navigation system or GPS, magnetic value and gravity meter outputs.

Magnetic Data Processing and Mapping

IntroductionProcessing magnetic data is considerably easier than processing gravity data (particularly marine and airborne gravity data). Correction for the time-varying component of the magnetic field is the most difficult phase of processing, and for high-quality surveys, we can avoid the problem by flying only during magnetically quiet times. Adjustment for line crossing differences is carried out in much the same manner as for gravity surveys. The intersection differences and adjustment statistics are a good measure of survey quality.

The correction for the Earth's core (vertical) field removes expected long-term variations in the field as well as long spatial wavelengths. The IGRF (International Geomagnetic Reference Field) is the most common core field model. The observed field minus the IGRF is often referred to as the magnetic anomaly. Upward or downward continuation of the magnetic anomaly is a computationally more difficult correction that amounts to filtering of the observed field. Literally, the anomaly field is recalculated at an observation plane higher (i.e., upward continuation) or lower (i.e., downward continuation) than the actual survey's observation plane. The usual objective of downward continuation is to enhance subtle, deep-sourced anomalies. As downward continuation reduces the separation between the magnetometer and the source rock, it actually enhances all anomalies and also tends to greatly amplify noise or mapping errors. Upward continuation, which increases the distance of separation between the source rock and the observation plane, smooths the field. A common application of upward and downward continuation is mapped data sets in which the surveys were flown at different elevations.

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Diurnal CorrectionCorrelation filtering can be effective in removing diurnal and other time-varying components of the magnetic field. Figure1 shows the effect of diurnal removal on a marine magnetic line where the base magnetometer was more than 100 km from the survey area.

Figure 1

The corrected profile fits in well with nearby lines, so we may consider the correction valid.The greater the field's time variation, the greater we may expect the correction and the distortion of the corrected field to be. The measures of effectiveness of the diurnal corrections are in the intersection statistics before and after correction, and also in the similarity that we can sometimes observe on parallel lines. A pair of lines crossing the same anomaly, one line during a diurnal event and the other during a quiet period, can give a level of confidence in the correction procedure if the corrected events are similar.Earth's Normal Field

We calculate the magnetic anomaly by subtracting the Earth's computed normal or main field. The normal field is the main magnetic field plus secular variations. We compute the normal field by evaluating the International Geomagnetic Field (IGRF) formula updated to the time of the survey. The formula is a tenth order spherical harmonic expansion of the Earth's magnetic field. Input variables are latitude, longitude, elevation, time and date.

Adjustment of Survey Line Crossing Differences

After correcting for the diurnal IGRF normal field, we survey line crossing differences and adjust and remove them, just as for marine gravity data. If the variations are not too great, the adjustment process can augment or even replace the diurnal monitor in removing time variations in the field.

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Magnetic Anomaly SignaturesQualitative SketchingMagnetic anomaly signatures are related tothe magnetization of the bodythe geometry of the body, including the distance from the observation levelthe local magnetic inclination and declination.This discussion presents a qualitative method for sketching magnetic effects of simple bodies which are not vertically magnetized, and describes simple, accurate graphical and tablelook-up methods for calculating magnetic fields of vertically polarized bodies. Computation of magnetic anomalies from complex 2-D models may be done using the 2-D magnetic modeling program included with this manual.Qualitative Sketching of Total Magnetic Anomalies

The following procedure provides a qualitative understanding of magnetic anomaly signatures. It involves a three-step process, as summarized in Figure1 and Figure 2 .

