Understand Magnetic Maps

1 May 2006

Magnetic maps contain valuable information that is unknown unless one has some understanding of the fundamental processes that create the patterns in those maps. This report is intended to aid that understanding. A casual and uninformed look at magnetic maps will indeed tell much about the shape and location of buried features. However, an informed study of a map can provide additional details about the depth, quantity, and identity of the magnetic materials that are underground. Basic knowledge of magnetic maps may also prevent foolish interpretations and wasteful excavations. The ideas in this report fall between those of a magnetic survey and its analysis; these bordering topics receive some discussion here, but that part of the report is not very thorough. Some considerations for the processing and interpretation of magnetic data are included; also, some of the ideas here may help with decisions about field work. This report is primarily for individuals who do magnetic surveys for archaeological applications; however, some of the topics may aid others who have different goals. There are only a few illustrations of magnetic measurements in this report (most illustrations have been calculated); this is because calculated maps isolate the important factors with greater clarity. An excellent compilation of magnetic maps of archaeological features has recently been published by Tatyana Smekalova (Smekalova, Voss, and Smekalov 2005); that publication also includes an archaeological analysis of those magnetic maps, a topic that is lacking in my report. The best overall introduction to magnetic surveys and their understanding remains the publication by Sheldon Breiner (Breiner 1973); my report is designed to supplement some parts of Breiner's publication. The appearance of magnetic maps changes with location on the Earth; latitude has the greatest effect. The maps that illustrate this report are typical of ones that can be measured in most of the USA, northern Europe, Australia, and South Africa; for most of the calculated maps here, the angle of inclination of the magnetic field is assumed to be 70°. In other parts of the world, there can be significant differences in the appearance of magnetic maps. These differences are mentioned here, but Breiner (1973) has a more complete description of these latitude effects. While this report mentions gradiometers, most of the illustrations and discussions are for total field magnetic surveys. Topics generally get more detailed later in the report, and also later within each section. When one paragraph has more details than usual, the word "(technical)" is put at the start of the paragraph. The electronic version of this report has hyperlinks, primarily to figures; these are indicated with blue text. The captions for the figures are detailed, and the most important information is with those figures (which are at the end of the report). If the report is read by looking at the figures, the initial blue text (Figure ##) in a caption has a link back to the primary discussion in the body of the report. Additional information about the figures is included in an appendix. Where a full page of figures has four panels, an individual panel

Page 1 Preliminaries may be enlarged by clicking on it. The main sections of this report are as follows: Preliminaries Different Styles of Magnetic Maps General Effects in Magnetic Maps The Magnetic Lows Induced and Remanent Magnetization Data Processing Analysis of Magnetic Maps The Components of the Magnetic Field Conclusion

Preliminaries A magnetic map illustrates changes in the magnetic field in an area. Objects that are underground can warp the simple patterns of the Earth's magnetic field into complex shapes. A study of these shapes on a magnetic map can reveal much information about the features that are underground. This information can include the location, size and shape, volume or mass, and depth of the features; in some cases, the age of a feature and its material (stone, soil, metal) may be estimated. Magnetic maps are created from numbers, often measured at a uniform interval in an area. Figure 1 shows a map that has a group of numbers in their correct spatial locations. Magnetic measurements are made with a magnetometer. There are many different types of magnetometers, and they are often given a prefix that describes a fundamental physical aspect of their operation: Overhauser, cesium, fluxgate, proton. All of these types of magnetometers are excellent for archaeological surveys. Each of these magnetometers measures the amplitude (also called the magnitude) of the Earth's magnetic field; this is complementary to a magnetic compass, which measures direction, but not amplitude. The technical name for this amplitude is flux density; in physics and engineering books, this name is designated with the letter B. The typical unit for this quantity is the nanotesla. The "nano" means billionth (US), while "tesla" honors an engineer with that name; note that the letter T is not capitalized when the unit name is spelled. A study of Figure 1 shows that there is a group of high numbers near the middle, and that the numbers are negative toward the upper right; however, it is difficult to see the pattern of the numbers. This pattern is clarified with the contour maps in Figure 2; each of these maps provides a different way of revealing the numbers in Figure 1. In the upper left corner of Figure 2 (panel A), lines are drawn much like those on a typical topographic map. In panel B, high, average, and negative readings are plotted as shades of white, gray, and black. The wire frame map (panel D) is excellent for seeing the peak in the numbers. The shaded relief map (panel C) is similar to this wire frame map if this bump was viewed from overhead, and it was illuminated from the upper left (northwest) side of the map.

Page 2 Different styles of magnetic maps

Different Styles of Magnetic Maps Each of the displays in Figure 2 has benefits and limitations. The line contour and gray scale displays are most commonly applied to magnetic maps. Line contour maps have two major advantages. The first advantage is that they allow a wide range of readings to be plotted. However, note that where the contour lines are very close together, they merge into a black area with little additional information, except that the readings are extreme. The second advantage of these contour maps is that they readily show areas where the magnetic field changes rapidly with location. This information is valuable for pairing magnetic highs with lows, and this is a fundamental part of understanding magnetic maps. The area between a paired magnetic high and low has a high lateral gradient; this is revealed by the close spacing of the contour lines. A magnetic low will usually be associated with the high toward which it has the greatest lateral gradient. If one has a printed copy of a line contour map, it may be possible to recreate the digital values that compose the map; this is seldom possible with the other styles of magnetic maps in Figure 2. Therefore, a line contour map has a greater archival value. It is generally not necessary to label contour lines with the values of the anomaly or field. This is because the actual values of the magnetic field are not too important; it is changes in the field that are important. Line contour maps can also be saved as graphics files that have a high resolution; they can be vector files, rather than raster files. The line contour maps in this report are all vector files; this allows them to be enlarged on a computer's monitor without losing resolution and the sharpness of the contour lines. If magnetic maps are not very complex, vector files can be smaller than bitmap files; on complex maps however, bitmap files will be smaller. The major disadvantage of a line contour map is the fact that it is difficult to compare readings across a wide area on a map. That is, it may be difficult to see patterns that are formed by similar readings across the width of a map; this is particularly true for large or complex magnetic maps. Gray scale maps eliminate this problem, and that is their greatest advantage. If one part of a map has a particular gray tone, then another part of the map with that same gray is caused by similar or identical magnetic readings. This continuity can be a great aid for clarifying the shapes of complex features that may be revealed in a magnetic map. The big limitation of gray scale maps is the small range of readings that can be displayed. More correctly, small amplitude anomalies cannot be displayed in those parts of the map where the surrounding values are high and also where they are low. If color can be added to a map, then a much wider range of magnetic values can be plotted faithfully. A shaded relief map, like that in panel C of Figure 2, has the advantage of familiarity, at least for someone who has seen vertical aerial photographs. These maps are called shaded, but they actually have no shadows; this is a benefit, for shadows could obscure important patterns in the maps. Dark tones in a shaded relief map mean that the surface in that area is pointed away from the direction of illumination. Shaded relief maps can accentuate linear features if the illumination is set to the correct angle; they can also

Page 3 Different styles of magnetic maps attenuate these features if the illumination is in a perpendicular direction. Shaded relief maps have the disadvantage that they can increase the complexity of the patterns. This is because a single high (mound) is now shown as a combination of dark and light; with a gray scale map, the high would have a single tone. The one outstanding benefit of a wire frame map is the fact that the amplitudes of readings are apparent, even to an inexpert viewer. The major disadvantage of this type of map is that peaks in the map can hide smaller anomalies that are behind them; in panel D of Figure 2, the low area behind the peak is invisible. These maps also do not locate the anomalies very clearly; peaks are shifted proportionally to their amplitudes. Wire frame maps are also called mesh or fishnet maps. Several of the different types of maps in Figure 2 may be combined to illustrate anomalies more completely or more clearly. It is even possible to combine or overlay a magnetic map with the map of another type of survey (such as a resistivity survey), by plotting them with two of the different styles in Figure 2. There are several different ways of selecting the interval between the contours in a line contour map; Figure 3 illustrates these. If a single interval is applied, it may not be possible to show both high amplitude and low amplitude anomalies clearly. In panel A, the contours at a high value merge to form a solid black area. If these high values are not very important, one may simply omit the contour lines for the largest anomalies; Figure 14 illustrates this. As a second possibility, the map may be drawn with two or more intervals between the contour lines, as in panel B. The abrupt change in the spacing between the contour lines locates where this switch has been made. A logarithmic interval between contour lines can also allow both high amplitude and low amplitude anomalies to be displayed; panel C shows an example. The contour interval for this map is approximately logarithmic, with lines at anomaly levels of 1, 2, 5, 10, 20, 50 and so forth; there is also a line at the zero level, and the same sequence continues for negative anomalies. If fewer contour lines are wished, the levels can be at 1, 3, 10, 30, 100, 300 and so on. In panels A - C of Figure 3, the contour line for 0 is drawn thicker than normal; this distinction can aid the understanding of a magnetic map. (technical) The zero level contour is the background field that has been determined for the area; this is the regional value of the Earth's magnetic field. Along this contour line, the magnetic field from the feature is perpendicular to the field from the Earth, at least if the feature is not too magnetic. Panel D of Figure 3 is an equal area contour map. One advantage of this type of map is that a good representation can be made of any data with an automatic procedure that does not require that a person study the readings in order to select the levels. One simply decides how many contour lines to draw in the map; for this example, contour lines are to be drawn at nine levels. Next, the gridded values of the map are sorted with a fast computer program. The first contour level is determined by simply counting 10 per cent of the way through the sorted list, and selecting the value at that point for a contour line. Then the count continues to 20 per cent for the next level, and so on to 90 per cent for the final contour level. While this procedure will guarantee a rather good map that reveals the data, it will be difficult to

Page 4 General effects in magnetic maps estimate the amplitudes of the anomalies from the map. Color can aid the visibility of a wide range of anomalies in a magnetic map; if several different colors are included, the amplitude range that can be revealed in the map is increased. Four different ways of employing color are illustrated in Figure 4.

General Effects in Magnetic Maps The magnetic maps in Figures 1 - 4 show the same pattern: At the center, high values are found in a rather circular area, and there is an arc-shaped region of low values on one side of those highs. This pattern is common in most magnetic maps; it is caused by an object that is rather small for its distance (depth underground). The object could be a brick, a magnetic stone, a refilled hole, or a metal can. The pattern is called an anomaly, which just means that it is different from the surrounding parts of the map. More specifically, this pattern can be called a dipolar anomaly (not a dipole anomaly); it is called dipolar because there are two small, adjacent areas, one with positive readings and the other with negative readings. Deeper objects cause broader magnetic anomalies; this effect is illustrated in Figure 5. The heading above each panel lists the peak magnetic anomaly; note that these peak values drop even faster than the anomalies broaden. While a magnetic survey can detect objects at any depth, they must be quite massive in order to be detected if they are deep underground. It is definitely true that all magnetic maps accentuate shallow features. It is also true that almost the entire reading of a magnetic survey is caused by an object that is thousands of kilometers distant: The core of the Earth. A later section of this report will discuss how depth may be estimated from a magnetic map. It is important to estimate depth, for older features may be deeper underground. There are several different types of magnetometers, and these may be distinguished in two different ways. One distinction is between instruments that measure the total magnetic field (examples: Overhauser and cesium) from those that measure the magnitude of the field in only one direction (example: fluxgate). The second distinction is whether the instrument is being operated as a gradiometer or as a simple magnetometer. With a gradiometer, there are a pair of moving magnetic sensors; these are almost always placed on a vertical line, and usually spaced by 0.5 or 1.0 m. The phrase “total field magnetometer” is sometimes applied specifically to an instrument that is not a gradiometer. However, the word magnetometer by itself means any type of instrument that measures magnetic quantities; a gradiometer is one type of magnetometer. Magnetic susceptibility meters are not usually called magnetometers, although the plotted measurements of these instruments may be called magnetic maps. These types of maps are not described here; a description of magnetic susceptibility and its value for archaeology has been given by Dalan and Banerjee (1998) and by Evans and Heller (2003). Figure 6 shows that the magnetic anomalies from three different types of magnetic instruments are similar, although not identical. If a magnetic map does not indicate which type of measurement was made, it will probably be difficult to determine this from the patterns