Figure 1

Figure 2

1. Determine the Magnetization of the Body. This discussion assumes uniform magnetism throughout the body, and no remanent magnetism. For this example, the body's magnetization is induced by the Earth's field. For a uniformly magnetized body, we can assume that the magnetic poles or charges are present only on the body's surface, since the internal poles cancel. The following simple rule shows how to qualitatively determine the magnetic charges present on every edge of the body ( Figure1 and Figure 2 ).We assume that the Earth's field vector F points in a downward direction in the northern (magnetic) hemisphere. The angle between F and the outward unit normal vector n (i.e., normal to each face), , is defined as . The surface magnetization of each face of the body is proportional to kFcos. Thus, if = 0, the surface charge will be maximum and positiveif 0 < < 90, the charge will be positiveif = 90, the charge will be zeroif 90 < < 180, the charge will be negativeif = 180 (outward normal and Earth's field in opposite directions), the charge will be maximum and negative.Using the above logic, we can determine the charge distribution for the body shown in Figure1 and Figure 2 . (Note: If remanent magnetism were present in the body, the surface charge density and distribution would be altered. However, we could still determine the surface charge density using the relationshipMnet = Minduced + Mremanent .2. Determine the Local Magnetic Anomaly. As shown in Figure1 and Figure 2 , we are representing the magnetometer as an isolated positive charge. Thus, the negative charges on the body's surface attract and the positive charges repel the magnetometer sensor. To compute the local magnetic anomaly, we merely take a vector sum of the attractions and repulsions caused by the body at each observation point. Note that the attractions and repulsions from the body are more intense at a low observation level than at a high level, because the charged surfaces are closer to the magnetometer at the lower level. This is why aeromagnetic surveys should generally be flown at as low an altitude as practical. Figure1 and Figure 2 show, qualitatively, how the net attractions and repulsions at an observation point would sum into a net local anomaly.3. Determine Total Intensity Anomaly (Effect of Inclination and Declination). As described in Section 13.0, the total magnetic intensity is measured by total field magnetometers. For most anomalies encountered in petroleum exploration, the local magnetic anomaly affects the Earth's magnetic field only to the extent of the projection of the local anomaly along the Earth's field vector. Thus, for the body geometry shown on Figure1 and Figure 2 , we have the total intensity anomaly, calculated as shown in Figure1 and Figure 2 , by projecting the local magnetic anomaly along the Earth's normal field vector. If the local magnetic anomaly projects in a direction to increase the total magnetic field, then a positive total intensity anomaly results. If the local magnetic anomaly component projects in a direction to reduce the total magnetic field, a negative anomaly results.The qualitatively determined relative total intensity anomaly is then sketched as shown on Figure1 and Figure 2 .Magnetic Effect, Infinite SlabThe magnetic anomaly over a magnetized infinite slab is zero, regardless of the direction of polarization or depth. This is because the charge effects of the upper and lower surfaces cancel each other. However, no geologic body is truly infinite in a horizontal direction. As we approach the edges of an "infinite slab," we will measure a magnetic anomaly. The fact that the magnetic anomaly away from the edges of a magnetized infinite slab is zero is also apparent from the observation that the magnetic anomaly is a constant times a first derivative of the gravity anomaly; if the gravity anomaly is constant (as it is over an infinite slab), the first derivative is zero. (Refer to the section titled "Gravity and Magnetic Attractions" under the heading "Magnetic Force Fields.").

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2-D Intrabasement Susceptibility Change

In the northern hemisphere, an anomalous magnetic body resulting from a change in basement susceptibility will polarize, with negative (attracting) poles on the south side and top, and positive (repelling) poles on the north side and bottom ( Figure 1 , Magnetic anomaly signature, 2-D intrabasement body, non-vertical field.

Figure 1

). However, the bottom will be at the Curie isotherm (at 13 miles depth, more or less) and is often considered to be at infinity. Thus, the positive (repelling) poles at the bottom exert little influence on the magnetometer. The positive anomaly will be present over the southern portion of the body (or south of the body, depending on the magnetic inclination). Note that the lower the magnetic inclination, the stronger the magnetization of the south facet of the body, and the further south the resultant maximum anomaly will be shifted. For the southern hemisphere, the maximum is displaced northward, toward the magnetic equator.

Accurate calculation of magnetic attractions of inclined polarized bodies requires sophisticated mathematics and computer. However, a special case of the infinite 2-D intrabasement body can be easily calculated: the body with vertical polarization.

We can use a simple graphical calculation technique to compute magnetic anomalies over vertically (or nearly vertically) polarized bodies. Although computer calculations are now used for most magnetic modeling, some of the graphical or hand methods can be used to help set up or evaluate the reliability of computer models.

We consider the bottom of the body to be at infinite depth. This allows us to consider all magnetic charge as being on the top of the body ( Figure 2 , Graphical calculation of magnetic anomaly signature, 2-D intrabasement body, vertical field ).

Figure 2

No charge is present on the sides of the body, because the vertical sides are parallel with the Earth's magnetic field. The vertical field, V = .035 k F , for measured in degrees, k in cgs, F in gammas, V in gamma. The body is drawn in a true scale cross section and the angles are measured. k is the susceptibility contrast.---------

Suprabasement Structural Anomaly

The body's polarization in the northern hemisphere is as follows:

negative attracting poles on south

top facets and positive repelling poles on north and bottom facetsIn Figure 1 ( Graphical calculation of magnetic anomaly signature, 2-D suprabasement body, vertical field.

Figure 1

), we have drawn a qualitative magnetic attraction curve above the body. Note that, unlike the intrabasement case, we cannot neglect the repelling poles from the bottom facet. The poles from the bottom facet tend to cancel the effects of the upper facet, thereby greatly reducing the amplitude of the resultant anomaly. This cancellation causes the amplitude of the suprabasement anomaly to be smaller than those of the intrabasement anomalies by roughly an order of magnitude or more. In general, computing magnetic attractions of non-vertically polarized suprabasement bodies requires sophisticated mathematical calculations. It is relatively easy, however, to determine magnetic effects of simple vertically polarized suprabasement bodies.

By following similar logic to the intrabasement, vertically polarized case, we may calculate the attraction from the suprabasement body graphically as described below. Note that this model is appropriate for basement horst blocks, anticlines, or grabens. The vertical field anomaly is given by:

V = 0.035kF(T-B)(1)

where k = susceptibility (cgs units)

F = Earth's field (gamma units)

T = plane angle subtended by top surface from each observation point

B = plane angle subtended by bottom surface from each observation point

(A natural scale sketch should be drawn and the angles measured)--------------------

3-D Intrabasement and Suprabasement

GSA Memoir 47 (Vacquier et al., 1963) gives attractions for many simple bodies which are rectangular in plan view. Figure 1 ( Typical magnetic model, total intensity, second-vertical derivative, Inclination = 20 ) shows one example of the bodies described in this reference.

Figure 1

For vertically polarized bodies which are circular in plan view, we may use solid angle tables to calculate the magnetic anomaly. Although computers handle most magnetic calculations today, familiarization with these simple hand methods can help an interpreter design and evaluate computer models. The equations for the vertical magnetic field (V) approximation are as follows (Nettleton, 1942):

Intrabasement Model: V = k F T(1)

where wT is the solid angle subtended by the top of the body in radians, V is in gamma, k is the magnetic susceptibility contrast (cgs) and F is the magnetic field in gamma.

Intrabasement Model: V = k F (T -B)(2)

where wB is the solid angle subtended by the bottom of the body, and k is the magnetic susceptibility (cgs).---------------

2-D Computer Models

Talwani (1965) developed methods for constructing 2-D magnetic models which EDCON adapted into its GMOD modeling software. GMOD is used to construct some illustrative 2-D magnetic models shown below.

Figure1 shows a magnetic basement horst block polarized by induced magnetism, in the northern hemisphere, with varying inclinations (0, 30, 60, 90).

Figure 1

Note the variation of the magnetic anomaly signature caused solely by the variation in magnetic inclination.

Figure2 shows the basement horst block from Figure 3 (at 60 N inclination) with a shallow lava flow and dike.

Figure 2

Figure 2 shows the basement horst block and lava flow only.

Figure 3

shows the basement horst block and a reverse polarized lava flow. Together, Figure 2 , Figure 3 , and Figure 4 show the effects of intrasedimentary magnetic material on magnetic interpretation and illustrate the importance of modeling the intrasedimentary magnetic material to get a proper understanding of its areal extent, polarity, and depth.

Figure 4

LATIHAN:

a. Calculate and graph the magnetic effect, V, of (i) the vertically polarized intrabasement body and (ii) the vertically polarized suprabasement structure shown in Figure1 and Figure 2 .

Figure 1

Comment on the comparison between the two anomalies.

Figure 2

Calculate the gravity anomaly from the suprabasement structure, assuming a density contrast of 0.20 g/cm3 between the basement horst block and the laterally adjacent sedimentary rocks. Show how the magnetic anomaly computed in Steps 1 and 2, is related to this gravity anomaly (refer to equation ).