Page 5 General effects in magnetic maps on the map itself. There are special considerations for understanding maps of magnetic gradient. It is conventional for the gradient to be calculated from the difference of the reading at the lower sensor minus the reading at the upper sensor. This allows a gradient map to show the same polarity for its anomalies as those in a map of the total field. Note that this convention is the opposite of other gradients in physics; it is otherwise customary to define gradients as positive if the reading increases with height. A gradient should always use the units of nT/m, and never nT/ft, even if the spacing between the magnetic sensors was in feet. With some instruments, only the difference in the field between the two sensors of a gradiometer will be measured and mapped; this difference will not be divided by the spacing between the sensors. Finally, none of these "gradiometer" measurements are true gradients; the sensors are too far apart to measure the true gradient of the magnetic field. What are the relative advantages of a survey that is done with or without a gradiometer? A gradiometer allows greater spatial resolution of buried features and it accentuates nearby or shallow features. If a single moving sensor is used rather than a gradiometer, the instrument will be lighter in weight and it will be easier to operate in brushy areas; while this instrument will detect features that are deeper, the correction of temporal changes in the magnetic field will be more difficult. A magnetometer with a single sensor can be operated in brush by holding it on a horizontal staff that can be pushed into foliage; this is difficult with any vertical gradiometer. While the measurement spacing with a gradiometer must be smaller than that with a magnetometer, that is not a fair comparison because of the greater spatial resolution that is possible with a gradiometer. Magnetometers can also be categorized by the physical principle of their operation (Dobrin and Savit 1988 p. 660 - 669; Robinson and Coruh 1988 p. 342 - 357). The main operational distinctions between these types may be summarized as follows: Proton magnetometers can be simple to operate, but they are very slow in making measurements. Overhauser magnetometers are much faster, and they require less electrical power for their operation. Cesium magnetometers can make measurements where the gradient of the magnetic field is fairly high; however, they require more power than other instruments and they are rather sensitive to the orientation of the sensors. Fluxgate magnetometers are even more sensitive to orientation; however, these instruments can make measurements even if magnetic gradients are extremely high. Fluxgate instruments can be noisier than other magnetometers, but they can also measure the magnetic field in one direction. More detailed comparisons between magnetometers have been given by Bartington and Chapman (2004) and by Hrvoic and others (2003). For archaeological surveys at historical sites, it can be valuable to have an instrument that has a high tolerance for magnetic gradients. This is because artifacts of iron and steel can be very magnetic, and anomalies may not be fully-mapped unless the instrument can still make good readings even with the high gradients that may be found near these metallic artifacts. When fluxgate sensors are operated as gradiometers, it is not practical to change the spacing between sensors; however, the other instruments allow this change. While the

Page 6 General effects in magnetic maps differences above can be very important for some specific applications, all of these different types of magnetometers can be suitable for archaeological surveys. The spatial resolution of a magnetic survey is reduced as features are deeper underground. Figure 7 illustrates this with a feature that has the shape of an E. Notice how quickly the shape becomes rounded; these illustrations show the truth of the statement that a magnetic map is a blurred image of buried features. The amplitudes of the anomalies decreases so much with increasing height that it is necessary then to decrease the interval between contour lines. Height or depth in this report means the distance between the magnetic sensor and the feature; this distance is the sum of two lengths: The height of the sensor above the ground, and the depth of the feature below the surface. The calculated maps in Figure 7 are for a total field magnetometer; Figure 8 shows how the resolution of a survey can be increased with a gradiometer. With a total field magnetometer, the amplitude of the anomaly from a small feature decreases with the cube of the distance to the feature. With a gradiometer, this decrease can approach the fourth power of distance. While it can be valuable to minimize the effect of nearby buildings on a magnetic survey (by using a gradiometer), it can also be valuable to detect deeper features (with a magnetometer, rather than a gradiometer). Figure 9 illustrates how a gradiometer attenuates deeper features. (technical) As the sensor spacing of a gradiometer approaches zero, the amplitudes of the anomalies caused by small features drop with the fourth power of distance; as the spacing gets very large, the exponent approaches three. Figure 10 shows some effects in magnetic maps that are important to remember. In the northern hemisphere, most magnetic anomalies will have a rather weak low to the north of a magnetic high; in the southern hemisphere, the pattern will be the same, but the low will be to the south. This is the same pattern that will be mapped if a magnetic object is overhead in the northern hemisphere (see panel B). Overhead objects that may be detected by a magnetic survey include metal roofs, water tanks, and electrical power transformers on poles. The features that are detected by a magnetometer are usually more magnetic than the surrounding soil; however, features that are less magnetic can also be detected, and the difference of their maps is important. Panel D in Figure 10 shows that these features will be detected primarily as magnetic lows. The detection of such a magnetic low requires that the soil itself be rather magnetic; magnetic soil is particularly likely near slow rivers and in areas with limestone bedrock. The limestone itself (along with sandstone) is essentially non-magnetic, and so buildings or rubble composed of sedimentary stone can be detected by their magnetic lows. Air cavities in magnetic soil and tunnels in magnetic rock, such as lava (Barba and others 1990), can also be detected as lows. While Figure 10 shows the mirroring of anomalies between the northern and southern hemispheres, Figure 11 shows how the patterns change in either hemisphere. Magnetic maps are simplest at the far north, for small features there cause high anomalies that are circular and centered on the buried features. At lower latitudes, the shapes of the anomalies from even simple features are more complex; both a high and a low are caused by a single

Page 7 General effects in magnetic maps object, and neither pattern may be centered over the feature. While this complicates magnetic maps, once the principle is understood, it causes no problems for understanding the patterns. (technical) At non-polar latitudes, it is possible to convert the measurements on a map so that high values are centered above each feature; this process is called a reduction to the pole (Blakely 1995 p. 330); it is generally not worth the effort. Since there will often be many different angles of magnetic remanence at archaeological sites, it is not practical to change all magnetic anomalies to their shape at the north pole in a single map. Two numbers are listed at the top of each panel in Figure 11. The Ie number shows the inclination or dip angle of the Earth's magnetic field. This angle increases with increasing latitude, although faster than the angle of latitude. The north magnetic pole is located where this angle is 90° at the Earth's surface; in the northern hemisphere, this point is currently west of Axel Heiberg Island in northern Canada. At an elevation of a few hundred kilometers above the Earth's surface, the inclination angle is 90° in northwestern Greenland; this is the northern geomagnetic pole, and aurora are centered on this point; note that this is called the geomagnetic pole, not the magnetic pole. Near the equator, the Earth's field is almost horizontal, and magnetic objects are revealed with magnetic lows. At non-equatorial locations, when magnetic surveys are done on vertical surfaces, lows can also be centered at magnetic objects. The reason is the same in both cases, and this explanation will be given later in this report; however, the general result can be summarized this way: Magnetic readings are high along and near a line that goes through a magnetic object in the direction of the Earth's field; magnetic readings are low in all other locations. There are other important effects of latitude. Figure 12 shows how a building foundation might be revealed by a magnetic survey in much of the world. As surveys are done closer to the equator, the anomalies from north-south walls can decrease until they become invisible; see Figure 13 (Radhakrishna Murthy 1998 p. 235). Elongated objects can cause unusual patterns in magnetic maps; Figure 14 shows examples; since the magnitude of the anomalies is not important, their highs have not been fully-contoured. The most common elongated feature that is found by magnetic surveys is a pipe. It appears that pipes that have been formed from sheet steel that has been rolled into a cylinder can cause the pattern shown in panel A; there may be little effect from remanent magnetization and the pipe has a linear low on the north side of the linear high. Smaller pipes may have been created by extruding or casting molten metal; these pipes appear to have a strong remanent magnetization along their length. As panel B illustrates, there can be a strong low at one end of the pipe and a high at the other end. Magnetic features that are long and vertical may be grounding rods, wells, or perhaps privies filled with metal. The lower two panels in Figure 14 reveal patterns from long, vertical objects. These are similar to the anomalies caused by compact objects, with one major difference: The lows that are associated with these elongated objects are much fainter than normal. The relative amplitudes of the magnetic high and low of an anomaly can be

Page 8 General effects in magnetic maps summarized by the ratio of the absolute values of these values. A compact magnetic object, such as the one in the calculated map of Figure 3, has a ratio of 10.5 (if the inclination of the Earth's field is 70°). The magnetic object that is 8 m long in panel C of Figure 14 has this ratio increased to 24. If the object has effectively an infinite length, it is equivalent to a magnetic monopole, which can be considered to be one end of a long bar magnet; the ratio of the amplitudes of the high to the low for a monopole is 157 (again assuming Ie = 70°). The anomalies at the ends of the horizontal pipe in panel B of Figure 14 are both monopolar; the associated highs and lows to the north of the main anomalies are too faint to appear in the contours of that map (the high/low ratio is 143). The large-area magnetic anomaly shown in Figure 15 has a ratio of its high to its low of 92. These magnetic measurements can be approximated by the magnetic map of a monopole (Figure 16). This suggests that there is a well near the peak of the magnetic anomaly. An excavation at this location was made by David Orr (National Park Service) and the top of an iron-filled and brick-lined dug well was uncovered there. The calculated map of Figure 16 clarifies other characteristics of a monopole and therefore a well: The low does not encircle the magnetic high; instead, the low readings are on one side of a straight line, and the high values are on the other side. This straight line goes in a magnetic east-west direction. The amplitude of a magnetic anomaly changes not only with distance to an object (Figure 5), but also with the distribution of the magnetic material. If a given quantity of magnetic material is located in a compact volume, the anomaly will be higher than if the material is spread out. This effect is revealed in Figure 17; it means that the quantity of material that is underground cannot be estimated from the amplitude of the anomaly alone, even if the depth is known. How closely spaced should magnetic readings be made? A survey is more economical if readings can be widely spaced, and a waste of time if they are unnecessarily close together. The first factor to consider is the height that has been selected for the magnetic sensor; this height has probably been chosen on the basis of convenience, and perhaps by knowing what spatial resolution is needed. If shallow features must be detected, the measurement spacing can be as small as about half the sensor height without making excessive and unneeded readings. The effects of changes in measurement spacing are revealed in Figures 18 - 20. For these surveys, the sensor height was about 0.8 m. The map made with a measurement spacing of 0.3 m (Figure 20) appears to define each anomaly very well. However, the map with a measurement spacing of 1.5 m (Figure 18) detects many important anomalies and also defines the brick wall quite well. The map in Figure 20 has 25 times the number of measurements as the map in Figure 18, and it required about ten times longer to do the survey. However, the map in Figure 20 is not ten times better than the map in Figure 18. This shows that the choice of measurement spacing is not an easy or a theoretical decision. One procedure that may minimize wasted time is to start a survey with a coarse spacing between readings, and then resurvey small areas that have revealed important anomalies

Page 9 General effects in magnetic maps with a finer spacing. If one was to look only at the magnetic map of Figure 18, made with a measurement spacing of 1.5 m, and not know the additional details that could be detected in Figure 20 (with a spacing of 0.3 m), one may never realize what remains invisible in the lower resolution map of Figure 18. That is, it may be difficult to tell by looking at a magnetic map that the measurement spacing may have been too broad. Fortunately or not, many other faults can be apparent in the measurements of a map, and Figure 21 shows some types of errors. A repetitive pattern, like that in panel A, must be due to the operator of the survey, and not to a failing of the equipment. A magnetic object is alternately near and far from the magnetic sensor; perhaps this is metal in a shoe, or it could be iron in the display console. The pattern can be prevented by eliminating every bit of iron that is possible, and staying as distant from the sensor as possible; these patterns are sufficiently irregular that it is very difficult to remove them once they have appeared in a magnetic map. Moving cars, trucks, and trains are always a problem for magnetic surveys; they are so massive that they are detected at a large distance, even with a gradiometer. With a total field sensor, the noise caused by moving vehicles is almost always a magnetic low; the anomaly with a gradiometer may be different. Why a low? This will be explained in more detail shortly, but it is due to the fact that the Earth's field is concentrated in the very magnetic vehicle, so the field must be reduced in areas more distant from the vehicle. Since the car may be nearby for several measurements, its passage will be revealed by a linear low along a line of traverse. A fairly good correction for the errors due to a passing vehicle is possible: Replace each bad reading with the average of the readings on adjacent and unaffected columns. Since lightning is a large electrical current, it creates a large magnetic field; this lightning noise is readily detected by magnetic surveys for a distance of 10 km or so. Each lightning strike will probably affect only one magnetic measurement; the polarity of the noise may be either positive or negative. These one-point errors, like those in panel C of Figure 21, can be removed from a magnetic map by replacing each faulty value with the average of the four adjacent good measurements. Median filtering can automatically remove isolated errors like these: Each measurement is replaced by the median of the values that are found in a small rectangular window around each point. Note that this process will change values even where that is not needed. The irregularities shown in panel D of Figure 21 are seen in many maps, particularly where the amplitudes of the anomalies are small. The complexity of the contour lines is caused by fundamental limitations and the noisiness of the electrical circuitry of the magnetometer; gradiometers, having two sensors, can increase this noise. This noisiness increases with the speed at which the magnetic measurements are made. At some sites, iron debris in the soil, or pockets of soil with differing magnetic properties, can contribute to a general noisiness like that seen in panel D. If a survey is done in a city with several electrified busses or trains that are 1 km or so distant, the magnetic field from the changing

Page 10 The magnetic lows electrical currents may also cause a random noise. While this type of noise can be masked by applying a window averaging to the measurements, this smoothing should not be done if the data are to be analyzed. Only the unaltered readings should be analyzed.

The Magnetic Lows The areas of low readings that are found in magnetic maps contain almost as much information as the high readings. The mixture of highs and lows in a magnetic map has some similarity to a weather map that shows contours of air pressure. Both types of maps have about the same number of highs and lows; however, these highs and lows are paired more closely in a magnetic map than in a weather map. The magnetic maps that have illustrated this report typically show low readings that are immediately adjacent to highs. These may be called dipolar (or perhaps bipolar) pairs of anomalies. The high readings and the associated and adjacent low readings are caused by a single object in the soil, not by two objects. While it is reasonable that a single magnetic object should cause high readings, the origin of the auxiliary low is explained in Figure 22. This figure shows how magnetic objects may shift and concentrate the natural magnetic flux from the Earth. In Figure 22, these flux lines are plotted as they dip down to the right. If there was no magnetic object in the middle of the area, the number of flux lines would remain the same, and all of the lines would be parallel. The magnetic object simply attracts nearby lines of flux into the object itself. That is, the flux lines are not created or destroyed by the magnetic object, they are just moved. Since the magnetic anomaly is proportional to the density of these flux lines, it can also be said that wherever there is a magnetic high, a low must be nearby. (technical) It might seem reasonable that one could construct a magnetic feature that causes no magnetic low. Why not put a smaller amount of magnetic material where that low would be measured; could the magnetic high from that new material then cancel out the low? It does not; it just shifts the low to the side. Notice in Figure 17 that even the triangular object has a magnetic low at the tapered end of the feature. If the inclination of the field is 90°, there is still a low that surrounds the circular high (panel A of Figure 11). Since the idea of the magnetic low is so important, it will be explained a second way. Rather than a big magnetic object, consider a small object, like that in the middle of the green circle in Figure 23; this may be a grain of magnetite (lodestone), or it could be a cannonball. This object is called a magnetic dipole; for this name, the object must be either small or at least compact (somewhat spherical, but even a cube is rather compact). The object does not actually have to be small, for the entire Earth is a good magnetic dipole. The lines of magnetic flux around the object are drawn in Figure 23 as rather oval shapes. These lines of flux are just the pattern that you will see if you set a permanent magnet on a table and you sprinkle iron particles around it; the iron will form chains along the direction of the flux lines. If this object is magnetized by the Earth's magnetic field, the primary field within the object will be in the direction of that field. However, in large areas outside the object, the direction of the field from the object will be opposite to the Earth's field.

Page 11 The magnetic lows

If a magnetic measurement is made at a location where this opposition is found, the resultant magnetic field will be lower than the Earth's field; this is a magnetic low. A magnetic survey that was done on the Moon would find highs without lows; see panel D of Figure 40. There are no lows because there is no surrounding field to oppose. The magnetic high that is nearly on top of a magnetic object has a small area; the magnetic low is infinitely large, for it extends over all space outside the small high. It is this wide-area low that causes passing cars to create lows in magnetic maps. Even though lows are generally much weaker than highs, the magnetic high from a car is so huge that its associated low can still be strong at a distance of 30 m or more. There is an interesting fact that can be important for the study of a magnetic map: The average of all of the readings of magnetic field in a map is a good approximation of the magnitude of the Earth's magnetic field. Stated another way, if the numbers for a magnetic map are anomalies (differences from the Earth's field), the sum of all of the readings on this map should be about zero. This seems impossible, since a magnetic object causes such high readings near it. While the magnetic lows are much weaker than the highs, these lows are found in such a large area that their entire effect is the same as a small area of strong highs. (technical) A description of this averaging to zero has been given by Blakely (1995 p. 68) for the vertical component of the magnetic field. This zero value (or background field) is important to know for the detailed study of a magnetic map; if an incorrect value is selected, then the estimate of the direction of inclination of the magnetic field in an object will be in error. Note that if the measurements of a magnetic map are spaced too widely, the magnetic highs might not be adequately sampled by the measurements, and the average of the anomalous measurements may be less than zero. The magnetic cross-section in Figure 23 plots the lines of magnetic flux from the small object; the flux lines from the Earth's field are monotonous and straight and not plotted there. When these flux lines from the Earth are added to those from the small object, the resultant is mapped in Figure 24; the general pattern is similar to that in Figure 22. The flux lines are warped near the object, and their density again indicates the magnitude of the magnetic field. Along the dashed line just above the object in Figure 24, these lines are seen to converge in one area and diverge in another, forming the magnetic high and low that are so familiar. Near a very magnetic object, the field that it creates may be much stronger than the field of the Earth. In that area, the sum of the fields remains almost the same as that caused by the object itself, and the pattern is still like that in Figure 23. Therefore, one might consider that a magnetic field has been created there. This central pattern is the field that is found around all strong permanent magnets. During a magnetic survey in the northern hemisphere, the dashed line in Figure 24 marks the path of magnetic measurements that could be made over a buried object; these readings reveal the magnetic high that is typically found above an object. If the flux lines in Figure 24 are rotated by about 90°, this would approximate conditions near the equator, where the Earth's field is almost horizontal. Then, measurements that were made over the

Page 12 The magnetic lows top of the magnetic object would find low readings, just like the low values that are plotted in panel D of Figure 11. In the northern hemisphere, if one makes magnetic measurements on a vertical surface, magnetic lows are also found next to magnetic objects. This condition can be created in Figure 24 by rotating the dashed line by 90° about the middle of the square so that the line is vertical. Figure 23 and Figure 24 illustrate two different ways of thinking about magnetic objects; both ways give an equivalent result and both ways of reasoning are correct. In Figure 23, one thinks of the object as creating a magnetic field; in Figure 24, one thinks of the object as warping the Earth's field. If an object is magnetized by the Earth (induced magnetization), then either approach works fine. However, if an object has remanent magnetization, then it is better to consider it as creating a magnetic field, as in Figure 23. This is because the magnetic field from that permanent or remanent magnetization is probably not in the direction of the Earth's field. Induced and remanent magnetization will be discussed in the next section of this report. Remanent magnetization can be revealed in a magnetic map and its direction can be estimated. This direction might indicate if an object has been burned or fired where it rests in the soil, or if it was fired or formed somewhere else and later moved to the location where it is found. The direction of remanent magnetization is the same as the direction that is determined from an archaeomagnetic sample that has been taken from an excavation. Like that archaeomagnetic sample, a magnetic map has the potential for revealing the age that a feature was created. This direction of remanent magnetization is suggested by the direction from a magnetic high to a low, and also by the ratio of the amplitudes of the anomaly high to the associated low. However, one must be careful, for this direction may be altered in a magnetic map. Figure 25 shows two sources of this change: The slope of the ground surface, and the warping of an anomaly by other anomalies that are nearby. It is not uncommon for a high in a magnetic map to have no low nearby that is clearly associated with the high. Figure 39 is a map where highs predominate. However, there is always a low associated with every high; this low may simply be invisible in a map. There are two general causes for the apparent lack of lows: A nearby high may have obscured a low; variability and noisiness in the measurements may also distort a low and make it unrecognizable. In Figure 39, the closely spaced objects cause highs that overlap (that is, objects are unresolved); many lows are squeezed out by these highs. Even where the north sides of objects are clear of other anomalies, these lows are indistinct. This is caused by the noisiness of the measurements; the noise may be due to the magnetometer's electronics, to the survey procedures, and to natural variability of the soil. In panel D of Figure 21, the high is clear, while the low is so distorted that it is almost invisible. In rare cases, a low that is associated with a high may be distant, as in the pipe example in panel B of Figure 14. The low spatial resolution of the map in Figure 39 is caused by the large height of the

Page 13 Induced and remanent magnetization magnetic sensor (0.95 m). When magnetic maps were measured with the magnetic sensor on the surface of the soil, the resolution was excellent. The amplitudes of the lows were much larger, and they were clarified into simple arc-shapes, such as that seen in Figure 3.

Induced and Remanent Magnetization Two types of magnetism create the anomalies in magnetic maps. Induced magnetism might be called the effect of a good magnetic "conductor"; Figure 22 is a typical illustration of this effect. Remanent magnetism is the effect of a permanent magnet. It is valuable to distinguish these two types of magnetism. It appears that steel usually has a high remanent magnetization, while iron may have a high induced magnetization. This difference may therefore allow the age of artifacts to be estimated. Figure 26 illustrates one way of thinking about the difference between induced and remanent magnetization; in fact, this figure summarizes a simple procedure that allows quantitative measurements of the two types of magnetization. When rotating the object, it is important that it be along a line that goes through the magnetic sensor and is in the direction of the Earth's field, in both its inclination and declination. The magnetic maps in Figure 27 and Figure 28 show how the anomalies change when an object with just induced or just remanent magnetization is rotated to different angles. One can see how these effects can create both the oscillating pattern (remanence) and the shift or offset (due to induced magnetization) in Figure 26. The amount of induced or remanent magnetization in an object is called its magnetic moment. This property can be quantified with the unit ampere-meter-squared, Am2. For objects that are weakly magnetic, a unit that is 1000 times smaller may be applied; this is called the milliampere-meter-squared, mAm2. These units quantify the total amount of magnetic material in an object. The same unit is applied to induced and remanent magnetization; the sum of these two quantities is called total magnetization. A car may have a magnetic moment of 500 Am2, while the magnetic moment of a brick may be 10 mAm2. In order to compare these quantities from one material to the next, one can divide each magnetic moment by the mass or the volume of that object; these values might be called relative magnetic moments. However, when the magnetic moment of an object is divided by its volume, the result is called the intensity of magnetization of the object; this has the unit of Amperes per meter, A/m. When the remanent magnetization of an object is divided by its induced magnetization, the result is called the Q ratio (sometimes referred to as the Koenigsberger ratio). In Figure 29, an object is assumed to have induced magnetization (Mi) and / or remanent magnetization (Mr). While the directions of these magnetizations remain the same for each map, the Q ratio changes. If the magnetization is only induced, the direction from the magnetic high toward the low is that of the Earth's magnetic field; if an object has been recently fired and magnetized in place, then its remanent magnetization would also point toward magnetic north. For the illustrations in Figure 29, remanent and induced magnetization point in two

Page 14 Data processing different directions; this figure shows how the angle from the magnetic high toward the low rotates from magnetic north toward the direction of remanence as the Q ratio increases. As many as four arrows in each panel indicate important magnetic directions. Note that the direction from the magnetic high to the low is never the direction of remanent magnetization, although it gets very close to that direction for a high Q ratio (Schnetzler and Taylor 1984). Also note that the direction of total magnetization and the direction of the high-low angle are not the same, although they are close together. The Q ratio affects the magnetic maps of clusters of objects. At archaeological sites, these clusters are found as lenses of discarded debris; brick walls are simply clusters of bricks that have differing directions of magnetization. Figure 30 illustrates how magnetic maps change with the Q ratio of randomly magnetic objects. The calculations for the figure were made over a layer of 121 dipoles, marked with X's in the figure. The random directions of remanent magnetization can create very complex magnetic maps, without any trace of a simple low to the north of the cluster. The individual anomalies that are apparent in the magnetic map of Figure 30 occur where the magnetizations of a group of nearby dipoles are accidentally oriented in about in the same direction. There are only about a dozen highs and lows in panels C and D of Figure 30; this is because of the low spatial resolution of the maps. Had the calculations been made closer to the layer of dipoles, there would have been 121 highs and 121 lows in each map. Brick walls are typically detected with maps that are similar to panel C in Figure 30; this is because the Q ratio for brick is often around 5 - 10. Walls constructed of magnetic stone show the same pattern (Barba and others 1996). The brick wall in Figure 20 is revealed with a simple and linear pattern; this is only because this wall was thoroughly heated and remagnetized in a fire that destroyed the building. The heat was sufficient to realign the remanent magnetization of the brick. The random directions of remanent magnetization of brick not only complicate a magnetic map, they also reduce the amplitude of the anomalies. A single brick may cause a larger anomaly than a small cluster of bricks; this is because the large remanent magnetization of one brick may be partly canceled out by an opposite direction of magnetization of an adjacent brick. If there is a large and compact mass of fired objects, such as pot sherds, the remanent magnetization may have essentially disappeared, leaving only induced magnetization.