JAWABAN:V = .035 k F top =.035 (.001 cgs)(50,000 gamma) top = 1.75 topwhere top is measured in degrees and V is expressed in gamma. Measure the angles subtended by the top of the intrabasement body, where the negative charge is, and plot as shown in Figure1 .

Figure 1

V = .035 k F (T - B)= 0.35 (.001 cgs)(50,000 gamma)(T - B)= 1.75 (T - B)Utilize the measured angles to the top (at 5000 ft) from Part 1 above; measure angles to the "base" (at 7000 ft) at the same observation points as T was measured. Take the difference between the angle to the top and angle to the base (T -B) and multiply by 1.75 to get V expressed in gamma.Comparison between the intrabasement and suprabasement anomalies:the intrabasement anomaly is of much larger amplitude.the intrabasement anomaly is greater than zero everywhere.the suprabasement anomaly goes below zero.if the plots of the intrabasement anomaly and the suprabasement anomaly were "normalized" to the same amplitude, the suprabasement anomaly would exhibit a much steeper gradient and a higher degree of curvature.g = .071tC = .071 (0.2 g/cm3)(2 kilofeet) C =.0284Cwhere C is the angle subtended by the average depth of the horst block (at 6000 ft depth) in degrees and g is expressed in mGal.Figure1 shows the result, having a peak amplitude of 2.92 mGal.Figure1 shows that the gravity anomaly shape from the horst is similar to the shape of the intrabasement anomaly. Actually, the angles to the intrabasement anomaly are subtended from 5000 ft (the top of the intrabasement body), whereas the angles subtended from the gravity anomaly are subtended from 6000 ft (the average depth of the horst block). Since the magnetic anomaly originates from 5000 ft as a sheet of negative charge, the intrabasement anomaly, normalized to the amplitude of the gravity anomaly, will have a little steeper gradient.Figure1 also shows that the magnetic anomaly over the basement horst block actually has much steeper gradients and more "curvature" than the gravity anomaly from the identical body. This is due to the canceling negative effect of the positively charged horst "bottom." Actually, the "horst bottom" positive charge is merely the absence of negative charge at the level of the downthrown basement faults under the horst itself. Referring to the following equation , we have:

M is the magnetization, which is equal to kH, where k = .001 cgs and H = 50,000 gamma (= 0.5 oerstad, cgs). Since we want units to be gammas, the polarization is 50 gamma, to agree with the units in which V is measured.After reducing the units, we evaluate G as 1.33 10-3 mGal/m. Thus,

= .88 x 10-3 mGal/m= .88 mGal/mDon't believe it? Try to compute g from a depth at 5998.3595 ft compared to 6001.6405 ft (one meter deeper, centered on 6000 ft). Subtract the two; the result is about .87 mGal/m.V is proportional to z(g). z(g) is maximum where V is maximum: over the center of the horst, where z(g) is .88 Gal/m.Note that where V = 0, the vertical gradient of gravity will be zero, and where V = -10 gammas, z(Dg) = -.27 mGal/m.Note also that the vertical gradient of gravity could be used to compute V.LATIHAN-2:

Calculate the vertical magnetic attraction of a vertically polarized intrabasement body, having a diameter of 15,000 ft, a depth of 5000 ft, and a magnetic susceptibility contrast with the surrounding rocks of .001 cgs. The total magnetic field is 50,000 gamma.

JAWABAN-2:

1. Sketch the problem (refer to Figure 1 ).

Figure 1

2. Define parameters for the solid angle chart. Depth = 5000 ft; Radius = 7500 ft;

therefore, Z/R = 5000/7500 = .67. We will use the solid angle chart ( Figure 1 ) along the vertical line at Z/R = .67.

3. Set up the following table:

X, ftX/ZT, radiansV, gammaComments

002.80140On Axis

500012.20110

1000020.9045

1500030.2914

2000040.126

2500050.084

a. Read solid angles from solid angle chart along the vertical line having the value of Z/R = .67. Read the appropriate values of X/Z to determine the solid angles by interpolating between contours.

b. Determine the magnetic polarization of the intrabasement body as follows:

V = k F T

= (.001 cgs)(50,000 gamma) T

= 50 Tc. Then, multiply each solid angle by 50 gamma to complete the table.

5. Note that the peak amplitude is 140 gamma. Compare that result to the 2-D intrabasement body calculated in Exercise 11, where the body had a depth of 5000 ft, a width of 15,000 ft, and a susceptibility contrast of .001 cgs in a 50,000 gamma ambient vertical magnetic field. The amplitude for the 2-D intrabasement body is 198 gamma. The 2-D body causes the greater anomaly because it subtends a greater solid angle than the disk-shaped body of identical depth and width.================================================Magnetic InterpretationMagnetics and Earths Crustal StructureThe source of Earth's magnetic field is not exactly known at present; a generally held belief is that it originates primarily from electrical currents within the Earth itself. The Earth's magnetic field is also influenced by extra-terrestrial sources such as the sun, sun spot activity seems to cause variations in the magnetic field (e.g., magnetic storms) of short period (less than one year) duration. Over longer periods, however, the Earth's magnetic field undergoes "secular" changes, gradual changes in magnetic elements at a given locality and, periodically, 180 degree reversals.As high quality magnetic data became available over oceanic areas in the years following World War II, it became clear that much of the Earth's ocean basins are characterized by alternative linear maximum and minimum magnetic trends ( Figure1 ). We refer to these alternating linear magnetic anomalies as stripes.

Figure 1

As the plate tectonic hypothesis has been refined over the last 30 years, researchers have discovered the presence of mid-oceanic ridges, and observed that new magma is being injected along these ridges. As new magma is injected, it helps to wedge apart existing oceanic crust and contributes to the expanding of the ocean basins. As the magma cools through the Curie temperature it is believed to become magnetically polarized, with a remanent magnetism vector in the direction of the Earth's local magnetic field at the time of cooling.The Earth's magnetic field is believed to have reversed itself many times throughout geologic time; it is further believed that such reversals can take place with periods as short as a few thousand years. Thus, the oceanic crust in the ocean basins is believed to contain a record of the history of normal and reversed polarity of the Earth's magnetic field. Figure2 illustrates the present sea floor spreading model, together with the magnetic data.

Figure 2

The magnetic data show more or less symmetrical additions of oceanic crust on each side of a mid-oceanic ridge. The symmetry of addition of oceanic crust is determined by correlating the magnetic anomalies on each side of the mid-oceanic ridge. The magnetic stripes are often broken by cross-trends, many of which seem to be strike-slip transform faults. Some regional fracture zones also terminate continuous trends of magnetic stripes.The plate tectonic theory hypothesizes that oceanic crust is created along the mid-ocean ridges and then ultimately rafted to continental margins, where it is subducted under the continent. It is then somehow reabsorbed back into the asthenosphere, possibly to be eventually "recycled" as magma at an oceanic ridge again. Generally, magnetic anomalies over continental areas do not exhibit the magnetic stripes common in ocean basins. Heirtzler (1985) described the change in the character of oceanic magnetic anomalies they approach continental margins, (both "passive" and "active"). He described, for example, that the magnetic stripes disappeared approximately 100 km landward from the axis of the Aleutian Trench. Heirtzler stated that the exact mechanism for the disappearance of the stripes was not well understood, but that the disappearance could be related to the oceanic plate going through the Curie isotherm, or to the seismic activity along the active continental margins.Paleomagnetic data and data on the direction of remanent magnetism, have been used to help formulate ideas on continental drift.To summarize, magnetic data have played a major role in the development of plate tectonic theory, and undoubtedly have helped researchers to gain a more complete understanding of the overall structure of the Earth. For a more detailed discussion of magnetic evidence for plate tectonics, refer to Pratsch (1992, pages 17-23).Magnetic interpreters benefit from studying continental scale magnetic maps by gaining insight into the nature of continental boundaries, basement composition, and structure over continental areas.--------------------

Geologic Applications and General Procedure

Geologic applications of gravity/magnetic interpretation, which include the following:

1. Mapping subsurface geology

reconnaissance basement mapping in frontier areas

definition of areas to acquire mineral rights or to conduct more extensive exploration

structural mapping in mature exploration areas; this might include: salt mapping, basement mapping, mapping top of high density rocks, etc.

definition of volcanic-covered areas2. Identifying "unknown intrusives" observed on seismic record sections (i.e., salt dome vs. igneous intrusive, reef vs. lava flow, etc.)