Data Processing This is the step that falls between making the magnetic measurements and plotting a map of the findings. This step is discussed because it may affect the appearance of a map and one's understanding of it. Magnetic measurements are affected by temporal changes in the Earth's magnetic field. A gradiometer automatically provides a good correction. If a gradiometer is not used, a second and stationary magnetometer (called a base station) may make readings in synchronization with those of the moving magnetometer; if so, the pairs of readings may

Page 15 Data processing simply be subtracted. If the readings of this base station are not synchronized with those of the moving magnetometer, good corrections for temporal changes are still possible if the times of all the readings are recorded: One just estimates the base station reading at each time that a mapping measurement is made. That base station value is subtracted from the mapping measurement; a linear interpolation can be made between the base station readings. If a base station fails, and no temporal correction of the magnetic measurements is made, magnetic maps may be affected as shown in the top panels of Figure 31; these calculated maps assume that traverses were along north-south lines. Weymouth and Lessard (1986) give examples of maps with uncorrected temporal change. Even without a base station, temporal effects in a magnetic map may be estimated by seeing how the readings change with time in areas of the map where magnetic anomalies are weak. The lower panels in Figure 31 illustrate that a moderately good correction may be possible. A more detailed discussion of the correction of temporal change has been given by Tabbagh (2003). Modern magnetometers make their measurements very quickly, and this allows one to explore large areas with a good spatial resolution. The close spacing of the measurements accentuates faults that were found with earlier and slower magnetometers, but which may not have been visible in their lower resolution maps. These faults are shown in Figure 32; similar faults are also apparent in parts of Figure 15. The errors are apparent as undulations on the contour lines. While these faults may not have a serious effect on the interpretation of a magnetic map, they definitely make the map look inferior. Figures 33 - 39 describe the correction of the faults in the original readings of Figure 32. The magnetic map of Figure 32 reveals about two dozen magnetic anomalies that are caused by circular blocks of glassy slag, a remanent of the iron industry of Denmark in about the year 1000 . The slag blocks were formed in pits below furnaces; the blocks contain some iron that is readily detected by a magnetic survey. The blocks are typically about 0.25 m thick and have a diameter of about 0.75 m; their upper surfaces may be about 0.3 m underground (Voss 1995). The magnetic measurements that create Figure 32 were surveyed along lines that went alternately to the north and south; the lines were spaced by 0.25 m. The undulations on the contour lines would be much less if the line spacing was 0.5 m, rather than 0.25 m; the small spacing between the lines of traverse accentuates changes in the direction of the contour lines. If the line spacing had been 1 m, it is unlikely that any undulations would be visible in the resulting map. It is the close spacing between the lines that accentuates the faults, but this narrow spacing is needed in order to have a high spatial resolution. It is easy to remove the undulations that are unwanted in Figure 32; see Figure 33. Since the data processing for this figure has altered the amplitudes and widths of the anomalies, an interpretation of this smoothed map would lead to errors in estimates of the depth and quantity of magnetic materials that are underground. It may be important to try to

Page 16 Data processing determine if the measurements of a published magnetic map have been smoothed; if the contour lines are seen to be too smooth for the stated measurement interval, then it is likely that the map has been altered for the worse, even though it may look prettier. The faults that are in the magnetic map of Figure 32 would have been greatly diminished or invisible if the survey was done with measurement traverses going in only one direction; Figure 34 shows the great improvement that is possible. However, this is not an efficient use of field time, and faults remain invisible in the map. The two faults that are discussed here are called heading error and locational error. It is possible to separate these faults with a study of the contours on a magnetic map; see Figure 35. However, it is easier to find these faults with a little arithmetic. First, check for heading error by calculating the averages of the readings along lines of traverse. Figure 36 shows the result for this example, and Figure 37 shows the improvement that a correction provides. The undulations that remain in Figure 37 are primarily caused by locational errors in the readings. The vertical columns of numbers in the map are incorrectly located; they have a shift that alternates between the north and the south direction. This shift can be quantified as shown in Figure 38. This fault may then be undone by correcting the coordinates of the readings, and the result in Figure 39 has a great improvement over the original map of Figure 32. This shifting of the measurements along lines of traverse is easiest to do if the distance is a multiple of the measurement or gridding interval; otherwise, interpolation between the readings (gridding) is required to determine the new values. The effects of bidirectional traverses may also be determined by measuring a single line in both directions. If this test is done exactly the same as the survey of a large area, it can furnish the information that is needed to correct both heading and locational error in the large-area survey. While both heading and locational error will be found in almost all original magnetic measurements, both effects may not be apparent or cause difficulty in specific maps and locations. The effects of heading errors are most apparent where the lateral gradient of the measurements is low. The effects of locational errors are most apparent where along-traverse gradients are high. One step in data processing is a reformatting of the readings. The original measurements will typically be stored in a computer file with a temporal or serial order; each line of data from the magnetometer will have two numbers for the coordinate of the location of the reading; that same line will also include the magnetic reading, and perhaps the time of measurement. These original measurements will then be converted into a matrix of numbers, without individual coordinates or times; this matrix will look much like the group of numbers in Figure 1. This conversion or reformatting is done with the process called gridding, and it is a part of most computerized mapping programs. The default settings of the program that does this gridding are almost never suitable for magnetic maps. This default setting will likely make a magnetic map that looks good, but the readings will probably have been altered so much that the magnetic anomalies have been modified and therefore it may not be possible

Page 17 Data processing to interpret the map correctly. If magnetic measurements are made at uniform intervals along lines, the gridding operation should exactly retain each original value; no values should be added or subtracted. Some magnetic surveys will have the readings at a slightly irregular spacing along lines of traverse; this is done because it is easier than to make them at a fixed and constant spacing. In this case, the gridding will change essentially all of the original readings to new values. It is important that the gridding be done so that each new value depends only on up to two or three original readings that are nearest each grid point along a line of traverse; this new value should not be affected by any of the readings on adjacent lines of traverse. If this procedure is not followed, then the magnetic measurements have been smoothed, and again an interpretation can give incorrect values for the depth and quantity of magnetic material. It is always best that data processing be the minimal amount that allows an adequate map. The failings of each possible process that might be applied to the data must be understood. Some of these failings are most apparent at locations on a magnetic map where there are abrupt or one-point changes in the magnetic field. The upper panels of Figure 40 show how two common faults may be recognized in a magnetic map. While magnetometers can make their measurements very quickly, the operators of the equipment cannot walk very fast. For this reason, the readings are often very closely-spaced along lines whose spacing is much greater. It is better if the two spacings are the same; magnetic maps are clearer and more certain if the spacing between measurement along traverses is the same as the spacing between lines of traverse. This is often not practical, and panel C of Figure 40 shows the distorted patterns that may appear on a magnetic map. The visual appearance of these distortions may be reduced by interpolating additional columns of values between the lines of measurement. These interpolated values are usually quite different from the measurements that would have been made at those missing locations; this means that an interpretation of the resulting map will lead to errors. A magnetic map, by itself, has little value; it is important that additional information be included with the text for each map. The most important item is what type of magnetic measurements are in the map (total field, vertical component, gradiometer). The height of the magnetic sensor, and the spacing between the sensors of a gradiometer should also be listed. The contour interval should be stated; alternatively, a gray or color scale is needed, or the amplitudes of some anomalies may be noted. The size of the area should be indicated with a scale on the map, and the direction of magnetic north should be marked. The interval between measurements along lines can be noted; this may be both in time and distance. The spacing between lines should be listed, and the traversing directions also. The information with a map can mention what material is at the surface and the topographic relief in the area. The equipment manufacturer and the model of the instrument can be noted. The date of survey and also the time could be important for a check on noise interference and perhaps temporal changes. Any data processing that was applied should be stated and described sufficiently so that an independent reader will know what has been done.

Page 18 Analysis of magnetic maps

Analysis of Magnetic Maps Several different types of analysis may be applied to magnetic maps. These types might be called Anomaly description, Archaeological identification, and Analytical interpretation; any one of these analyses might be called a geophysical interpretation. An anomaly description might result in something like "An L-shaped pattern is located at ..." or "Of 83 identified anomalies, 28 per cent had amplitudes greater than 5 nT". This type of analysis summarizes and counts anomalies, and possibly does some categorization of them by their shape or amplitude. Perhaps a map is included that has a simplification of the anomalous patterns into straight or curved lines. No technical knowledge of geophysics is required for this type of analysis. An archaeological identification might result in a statement such as "This anomaly may be caused by a Bronze-age burial tomb", or "These lines mark the walls of ancient garden terraces". This type of analysis requires archaeological knowledge, and it can be the most valuable analysis of all. This analysis is based on knowledge of the archaeological features that are expected at the site where the survey was done; the interpreter probably has experience with excavations that have been done after geophysical surveys at similar sites. An analytical interpretation may also be called a technical, a quantitative, or a parametric analysis. This might result in statements such as "A mass of iron that could be as large as 4 kg could be as deep as 1.3 m at this point" or "A volume of soil with a susceptibility of 0.02 has the cross-section shown in the figure". This type of analysis requires a moderately good knowledge of geophysics. All of these types of analysis are valuable. They may also be combined. An archaeological identification along with an analytical interpretation can be particularly rich in information for the archaeologist. Little assistance is needed for an analysis that is an anomaly description. I do not know enough about archaeological identification to be of much help to you. However, an introduction to some of the ideas of analytical interpretation is included here. Figure 41 is a graph that shows a line of data that crosses over a compact magnetic object, marked with a green circle at the bottom. This graph illustrates an excellent way of estimating the depth of an object: It is simply equal to the width of the anomaly at half of its peak amplitude. This "depth" is the sum of the actual depth of the object underground plus the height of the magnetic sensor above the surface. This approximation is accurate for compact objects; if an object is spread out into a lens, this procedure would give an estimate of depth that is greater than the actual depth; it is not always possible to determine from a magnetic map if an object is spread out and not compact. The width is best measured along a line that goes through the peak of the anomaly and has a direction toward the associated magnetic low; this may be along a magnetic north-south line. However, the width of the anomaly caused by a compact feature is about the same along an east-west line. If an anomaly high is not very circular, this may mean that the object is not compact; however, an average of the diameters of that anomaly can still provide a valuable estimate of maximum depth. This procedure is correct for a total field

Page 19 Analysis of magnetic maps magnetometer; if a magnetic map from a gradiometer is being studied, the depths with this procedure will likely be a bit too shallow. The procedure can be applied to surveys that have been done at a wide range in the inclination of the Earth's magnetic field (Radhakrishna Murthy 1998 p. 242). If the anomaly is predominantly a magnetic low, this procedure can be applied to that low. The half width rule can also help with the analysis of linear magnetic anomalies caused by long features; this assumes that the features have a compact cross-section. In Figure 17, the calculated anomaly of the square prism has a half width of 1.5 m; this is also the distance between the calculation surface and the middle of the prism. While features must be compact for this simple analysis, they do not have to be small. If a feature is compact or rather spherical, then the depth estimate is to its middle, no matter how large it is. In fact, it is not possible to say much about the size of a feature from the shape of its magnetic anomaly; however, the peak amplitude of the anomaly might provide information about the volume or mass of the feature. The equation in the upper right corner of Figure 41 shows the method. Since the analysis indicates that the magnetic moment of the object is about 1 Am2 (which was the assumption for the calculation), the anomaly could be caused by iron having a mass of 30 kg. While there are many possible errors in this type of estimate, it is valuable to be able to distinguish the anomaly of a nail from a cannonball; without this analysis, that distinction could not be made just by looking at the magnetic map. The green symbols on the calculated magnetic maps in this report locate the magnetic sources; these are not at the peaks of the magnetic anomalies. These calculated maps allow one to estimate the offset between this peak anomaly and the center of the magnetic feature. This offset is typically a short distance from the magnetic high toward the magnetic low. If this offset is not considered, a small test excavation that is placed at the peak of a magnetic anomaly may fail to locate a small feature. If a feature is larger, such as one of the squares in Figure 10, the anomaly may be significantly offset from the feature; an excavation on the edge of the anomaly may fail to detect the edge of the feature. By failing to detect that edge, the feature may not be identified as anything unusual. Analytical interpretations often require elaborate mathematics or specialized computer programs. These procedures are valuable, but they can hide fundamental and simple ideas about magnetics. Fortunately, it is possible to approximate the anomaly of one type of feature using simple geometry; Figure 42 shows the method, which is described in detail by Nettleton (1942). At a time when it was not practical to use computers for analysis, this procedure was applied by Elizabeth Ralph (University of Pennsylvania Museum) for the analysis of a buried wall in southern Italy (Rainey and Lerici 1967 p. 60). Some general principles of magnetics can aid the interpretation of magnetic maps. The anomalies of features remain the same if the distance to the features divided by the size of the features remains constant; this assumes that the magnetic moment of the features increases with their size, or that their susceptibility remains constant. A spherical magnetic shell causes the same anomaly as a solid sphere, except perhaps for amplitude. An infinitely broad and flat magnetic stratum is completely invisible to a magnetic survey (Blakely 1995 p.

Page 20 The components of the magnetic field

285). This means that one may add or subtract any infinite strata without altering an analysis. It is easiest to study a hole in a magnetic solid by assuming that the hole has a negative value for its magnetic moment, while the value for the surrounding is zero. Many geophysical books give good introductions to the procedures for the technical analysis of magnetic maps. For a full understanding of quantitative interpretation, there is no publication that is better than the book by Blakely (1995). Some of the clearest descriptions of magnetic principles have been given by early authors (Heiland 1940; Haanel 1904). Perhaps many of the writers of current books once read those authors and found the topics so clear that they thought it was not necessary to repeat the discussions in their books. Since the units for magnetic quantities are different in these early books, that can make them more difficult to read.

The Components of the Magnetic Field The magnetic field is a vectorial quantity; it has both a magnitude and a direction. Three numbers describe the magnetic field at any point, but usually only one of these numbers is measured or mapped. The upper two panels in Figure 43 shows maps of the different patterns that are measured with two types of magnetometers; fluxgate magnetometers often measure just the vertical component of the magnetic field. Both maps are similar, and both are valuable for magnetic exploration. The total field map in panel A of Figure 43 can be calculated from the maps of three perpendicular components of the magnetic field, shown in panels B - D. This must not be a simple addition of the readings from each map (that is called a scalar addition); instead, it must be a vectorial addition, which is the square root of the sums of the squares of the magnetic fields in the three maps. While the magnetic field can be described by three measurements that have been made in perpendicular directions, it can also be described by a magnitude (panel A of Figure 43) along with two angles. These angles are the inclination (vertical angle) and declination (horizontal angle) of the magnetic field. Calculations of these directions are plotted at the top of Figure 44 for the same object that is mapped in Figure 43. Note that changes in the angle of the field are very small. The declination angle can be measured with a typical magnetic compass; indeed, a simple compass can be suitable for detecting very massive iron objects. The inclination angle can be measured with what is called a dip meter; this is just a magnetic compass whose needle swings in a vertical direction. A dip meter can be made moderately sensitive to magnetic features by counterbalancing the tendency of the needle to point in the direction of inclination of the Earth's field. The gradient of the magnetic field that is measured most commonly is the vertical gradient (Figure 6). However, it can also be valuable to measure horizontal gradients; the lower two panels in Figure 43 show the maps of these gradients for a single dipolar object. Since these maps show three associated anomalies from a single object, these anomalies are more complex than those from other magnetic measurements; this same complexity is apparent in the shaded relief map in Figure 2. In spite of their complexity, these horizontal

Page 21 Conclusion gradients aid some types of magnetic surveys. A survey with sensors to the left and right of the line of traverse can double the rate at which an area is explored for rare features. With airborne surveys, it is difficult to mount sensors along a vertical line, for this increases wind resistance; horizontal sensors are easily positioned inside an aircraft, for example at the tips of the wings. If a magnetic map is measured with adequate resolution, then the different maps in Figures 43 and 44 may generally be converted from one to the other by applying mathematical procedures. These ideas have been summarized by Gunn (1975). This leads to the important result that a magnetic map that has been measured with one component cannot be said to be superior to another map that has a different component.

Conclusion Magnetic maps contain much more information than just the shape and pattern of the high readings. Why waste this information?

You are welcome to copy this report and give it to anyone else. Should you distribute any part of the report widely, such as on the internet, please tell me.

Bruce W. Bevan Geosight 356 Waddy Drive Weems, Virginia 22576 USA

Details About the Figures Figure 1: The values of the anomaly have been calculated; they assume a magnetic dipole at a depth of 1 m below the calculation surface; this dipole has a magnetic moment of 1 Am2 and it is located at the middle of the plot. The Earth's field was assumed to have the parameters: Be = 57,000 nT; Ie = 70°; De = 30° (grid angle); the dipole is magnetized in the direction of the Earth's field. The numbers are centered on the calculation points. Figure 2: Each of these maps has the same data, and it is described in the note for Figure 1. For these maps, the calculations were made at intervals of 0.1 m; the range of the anomaly values is -17.3 nT to 181.2 nT. Figure 3: Again, the data are the same as that in Figure 2. With the multiple interval plot, contours are drawn with a spacing of 2 nT between -20 and +20 nT; this spacing is 20 nT for contour lines having values greater than 20 nT. In the map with a logarithmic interval, contours are at levels of -10, -5, -2, -1, 0, 1, 2, 5, 10, 20, 50, and 100. In the equal area plot, the contours are at levels of -7.9, -4.9, -3.5, -2.6, -1.8, -1.0, 0.1, 1.7, and 13.6. It appears that an equal area plot is used by the Geometrics program called MagMap2000. Figure 4: The same data is plotted here as that in Figure 2. Figure 5: This is the same dipole that has been applied to prior examples. As before,

Page 22 Details about the figures the direction of magnetization of the dipole continues to be that of the Earth's field. Figure 6: The dipole source for the calculations is the same as that in Figure 1; for the gradient maps, the lower sensor was assumed to be 1 m above the dipole. The sensor separation for the gradiometer measurements was assumed to be 1 m for the total field, and 0.5 m or the vertical component. The contour interval is either 5 nT or 5 nT/m. Additional types of total field magnetometers include potassium, rubidium, and helium instruments. The anomaly range in the three panels is: A = -17.3 to 181.2 nT; B = -20.2 to 158.8 nT/m; C = -23.3 to 268.8 nT/m. Figure 7: Pottery kilns may have this shape (Smekalova, Myts, and Melnikov 1995); in order to have the highest spatial resolution of these kilns, the authors made their measurements with the magnetic sensor directly on the surface of the soil. Each arm of the E-shaped feature has a square cross-section with sides that are 0.5 m wide. The height of the sensor is determined from the upper surface of this feature, which has a magnetic susceptibility of 0.01. The Earth's field has parameters: Be = 57,000 nT; Ie = 70°; De = 45°. The anomaly range in the four panels is: A = -21.4 to 85.2 nT; B = -9.1 to 41.7 nT; C = -4.9 to 27.4 nT; D = -3.0 to 19.9 nT. Figure 8: The magnetic model is identical to that in Figure 7. The calculations were made of the total field, and the vertical spacing between the sensors was assumed to be 0.5 m. The anomaly range in the four panels is: A = -58.9 to 113.0 nT/m; B = -14.8 to 44.6 nT/m; C = -7.0 to 22.9 nT/m; D = -3.8 to 14.8 nT/m. Figure 9: These calculations are for magnetic dipoles. The Earth's field was assumed to be: Be = 57,000 nT; Ie = 70°. Figure 10: The square feature (green outline) has a thickness of 0.5 m, and the calculations were made at a height of 1.5 m above the top of its surface. The magnetic susceptibility of the feature is +/-0.1, and the (total field) contour interval is 20 nT. The Earth's field was assumed to have the parameters: Be = 57,000 nT, Ie = +/-70°, De = 0. The anomaly range in the four panels is: A, B, and C = -42.5 to 263.4 nT; D = -263.4 to 42.6 nT. Figure 11: The parameters of the square feature are the same as those in Figure 10, and the sensor height is also 1.5 m. For these total field maps, the contour interval is 10 nT. The anomaly range in the four panels is: A = -11.0 to 281.8 nT; B = -55.9 to 220.5 nT; C = -89.9 to 101.5 nT; D = -84.1 to 26.6 nT. Figure 12: The cross-section of the modeled foundation is a square with sides that are 0.5 m long. The total field calculations were made at a height of 0.5 m above the top of this feature, and the contour interval is 5 nT. The feature has a susceptibility of 0.01. The parameters of the Earth's field were assumed to be: Be = 57,000 nT; Ie = 70°; De = 0. Figure 13: The parameters are exactly the same as for Figure 12 with the exception that Ie = 0. If the north-south walls are not perfectly regular, then segments of those walls will be detected on a magnetic survey. Figure 14: For each of these calculations, the Earth's field was assumed to have the parameters: Be = 57,000; Ie = 70°; De = 30°; the calculations were made at a height of 0.5 m above the top of the features. In panels A - C, the magnetic moment of the 8-m long bar was

Page 23 Details about the figures set at 10 Am2; in panel D, the strength of the monopole was -10 Am. The anomaly range and contour interval in the four panels is: A = -246.2 to 790.5 nT, contours at 25 nT; B = -384.6 to 379.3, contours at 25 nT; C = -17.0 to 406.7, contours at 1 nT; D = -24.2 to 3774.2, contours at 2 nT interval. Figure 15: This survey was done in June, 1992, with an Overhauser magnetometer (model GSM-19FG, manufactured by Gem Systems) at the US Civil War battlefield at Petersburg, Virginia. The height of the total field sensor was 0.8 m, and a base station magnetometer allowed the correction of temporal changes. Bidirectional traverses were made in an east-west direction and the measurement spacing and line spacing were both 2.5 ft. Magnetic north was about 7° west of grid north during this survey. This survey is described in an earlier publication (Bevan 1996). Figure 16: The magnetic parameters of the calculation were those from the site: Be = 53,200 nT; Ie = 66°; De = -7°. The monopole was located at E526.1 S144.8 at a depth underground of 6.2 ft (1.9 m); its strength was -193.4 Am. Figure 17: The cross-sectional areas (A) of the square, rectangular, and triangular prisms are: 1 m2, 8 m2, and 4 m2. The magnetic susceptibilities are listed as k values in the figure. The flux density of the Earth's magnetic field (Be) was assumed to be 57,000 nT. The magnetic moment per unit of length for each prism is then A * k * Be / (400 * pi) = 0.91 Am. The calculations were made with aid of the algorithm of Won and Bevis (1987). Figure 18: This cellar locates the Taylor House on the battlefield of the US Civil War at Petersburg, Virginia. The survey was done on 13 August 1991, and it is described in an earlier report (Bevan 1996). The instrument was a Gem Systems model GSM-19FG Overhauser magnetometer, which measures the total magnetic field of the Earth; temporal corrections were made with a base station magnetometer. The sensor height was 0.85 m and unidirectional traverses were made going toward the east; the line and measurement spacings were both 5 ft. The change in the spacing of the contour lines shows where the interval switches between 5 and 25 nT. Figure 19: The same area was explored for this map as in Figure 18. This survey was done on 27 January 1992, and the sensor height was 0.8 m. For this map, lines of measurement traverse went alternately to the east and west. Except for this, the equipment and procedures were the same as those for Figure 18. Figure 20: This survey was done during the period of 25 - 27 June 1992; the procedures and sensor height were the same as those for the map of Figure 18, although traverses were made to the west only. For these surveys, the magnetic sensor was carried on the end of a horizontal bar. Figures 18 and 19 could have been derived from the measurements of this survey (by simply decimating the data), but separate surveys were done for each map; this resulted in an interesting finding about seasonal changes in the magnetic anomaly of the brick foundation. Figure 21: The dipole source at the middle of each map is the one in Figure 1. In panel A, every other point is up to 5 nT too high then up to -5 nT too low. For panel B, five readings along north-south lines were altered at two locations into triangular lows that