3. Aiding in discovery of additional oil & gas fields in a region, once some fields are discovered, to help define the gravity/magnetic signature

4. Extending subsurface interpretations from seismic data into areas where no seismic data are availableThese same applications apply to magnetic measurements, as does the general procedure that we should follow when we acquire or interpret gravity/magnetic data:

Step 1: Analyze geology of the area

Step 2: Determine gravity/magnetic response to known or expected geological features (a) by modeling and (b) empirically.

Step 3: Design gravity and/or magnetic survey, or analyze the quality of the available data to solve the geological problem at hand

Step 4: Interpret the gravity and magnetic data from known to unknown areas: (a) Determine residual gravity (or mag residual), and (b) Interpret residual gravity (or mag residual)---------------------------Applying Local Geological KnowledgeTo produce reliable gravity/magnetic interpretations, we must learn as much about the local geology as possible. This involves answering the following questions:What type of basement rock is likely to be present?Are volcanic rocks likely to be present?Is the sedimentary section clastic, carbonate or both?If both clastic and carbonate rocks are present, is there a distinct geologic contact between the two?Are minerals such as salt, gypsum, or anhydrite present?Are reefs, shale diapirs, salt structures, igneous intrusives, or other such features expected?What subsurface control and surface geology control is available?What density and magnetic susceptibility control is available?What is the dominant structural style of the region, and is there a predominate structural "strike" expected?What is the expected depth of burial and areal extent of the features of greatest geological interest?What is the local magnetic inclination, declination, and average total field?What is the near-surface geology?------------------------------------------

Determining Gravity/Magnetic Response

It is important to determine the gravity and magnetic response to the local geology. Ideally, we should estimate this response in two ways:

theoretically, by modeling known or expected geologic features empirically, by examining gravity and/or magnetic data within the study area and comparing actual responses to known geologic features.In unsurveyed areas, the empirical analysis of gravity and/or magnetic response will not be possible.

Model Response

We can apply the concept to calculating theoretical magnetic responses to local geologic features of interest. For example, are igneous intrusions of a certain geometry, lava flows of a certain size and depth, or basement faults of a certain throw expected? Is the basement expected to be generally magnetic or generally non-magnetic? We can construct simple magnetic models to determine the probable shape of expected observed anomalies. If no actual susceptibility data are available, we can only estimate the amplitude of the anomaly by making an initial guess at the magnetic susceptibility.

Empirical Response

If we have magnetic data for some or all of our area of interest, we should compare the observed magnetic anomalies with the calculated magnetic response. Invariably, we will need to adjust the geologic and/or susceptibility model the first time that we make such a comparison. Making this adjustment provides us with valuable information that we can apply throughout the area of interest.

Magnetic susceptibilities can vary greatly with small changes in lithology. We construct the initial magnetic model with assumed magnetic susceptibilities. If the shape and wavelength of the character of the observed magnetic anomaly approximately fit the initial model, then we can adjust the susceptibilities to give a fairly good fit. The model response will vary linearly with a change in susceptibility.

Typical magnetic susceptibility estimates to begin modeling might be as follows:

LithologySusceptibility

sedimentary rock0 cgs

acid igneous rock1000 x 10-6 cgs

basic igneous rock2500 x 10-6 cgs

In building the model, we continue to adjust susceptibilities, add intrabasement blocks, add intra-sedimentary magnetic bodies, etc., until we can obtain a good fit between calculated magnetics and observed magnetics over known or assumed geologic features.

In some instances, we may see much larger magnetic anomalies from basement structures than we can be reasonably explain based on structural uplift alone. These anomalies probably have both an intrabasement susceptibility change and a suprabasement structural component. In other instances, there may be no observable magnetic anomaly from a known basement structure due to a non-magnetic basement. Sometimes, a shallow, thick lava flow can obscure the underlying basement anomalies.