Page 24 Details about the figures extended to a depth of -5 nT. In panel C, the spikes had either polarity. Rather than a median filter, it may be better to calculate the laplacian at each point (this is the difference between the value there and the average of the four adjacent values); if this laplacian exceeds a threshold, the original reading can be replaced by the average of the four adjacent readings. A pseudorandom number generator furnished the continuous noise pattern in panel D. Figure 22: Each flux line was traced with short line segments. The direction of flux lines distant from the magnetic feature was set at the value for the Earth's field (70°). After one short segment was drawn, the direction for the next segment was determined by the ratio of the calculated magnetic field in the horizontal and vertical directions. At the boundary of the magnetic feature, the direction changes abruptly: The ratio of the tangent of the angle of the flux to the magnetic permeability is the same on both sides of boundaries (Lorrain and Corson 1970 p. 402; Grant and West 1965 p. 317). As this figure shows, the angle of a flux line is farthest from the normal to a magnetic boundary in the more magnetic material. In order to show the divergence and convergence of the flux lines, the magnetic susceptibility of the feature was assumed to have a very high value; however, no correction was made for demagnetization. Figure 23: These flux lines were plotted just as those in Figure 22, except that there are no boundaries to cross for this example. This object has been assumed to be a magnetic dipole. While the flux lines look rather oval, they are not actually elliptical and they delineate a more complex curve. Unlike Figures 22 and 24, the spatial density of flux lines in this figure is not proportional to the field. Figure 24: The dense flux lines near the object have not been drawn. Figure 25: The central dipole in each map is the standard dipole of Figure 2. For panel D, a second dipole with a moment of 20 Am2 has been added at a depth of 6 m below the sensor surface; the direction of magnetization of this dipole is the same as the Earth's field. Figure 26: For an accurate test, The object should remain at a constant distance from the magnetic sensor as it is rotated. Figure 27: The rectangular box has a thickness of 2 m and a magnetic moment of 1 Am2; the calculations of the total field were made at a height of 1 m above the top of the box. The parameters of the Earth's field were assumed to be: Be = 57,000 nT; Ie = 70°; De = 0. The amplitude of the magnetic high changes only within the range of 8.0 to 8.2 nT for these four calculated maps; the anomaly is highest when the length of the box is oriented north-south. These illustrations show why it is important to have a compact sample when its magnetic properties are measured with the procedure in Figure 26. Figure 28: Except for the change from induced to remanent magnetization (in a horizontal direction) the parameters of the calculations are the same as for Figure 27. In panel D, note in particular that the anomalies have been shifted to the south. As with the illustration in Figure 27, the amplitudes of the magnetic highs and lows change very little with rotation; the magnitude of these anomalies ranges between 4.2 and 4.4 nT.

Page 25 Details about the figures

Figure 29: The induced magnetization has a direction I = 70°, D = 30°; the remanent magnetization has a direction I = 30°, D = -45°. The vectorial sum of the two magnetizations remains 1 Am2 for the calculations of each panel. Only the horizontal angles of the directions are plotted in the figure. The Earth's field has the assumed magnitude of 57,000 nT. In panel D, the angle from the magnetic high to the low is 1.9° east from the direction of remanent magnetization. Figure 30: The Earth's field was assumed to be: Be = 57,000 nT; Ie = 70°; De = 0. A total of 121 dipoles have been placed in a regular matrix on a single level, which is 0.5 m below the calculations; the algebraic sum of the magnetic moments for each dipole is 0.01 Am2. The directions of remanence are randomly chosen over a sphere; these directions remain the same in panels B - D. If n is the number of dipoles (each with the same magnetic moment, composed of both induced and a significantly larger remanent component), then the anomaly will be change as follows with n: n * induced + (square root of n) * remanent. Therefore, if n is small, the anomaly may be mostly from remanence, and if n is large, it may be mostly from induction. The anomaly range in the four panels is: A = -43.9 to 115.9 nT; B = -23.9 to 69.7 nT; C = -19.2 to 45.2 nT; D = -58.1 to 46.6 nT. Figure 31: The basic magnetic map in Figure 2 has been altered by adding a magnetic field to the calculated values; this addition increases in a linear fashion from the left to right throughout the grid to a maximum of 20 nT. The partial corrections were done by subtracting the reading at the north end of each column from every reading on that column. As alternatives, one could also subtract the median or mode value of each column from that column, or similarly subtract the average reading of each column after the readings farthest from the average have been removed. Figure 32: This survey was done on 6 September 1995 using an Overhauser magnetometer (a model GSM-19GW, manufactured by Gem Systems). It was operated in its difference mode, and was connected to a second stationary sensor for temporal correction. One operator carried the sensor, while a second operator (at a distance of about 2 m) carried the readout console. The measurement interval along lines was 0.5 s and about 0.1 m; the line spacing was 0.25 m and traverses went alternatively to the north and south. The 14,954 measurements in this gridded map were made in a span of three hours. Each north-south column of readings (with a slightly irregular measurement spacing) was converted to a uniform interval of 0.25 m by a quadratic interpolation between the measurements. Note that the contour lines on the north sides of anomalies show lesser undulations than on the south side; this is because the two errors partially cancel each other on the north side, while the errors are magnified on the south side. This project was described in a 192-page report that was prepared for Olfert Voss (this and the following seven figures were taken from that report). A summary of the report was published by Bevan and Smekalova (2001); however, the original report has many more details about this survey and its analysis. The striations on the contour lines in Figure 15 have the same origin as those in this figure. Figure 33: The smoothing was done with a weighted average. The weighting of the

Page 26 Details about the figures three readings on the central north-south column was two, while the weighting of the six readings on the adjacent columns was one; the sum was divided by 12. Figure 34: For this survey, the measurement spacing was closer than it needed to be for the sensor height that was chosen; this close spacing was selected for this test in order to ensure the best possible data for this magnetic map, and to be certain that all of the features that might possibly be detected at this sensor height would be revealed. Figure 35: The simplified contour line at the top encloses higher readings within the oval. The polarity of the line shifts that are found on other contour maps may be the opposite of what is shown here. The polarity of the heading error is dependent on the location and Q ratio of the iron that causes the fault. The polarity of the locational error may change with the operator, and how the sensor is carried. The amplitude of the locational error will probably increase with traverse speed. Figure 36: For some data, it can be important to eliminate the readings that were made near strong anomalies before calculating these line averages; that care was not needed for this map. The heading error was found to be very consistent during this survey. This consistency is not always found, particularly when there is a change in equipment operators, or the survey takes more than a day. Figure 37: The correction works best where there is a low lateral gradient in the magnetic map. The addition was made to only half of the data, rather than adding and subtracting a smaller amount from all of the data; this is because the analysis of a magnetic map is essentially unchanged if any small constant is added to all values. Figure 38: For the cross-correlation, one of each pair of lines being examined was shifted in increments of 0.01 m while interpolating the values at the coordinates of the adjacent line; the distance for the greatest correlation is plotted in this figure. Figure 39: It is likely that most of the faults that remain in this magnetic map are errors in location. These faults appear to be primarily caused by an imperfect registration between the fiducial markers that were put in the data when crossing 1-m intervals along traverses and the magnetic field readings; this is because the time delay between a fiducial marker and the following reading had no effect on the coordinate given that following reading. Figure 40: The basic magnetic source of Figure 2 is centered in each of these maps. In panel A, the averaging window was 3x3 measurements or 0.3 m square; this averaging had little effect on the central anomaly. In panel B, the calculations were made at intervals of 0.5 m, and then interpolated to a spacing of 0.1 m; that is, four columns and rows were inserted for every original. In panel C, calculations were made at intervals of 0.1 m along north-south lines that were spaced by 1 m; while all of the calculations are correct, the interpolation of the contours distorts the anomaly. In panel D, the direction of the remanent magnetization was its usual value (Ir = 70°; Dr = 30°); the background field was set to zero. The rather circular contour lines shift as the Ir-Dr angle changes. If Ir = 90°, then the contours would be centered in the map. Figure 41: The magnetic moments are reasonable values for the different materials, and are based on my measurements of many samples. The magnetic moment listed for a

Page 27 References brick wall should also be suitable for a cluster of potsherds; this value is lower than that for fired earth because of the random directions of remanent magnetization in the brick wall. The half width rule has been described by Breiner (1957 p. 31) and by Telford, Geldart, and Sheriff (1990 p. 87). Other depth rules have been discussed by Mares (1984 p. 134), Radhakrishna Murthy (1998 p. 246), and Blakely (1995 p. 238). Figure 42: The units of the vertical axis are in nT if the Earth's field is vertical with a magnitude of 57,000 nT and the susceptibility of the prism is 0.01. The basic idea of this procedure can be extended to the calculation of the magnetic anomalies of polyhedra with the aid of the solid angles of their facets (Singh and Guptasarma 2001; Furness 1994). Figure 43: The standard dipole of Figure 2 is used here again. The Earth's field has the values: Be = 57,000; Ie = 70°; De = 30°. The dipole is located at the middle of each map and at a depth of 1 m below the calculation surface; the magnetic moment is 1 Am2. The contour interval is 5 nT. The negative of the vertical component is displayed so that the polarity will be the same as that in panel A. The anomaly range in the four panels is: A = -17.3 to 181.2 nT; B = -9.3 to 191.1 nT; C = -91.7 to 74.6 nT; D = -86.5 to 77.2 nT. Figure 44: The standard dipole of Figure 2 and 43 is applied here. The anomaly range in the four panels is: A = 69.58 to 70.13°; B = 29.76 to 30.24°; C = -229.4 to 194.5 nT; D = -248.1 to 186.7 nT.

References Barba, Luis, Karl Link, Agustin Ortiz, and Albert Hesse, 1996. Magnetic study of archaeological stone foundations at Loma Alta, Michoacan, Mexico. Page 786 - 788 in Expanded Abstracts of the 66th SEG Annual Meeting, Society of Exploration Geophysicists (Tulsa, Oklahoma). Barba P., L. A., Linda Manzanilla, R Chavez, Luis Flores, and A. J. Arzate, 1990. Caves and tunnels at Teotihuacan, Mexico; a geological phenomenon of archaeological interest. Chapter 24 (p. 431 - 438) in: Archaeological Geology of North America, edited by Norman P. Lasca and Jack Donahue. Geological Society of America (Boulder, Colorado). Bartington, G., and C. E. Chapman, 2004. A high-stability fluxgate magnetic gradiometer for shallow geophysical survey applications. Archaeological Prospection 11:19 - 34. Bevan, B. W., and T. N. Smekalova, 2001. Magnetization directions of iron slag in Denmark. Page 7 - 25 in: Filtering, Optimisation and Modelling of Geophysical Data in Archaeological Prospecting, edited by Mauro Cucarzi and Paola Conti. Fondazione ing. Carlo Maurilio Lerici (Rome). Bevan, Bruce W., 1996. Geophysical Exploration for Archaeology. Geosight Technical Report Number 4. Geosight (Weems, Virginia). Blakely, Richard J., 1995. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press (Cambridge). Breiner, S., 1973. Applications Manual for Portable Magnetometers. Geometrics (San Jose, California). Available in PDF form on the web at: www.geometrics.com

Page 28 References

Dalan, Rinita A., and Subir K. Banerjee, 1998. Solving archaeological problems using techniques of soil magnetism. Geoarchaeology 13(1):3 - 36. Dobrin, Milton B., and Carl H. Savit, 1988. Introduction to Geophysical Prospecting, fourth edition. McGraw-Hill (New York). Evans, Michael E., and Friedrich Heller, 2003. Environmental Magnetism. Academic Press (Amsterdam). Furness, Peter, 1994. A physical approach to computing magnetic fields. Geophysical Prospecting 42(5):405 - 416. Grant, F. S., and G. F. Grant, 1965. Interpretation Theory in Applied Geophysics. McGraw-Hill (New York). Gunn, P. J., 1975. Linear transformations of gravity and magnetic fields. Geophysical Prospecting 23(2):300 - 312. Haanel, Eugene, 1904. On the Location and Examination of Magnetic Ore Deposits by Magnetometric Measurements. Department of the Interior (Ottawa). Heiland, C. A., 1940. Geophysical Exploration (1968 reprint). Hafner Publishing (New York). Hrvoic, Ivan, Greg M. Hollyer, Mike Wilson, and Anthony Szeto, 2003. Development of a high sensitivity potassium magnetometer for near surface geophysical mapping. First Break 21(May):81 - 87. Lorrain, Paul, and Dale Corson, 1970. Electromagnetic Fields and Waves, second edition. W. H. Freeman (San Francisco). Mares, Stanislav, 1984. Introduction to Applied Geophysics. D. Reidel (Dordrecht). Nettleton, L. L., 1942. Gravity and magnetic calculations. Geophysics 8:293 - 310. Radhakrishna Murthy, I. V., 1998. Gravity and Magnetic Interpretation in Exploration Geophysics. Memoir 40 of the Geological Society of India (Bangalore). Rainey, Froelich G., and Carlo M. Lerici, 1967. The Search for Sybaris, 1960 - 1965. Lerici Editori (Rome). Robinson, Edwin S., and Cahit Coruh, 1988. Basic Exploration Geophysics. John Wiley (New York). Schnetzler, C. C., and P. T. Taylor, 1984. Evaluation of an observational method for estimation of remanent magnetization. Geophysics 49(3):282 - 290. Singh, Bijendra, and D. Guptasarma, 2001. New method for fast computation of gravity and magnetic anomalies from arbitrary polyhedra. Geophysics 66(2):521 - 526. Smekalova, Tatyana N., Olfert Voss, Sergey L. Smekalov, 2005. Magnetic Survey for Archaeology. Publishing House of Polytechnic University (St. Petersburg). Smekalova, T. N., V. L. Myts, and A. V. Melnikov, 1995. Magnetometric investigation of Medieval pottery centers in mountainous Crimea. Pages 441 - 448 in: Archaeometry in South-Eastern Europe (PACT 45), edited by I. Liritzis and G. Tsokas. PACT Belgium (Rixensart). Tabbagh, Jeanne, 2003. Total field magnetic prospection: Are vertical gradiometer measurements preferable to single sensor survey? Archaeological Prospection. 10:75 - 81.

Page 29 References

Telford, W. M., L. P. Geldart, and R. E. Sheriff, 1990. Applied Geophysics, second edition. Cambridge University Press (Cambridge). Voss, O., 1995. "Snorup - an iron producing settlement in West Jutland, 1st - 7th century AD". Proceedings of the Conference: The Importance of Ironmaking. May 8 - 13, Stockholm University (Norberg, Sweden). Weymouth, J. W., and Y. A. Lessard, 1986. Simulation studies of diurnal corrections for magnetic prospection. Prospezioni Archeologiche 10:37 - 47. Won, I. J., and Michael Bevis, 1987. Computing the gravitational and magnetic anomalies due to a polygon: Algorithms and Fortran subroutines. Geophysics 52(2):232 - 238.

Publication history: 22 May 2006, corrected typographical errors. 1 May 2006, original report.

Page 30 Numerical values 3 -1.1 -1.5 -1.8 -2.3 -2.7 -3.0 -3.2 -3.0 -2.7 -2.3 -1.9 -1.5 -1.2

-1.4 -1.8 -2.4 -3.2 -4.0 -4.7 -5.0 -4.8 -4.2 -3.4 -2.6 -2.0 -1.5

2 -1.6 -2.2 -3.1 -4.3 -5.9 -7.4 -8.3 -8.0 -6.7 -5.1 -3.7 -2.6 -1.9

.9 .2 .1 .6 0 3 3 0 -1.8 -2.5 -3.6 -5.4 -7.8 -1 -1 -1 -1 -7.5 -5.1 -3.4 -2.3

.4 .3 .9 .2 1 3 7 4 0 -1.7 -2.5 -3.5 -4.9 -6.5 -8.6 -1 -1 -1 -1 -6.5 -4.1 -2.7

4 2 .4 .5 .0 . . 4 1 -1.5 -2.0 -2.2 -0.9 7 29 36 -0.1 -1 -1 -7.4 -4.6 -3.0

1 8 .5 . 9.0 5.0 . 0 5 0 6 -1.2 -1.2 -0.1 30 1 1 53 -4.0 -9.7 -7.0 -4.6 -3.0

0 5 0 .4 .4 . . 1.7 . .6 1 8 3 3 -0.8 -0.4 33 95 1 55 -6.2 -5.7 -4.0 -2.8 North coordinate, m coordinate, North

9 4 7 7 -1 .0 .7 .5 . . . . .6 -0.5 0 1 6 18 39 45 22 2 -3.7 -4.1 -3.2 -2.4

0 1 .1 .2 .6 .1 . . .8 .4 -0.3 0 1 3 8 13 13 6 0 -2.4 -2.8 -2.4 -1.9

-2 .1 .6 .7 .1 .1 .7 .6 -0.2 0 0 1 3 4 3 1 -0.5 -1.7 -2.0 -1.8 -1.5

.2 .6 .0 .2 .9 .1 -0.2 -0.0 0 0 1 1 0 0 -0.7 -1.2 -1.4 -1.3 -1.1

-3 .0 .1 .2 .2 .0 -0.2 -0.1 0 0 0 0 0 -0.3 -0.7 -0.9 -1.0 -1.0 -0.9 -3-2-10123 East coordinate, m

Figure 1: The numbers of a magnetic map. This matrix shows readings at intervals of 0.5 m, as they may be measured with a magnetic survey. The values are positive or negative depending on if the reading was greater or less than the value of the Earth's field. The Earth's magnetic field was assumed to be 57,000 nanotesla (abbreviated nT). Therefore, the number 165 means than the total field at that point was actually 57,165 nT. It is difficult to see the pattern of these numbers, so this matrix is almost always converted into a contour map, like those in the following figures. Line contour Gray scale 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Shaded relief 3 C Wire frame 2 D

1

0

-1

North coordinate, m -2

-3 -3-2-10123 East coordinate, m

Figure 2: Four different types of maps. Each has important advantages. A line contour map is excellent for showing high lateral gradients in the measurements by the close spacing of the lines; tick marks along the contours of this map reveal magnetic lows. A gray scale map indicates the pattern of readings that are similar, even if the areas are distant from each other on a map. A shaded relief map has the familiar appearance of an aerial photograph. A wire frame map clarifies the amplitudes of the readings. Constant interval Mulltiple interval 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Logarithmic interval Equal area 3 3 CD 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 3: Four different types of line contour maps. These differ in the spacing or interval between contour lines. A constant interval map readily shows the amplitudes of anomalies. If multiple intervals are used, high and low amplitudes may be displayed more completely. With a logarithmic interval, extremely wide ranges of readings can be seen. An equal area map leaves no large blank areas; for this type of map, the area enclosed between each adjacent pair of contour levels is the same. Colored line Stepped spectrum 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Continuous colors Stepped colors 3 3 C D 2 2

1 1

0 0

-1 -1

North coordinate, m -2 m coordinate, North -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 4: Four different applications of color. It is conventional that high values be plotted as red, orange, or yellow, while low values are plotted as green or blue. If the map has colored lines, it is possible to make a good print of it with black ink. A stepped spectrum map allows the display of a wide range of readings. The map with continuous colors allows one to easily distinguish areas with high and low readings. A compromise between these maps can be made with the version showing stepped colors. Depth 0.5 m, 25 nT contours, peak 1419 nT Depth 1 m, 5 nT contours, peak 181 nT 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Depth 2 m, 1 nT contours, peak 23 nT Depth 4 m, 0.2 nT contours, peak 2.8 nT 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 5: The effect of depth. If an object is deeper underground, its anomaly is broader, and its amplitude is lower. The peak of the anomaly also moves away from the middle of the object, marked with an X here. For small or compact objects, if distance is doubled, then the peak amplitude of the anomaly drops by a factor of about eight. Compare the peaks at a depth of 0.5 m and 1 m; their ratio is 7.8, which is close to the value 8. Total field Vertical gradient of total field 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Vertical gradient of vertical component 3 C 2

1

0

-1

North coordinate, m -2

-3 -3-2-10123 East coordinate, m

Figure 6: The three most common types of magnetic measurements. Total field readings are made with a single magnetic sensor; this will likely be part of a cesium, Overhauser, or a proton magnetometer. If two of these sensors are aligned one above the other, then the magnetic gradient is measured (panel B). A slightly different magnetic gradient is measured with a fluxgate magnetometer (panel C). For this instrument, only that part of the magnetic field in the vertical direction is measured. With a gradiometer, the difference in the readings between sensors at two heights is determined; this difference is divided by the spacing between the sensors to give a magnetic value in nT/m. Height: 0.3 m; contours: 10 nT Height: 0.6 m; contours: 5 nT 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Height: 0.9 m; contours: 3 nT Height: 1.2 m; contours: 2 nT 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m -2 m North coordinate, -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 7: The blurring of shapes with increasing height (or depth). The E-shape of this feature becomes more rounded at a greater distance. This is a failing that magnetic surveys share with all other types of geophysical exploration. The resolution of buried features can be improved by using a gradiometer (see Figure 8) or by reducing the height of the magnetic sensor. Height: 0.3 m; contours: 10 nT/m Height: 0.6 m; contours: 5 nT/m 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Height: 0.9 m; contours: 3 nT/m Height: 1.2 m; contours: 2 nT/m 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 8: The increased resolution of a gradiometer. These maps can be compared to Figure 7. The gradiometer map at a height of 0.9 m (panel C) shows about the same resolution as a total field map at a height of 0.6 m (panel B in Figure 7). The price for having a greater resolution with a gradiometer must be paid by making measurements at a closer spacing. 300 300 Compare total field and gradient

Total field magnetometer Gradient, 0.5 m spacing Gradient, 1.0 m spacing

200 200 Magnetic gradient, nT/m gradient, Magnetic 100 100 Magnetic anomaly, nT anomaly, Magnetic

surface 0 0 Magnetic gradient, nT/m nT/m gradient, Magnetic

M = 1 Am2 depth = 1 m M = 27 Am2 depth = 3 m -100 -100 -6-4-20246 North coordinate, m

Figure 9: The decreased sensitivity of a gradiometer for deep objects. Two objects (green circles) are at different depths, and the deeper one is more magnetic. With these parameters, the total field magnetometer detects both objects with about the same peak anomaly. With the gradiometer, the deeper object has a weaker anomaly. This attenuation of deeper objects increases as the spacing between the gradiometer's sensors is smaller. Northern hemisphere Overhead feature 6 6 A B 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

A C -6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Southern hemisphere Less magnetic feature 6 6 C D 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

B D -6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Figure 10: Important effects in magnetic maps. Panel A shows the typical map of a buried feature; the magnetic low is toward the north. If this feature was overhead (panel B), or the survey was done in the southern hemisphere (panel C), the magnetic high would be toward the north. If the feature was less magnetic than the surrounding soil, then the principle magnetic anomaly would be a low (panel D). Ie = 90; Be = 57,000 nT Ie = 60; Be = 52,000 nT 6 6 A B 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

-6 -6 -6 -3 0 3 6 -6-3036 East coordinate, m East coordinate, m

Ie = 30; Be = 41,000 nT Ie = 0; Be = 34,000 nT 6 6 C D 3 3

0 0

-3 -3 North coordinate, m North coordinate, North coordinate, m

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Figure 11: The effect of latitude in magnetic maps. Near the north pole (panel A), the magnetic field is strong, and highs are centered on magnetic features. Near the equator (panel D), the Earth's field (Be) is weaker, and lows are centered on magnetic features. Magnetic anomalies are fainter and more complex at the equator than at the pole. At intermediate latitudes, a magnetic low is found north of the magnetic high. Square feature 6