In any case, we should perform all relevant empirical model response work to design the interpretation procedures.-------------------------------

Data ExaminationPrior to interpreting any magnetic data set, we must examine the basic data to see if they are adequate to solve the exploration problem at hand. The following criteria are important:Suitability of the line spacing and direction for the particular geologic targetsFlight altitudeQuality of survey levelingQuality of mapping (is herringbone obvious in the contours?)Quality and availability of survey profilesType of magnetometerDigital data availability--------------------------------

Removal of Regional Effects

After analyzing the local geology, determining the gravity/magnetic responses to known or expected features, designing the survey and analyzing known data, we can begin the actual magnetic interpretation of the area of interest. As with gravity interpretation, we need to design for constraints on the process, including

known basement or other relevant mapped formation outcrops

subsurface depth control (such as depth to basement, minimum depth to basement, projected depth to basement, etc.)

other relevant surface geology control, such as areas of volcanic outcrop, known faults and fault patterns, basement composition, density, and magnetic susceptibility, sedimentary rock outcrop patterns, etc.

subsurface and/or seismic control on magnetic susceptibilities from samples, or modeling of known structures

We can use all of the above geologic constraints to help determine the residual magnetic field and to interpret residual magnetic anomalies.

In general, it is simpler to remove large-scale regional effects from magnetic data than from gravity data. This may be because local magnetic effects originate with sources shallower than the Curie isotherm (generally ~ 20 km) and because usually, the sedimentary section is essentially non-magnetic. Basically, we remove the Earth's normal field, as discussed immediately below, and then begin interpreting the resultant ?total magnetic intensity Earth's field removed. Frequently, we apply mathematical operators to magnetic data to enhance certain anomalies or to attempt to make the anomalies appear as they would at the magnetic pole, instead of the actual inclination where the anomaly was observed.

Removal of Earth's Normal Field

The Earth's magnetic field varies as a function of latitude, longitude, and time. We refer to the average or regional magnetic field of the Earth as the Earth's normal field. We often remove the Earth's normal field using the IGRF. Often, for small areas, we can approximate the Earth's field by a plane, and simply remove it by subtraction.

Removal of the Earth's normal field does not assist in resolving interference between local magnetic anomalies, or in resolving interference between local intrabasement and suprabasement anomalies.

Mathematical Operators

We can use many mathematical operators to filter or resolve residual anomalies from magnetic maps. Filtering can be done in the space domain by convolution operators or in the frequency domain using Fourier transform theory (Fuller, 1967). Filtering by convolution and frequency domain filtering is simply expressed as follows:

Consider:

T (X,Y) = DATA SET (space domain)

F (U,V) = FILTER (space domain)

R (X,Y) = RESIDUAL OUTPUT (space domain)1. Space Domain Filter

A. Convolution (*)

T (X,Y) * F (U,V) = R (X,Y)2. Frequency Domain Filter

A. Fourier Transform

T (X,Y) T (x,y)

F (U,V) F (u, v)B. Multiplication of Transformed Data with Filter

(T (x,y)) (F (u,v)) =R (x,y)C. Inverse Transform

R (x,y) R (X,Y)

Typical mathematical operators include the following:

Reduction-to-pole: The reduction-to-pole operator approximately removes the shift of the magnetic anomalies due to inclined (non-vertical) polarization of the body. Reduction-to-pole makes the magnetic anomaly appear as it would at the magnetic pole, with the positive anomaly directly over the causative body (if the body has vertical sides). The reduction-to-pole procedure helps outline the location of the sources for the magnetic anomalies. Reduction-to-pole filters are frequently run in conjunction with other filtering operations ( Figure 1 , "Reduction-to-pole" of total magnetic field. ).

Figure 1

At low magnetic latitudes, where the Earth's magnetic field is nearly horizontal, reduction-to-pole operators can be unstable.

Derivatives and integrals: Derivative operators help resolve higher frequency components from the magnetic field. For example, the second-vertical-derivative operator shows the curvature of the total intensity. Curvative refers to departure of the magnetic anomaly map from planar contours. Integral operations, by contrast, emphasize lower frequencies. For bodies with vertical sides the second-vertical-derivative of the magnetic field reduced to pole tends to outline the source bodies.

Figure 2 ( Total magnetic intensity,

Figure 2

southeast Missouri, USA ) and Figure 3 ( Second vertical derivative, southeast Missouri ), respectively, are a total magnetic intensity map and second-vertical- derivative map from an area in southeastern Missouri, USA.

Figure 3

Note the amplification of higher frequency anomalies on Figure 3 .

Wavelength Filters: Band pass, high-pass and low-pass filters allow examination of certain frequency components of the magnetic field. High-pass filters generally tend to emphasize energy which comes from shallower bodies. Keep in mind, however, that most shallow bodies have substantial low-frequency components, which will be distorted in the simple high-pass process. Thus, band pass filters will not perfectly separate shallow, deep, or intermediate sources. However, band pass filters do qualitatively enhance anomalies from sources in certain depth ranges.

Upward and Downward Continuation: If we know the magnetic (or gravity) field everywhere on a surface, we may compute it at either a higher or lower level, although the field may not be continued to a level which traverses magnetic (or density) sources. Upward continuation acts as a low-pass filter and tends to de-emphasize shallower anomalies. If we know accurately a magnetic field on a map on one level, we may continue it quite accurately up to a higher level. Downward continuation, on the other hand, amplifies high frequencies and tends to be quite unstable, because high frequency noise is greatly amplified. Also, we must take care not to downward continue through magnetic sources. When properly done, downward continuation can be quite useful, because the magnetic maps on lower levels will show more detail than the total intensity map. Figure 4 shows a downward continuation of the total magnetic intensity map shown on Figure 2 .

Figure 4

Note the extreme amplification of the magnetic anomalies on Figure 4 .

Strike Filters: Strike filters pass anomalies which trend in certain directions.-----------------------------

Effect of Local Inclination and DeclinationMagnetic anomaly signatures are related to the causative body's susceptibility and geometry, and to the local magnetic inclination and declination. It is important to study anomaly curves for theoretical bodies in the local magnetic latitude of a given interpretation to obtain a sense for the location of the causative body relative to the anomalies and their approximate shapes. Figure1 gives an example of the variation in magnetic anomaly signature from a basement horst as magnetic inclination is varied.

Figure 1

Thus, the first step in interpreting Residual Magnetic Data is to determine the local magnetic elements. Figure 2 ( Earth's magnetic field,

Figure 2

total magnetic intensity )and Figure 3 ( Earth's magnetic field, inclination ), respectively, show the approximate average total magnetic intensity and inclination of the Earth's normal magnetic field.

Figure 3

Accurate maps of these magnetic elements can be obtained from the U.S. Geological Survey (1983) Miscellaneous Investigation Series Map I-1457 (declination and yearly change), Map I-1458 (inclination and yearly change), and Map I-1461 (Earth's normal total magnetic intensity). Keep in mind that the magnetic elements for a particular region vary with time, and these elements are modeled every five years. Be sure to use the magnetic field element model for the correct date/year of the survey (e.g., 1980, 1985, 1990, 1995 epochs). With this information, we can construct theoretical models to show magnetic effects of expected geologic features at the local latitudes. Such studies can help us get a feel for the locations of the bodies and body edges that cause magnetic anomalies in the locality.--------------------------

Qualitative Quick Look InterpretationIn many cases, we can qualitatively interpret magnetic maps to determine fault locations, general basement fabric, and composition. Remember that magnetic maps in themselves are not basement structure maps, that the largest anomalies are likely not due to basement structure, and that some of the smallest anomalies may be the most structurally significant.

Before undertaking any qualitative interpretation, it is necessary to determine the local magnetic elements and the effect of these local elements on magnetic anomaly signatures.

Depth Estimation

One of the most common uses of magnetic data is determining the depth to magnetic anomaly sources, principally depth to basement or to magnetic source (if intrasedimentary). Since the amplitude of magnetic anomalies varies greatly according to the susceptibility of the causative bodies, amplitude in itself is not a criterion for depth estimation. Anomaly shape or sharpness is a better measure of the depth to the magnetic sources.

Figure 1

Figure 1

[c] and [d]: airborne magnetometer at elevations 300, 1300 and 6300 ft, respectively, above surface ) shows a magnetic survey flown at three levels and a gro