3

0 North coordinate, m coordinate, North

-3

-6 -6 -3 0 3 6 East coordinate, m 40 NS line 30

20 EW line

10

0

-10

-20 -6 -3 0 3 6 Line coordinate, m

Figure 12: The magnetic anomaly of a square feature with a square hole. This map therefore approximates the anomaly of the foundation of a square building. Magnetic lows are found on the north sides of both east-west walls. Profiles along north-south and east-west lines are plotted below. The amplitudes of the anomalies are slightly lower along the east-west profile. This effect increases at lower latitudes; see Figure 13. Square feature at equator 6

3

0 North coordinate, m coordinate, North

-3

-6 -6 -3 0 3 6 East coordinate, m 20

10

0 EW line -10

NS line -20

-30

-40 -6 -3 0 3 6 Line coordinate, m

Figure 13: Invisible walls at the equator. This feature is the same as that in Figure 12. When magnetic maps are measured near the equator, features that extend in a north-south direction may not be detected. Magnetic anomalies are created where the Earth's field crosses the boundary between materials that differ in their magnetism. Since the Earth's field is horizontal here, no magnetic boundaries are crossed along the north-south walls until the east-west walls are encountered. Magnetized in Earth's direction Magnetized along length 6 6 A B 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Vertical, magnetized in Earth's direction Monopole 6 6 C D 3 3

0 0

-3 -3 North coordinate, m North coordinate, m coordinate, North

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Figure 14: Anomalies of long, thin objects. These objects are typically pipes or shafts; they may be gun barrels or wells. A corrugated iron pipe may be detected as in panel A, although a cast iron pipe may cause the very different anomaly in panel B. If this iron pipe is vertical in the earth, then the anomaly can be like that in Panel C. Wells may be revealed on magnetic maps similar to the patterns shown in panels C or D; if the iron extends to a great depth, then panel D illustrates the anomaly. Magnetic anomaly of a well near Fort Morton -50

-100

-150 North coordinate, ft

-200

-250 450 500 550 600 East coordinate, ft

Figure 15: The magnetic map of a well. The anomaly extends over a wide area; the north-south span of the map is 200 ft (61 m). The map is drawn with three contour intervals; changes in line spacing reveal these breaks. The highest anomalies have a contour interval of 100 nT; intermediate contours are at 20 nT intervals; the remaining weaker anomalies are plotted with a contour interval of 5 nT. The highest anomaly, at E527.5 S145, has an amplitude of 2763 nT; the anomaly low to the north has a value of -30 nT. Calculated field of the monopole model of a well near Fort Morton -50

-100

-150 North coordinate, ft

-200

-250 450 500 550 600 East coordinate, ft

Figure 16: An approximation of the magnetic map of the well. This calculation shows the same general pattern as the measurements in Figure 15. The magnetic map of a well may be very similar to the map of a magnetic monopole, which is a mathematical approximation of the end of a very long magnetic object. The green X in the figure locates this monopole, which is only 1.4 ft (0.4 m) distant from the magnetic high that it causes. Calculated anomalies of 2-D prisms 80 Be = 57,000 nT; Ie = 70o; De = 0 Calculations 1 m above tops of prisms

60

40

20

0 Magnetic anomaly, nT anomaly, Magnetic

-20

-40 -6-4-20246 North coordinate, m

Three prisms: Square, k = 0.02

Rectangular, k = 0.0025

Triangular, k = 0.005

Figure 17: The effect of the concentration or dispersal of magnetic materials. As materials are spread out, their anomaly decreases. These calculations were made for three features that extend for a long distance perpendicular to the page. The amount of magnetic material per unit length is the same for each of the three features. The feature with a square cross-section gives the strongest anomaly, while the feature with a rectangular cross-section has the weakest anomaly. Measurement spacing = 5 ft (1.5 m), contours at 5 and 25 nT interval 120

100

80

60 North coordinate, ft

40

20 -120 -100 -80 -60 -40 -20 0 20 40 East coordinate, ft

Figure 18: The magnetic map of the buried brick wall of a cellar. The green rectangle locates this cellar. Only part of the wall was detected, for the brick had been removed from the northern wall. Although this survey was done with a large spacing between the measurements (5 ft = 1.5 m), the part of the cellar wall that remains was delineated. The two following maps show how resolution improved with a closer spacing between the readings. Measurement spacing = 2.5 ft (0.8 m), contours at 5 and 25 nT interval 120

100

80

60 North coordinate, ft

40

20 -120 -100 -80 -60 -40 -20 0 20 40 East coordinate, ft

Figure 19: A higher resolution magnetic map of the area shown in Figure 18. For this survey, the spacing between the readings was 2.5 ft (0.8 m) in both the north-south and east-west directions. More anomalies are now apparent in this map, and the areas of the anomalies are smaller. Four times as many measurements were made for this map as for the map in Figure 18. Measurement spacing = 1 ft (0.3 m), contours at 5 and 25 nT interval 120

100

80

60 North coordinate, ft

40

20 -120 -100 -80 -60 -40 -20 0 20 40 East coordinate, ft

Figure 20: A very high resolution magnetic map. The measurement spacing was only 1 ft (0.3 m) for this survey. It is likely that the resolution of a magnetic map of this area would not be improved if the measurement spacing was reduced below 1 ft. The anomalies on this map are small and detailed. However, the magnetic anomaly of the brick foundation is hardly more distinct here than in was in the map with a measurement spacing of 5 ft (Figure 18). Noise: Approximate a magnetic pace Noise: Approximate 2 passing cars 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Noise: +/-10 nT spikes for 2 percent of data Noise: Uniform random for all data to +/-5 nT 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 21: Errors in magnetic maps. These faults may be found in both total field and gradient maps. Panel A shows the pattern that may be caused by a magnetic object that is repeatedly close to the magnetic sensor; shoes can cause this pattern. Passing vehicles usually cause the magnetic readings to drop; panel C shows a pair of linear lows (at W1 and E1), aligned with the north-south direction of traverse. Lightning can cause a few one-point errors, like those in panel C. The most common type of noise is that in panel D; imperfections in magnetometers are the typical cause of this type of error. Figure 22: Warping of flux lines in a magnetic object. This shows the cross-section of a long object. The paths of the lines of magnetic flux from the Earth are plotted. Since the feature within the green square is more magnetic than the surrounding, flux lines are concentrated in that feature. The magnetic anomaly that is measured is proportional to the spatial density of these flux lines. Just above the feature, along the dashed line, these flux lines are closer together, causing a magnetic high. To the north of the feature, the lines are spaced more widely, yielding a magnetic low. Figure 23: The magnetic field of a small object. This object is located at the green circle. It is magnetized by the Earth's field, and the rather oval lines show the paths of magnetic flux from the object; these lines are too dense to draw in small sectors above and below the object. The flux lines are drawn as red where they will add to the Earth's magnetic field, causing high readings. The lines are blue where they will subtract from the Earth's field, and where a magnetic low will be found. Magnetic measurements along the dashed line will yield the typical dipolar magnetic anomaly that is plotted at the top. Figure 24: A summation of the Earth's magnetic field with that from a small object. This is simply a redrawing of Figure 23, after the Earth's field has been added to the field from the small object. As with Figure 22, a magnetometer will read higher values where the lines of magnetic flux are closer together (directly over the object) and lower values where the lines are farther apart (on the north side of the object). The curve above is a plot of this change along the dashed line that goes through the flux map. Slope down to west Flat surface 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Slope down to south Lateral interference 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 25: Magnetic lows that are rotated due to topography. If a magnetic map is measured on a flat surface, the low readings can be toward magnetic north, as in panel B. If the ground surface slopes down by 20° toward the west, this low is rotated to the west; see panel A. A similar slope to the south can also cause a rotation of the anomaly, and panel C shows also that the anomaly peak has moved to the south of the source (the green X). A magnetic low can be shifted by the anomaly of a nearby object; panel D illustrates this effect. Figure 26: Distinguishing remanent from induced magnetization. Check the reading at a magnetometer when the test object is distant. Then, bring the object close to the magnetic sensor and rotate it a few times. The readings will oscillate about an average value. The difference between that average and the field with no object nearby is proportional to the induced magnetization. The amplitude of the oscillations is proportional to the remanent magnetization of the object. This curve is a plot of how a sequence of readings can allow these two magnetic sources or effects to be distinguished. Rotation = 0 Rotation = 30 degrees 6 6 A B 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Rotation = 60 degrees Rotation = 90 degrees 6 6 C D 3 3

0 0

-3 -3 North coordinate, m North coordinate, m coordinate, North

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Figure 27: Changes in the magnetic map of a rotating object. This box-like object (green rectangle) is magnetized by induction; that is, it has induced magnetization. As the object is rotated, the magnetic low remains on the north side of the object, although the shape of the anomaly otherwise changes. Rotation = 0 Rotation = 30 degrees 6 6 A B 3 3

0 0

-3 -3 North coordinate, m North coordinate, m

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Rotation = 60 degrees Rotation = 90 degrees 6 6 C D 3 3

0 0

-3 -3 North coordinate, m North coordinate, m coordinate, North

-6 -6 -6 -3 0 3 6 -6 -3 0 3 6 East coordinate, m East coordinate, m

Figure 28: Rotating an object that has remanent magnetization. In this case, the magnetic low rotates with the object. For these calculations, the remanent magnetization is directed along the length of the box, which is otherwise the same as that in Figure 27. Note that there are small changes in the anomalies with rotation. These differences are caused by the fact that the direction of the Earth's field remains the same, while the direction of the field from the box changes; the summation of the two fields therefore changes as the box rotates. Q = 0 (only Mi) Q = 0.5 (Mr = 0.5 * Mi) 3 3 Earth's ABfield 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Q = 1 (Mr = Mi) Q = infinity (only Mr) M 3 L E 3 C R D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 29: Rotation of a magnetic low due to the contribution of remanent magnetization. With induced magnetization alone (panel A), the low is toward magnetic north. With remanent magnetization alone (panel D), the low is close to the direction of the remanence. Panels B and C show how the low rotates as the remanence increases, while induction decreases. Arrows in each panel indicate as many as four directions: green E = Earth's field; red R = remanent magnetization; black M = total magnetization; blue L = angle from high to low. The direction from the high to the low is not the same as the direction of total magnetization. Induced alone Remanent = induced 2 2 A B 1 1

0 0

-1 -1 North coordinate, m North coordinate, m

-2 -2 -2-1012 -2 -1 0 1 2 East coordinate, m East coordinate, m

Remanent = 3 * induced Remanent alone 2 2 C D 1 1

0 0

-1 -1 North coordinate, m North coordinate, m North coordinate,

-2 -2 -2 -1 0 1 2 -2 -1 0 1 2 East coordinate, m East coordinate, m

Figure 30: Magnetic maps of a cluster of objects. If each object is magnetized by induction, the magnetic pattern is the common and simple one shown in panel A. If each object has only remanent magnetization, and the direction is different for each object, then the map is quite complex, as seen in panel D. If there is a "mixture" of remanent and induced magnetization, then the magnetic map can be moderately complex but still show a magnetic low to the north. Temporal change: Unidirectional traverse Temporal change: Bi-directional traverse 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Partial correction of above Partial correction of above 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 31: The effect of uncorrected temporal change in the Earth's magnetic field. If a magnetic survey is done without a base station or gradiometer, magnetic anomalies can be distorted. The maps in the upper two panels should look like the map in Figure 2. The two lower panels show how partial corrections may be made by estimating the temporal change and subtracting it. In practice, the correction is more difficult than these illustrations suggest, for magnetic maps and temporal changes are generally more complex. Figure 32: A striated magnetic map. Most magnetic maps will have the two faults that cause these striations (which are undulations or waves on the contours). The following figures illustrate the correction of these faults. This magnetic map illustrates the detection of buried blocks of iron-containing slag near the town of Snorup in Denmark. The survey was done for Olfert Voss (Nationalmuseet) by Tatyana Smekalova (St.-Petersburg State University) and myself. The contour interval is 2 nT, and the sensor height was 95 cm. Figure 33: A simple but unsuitable elimination of the striations. Each reading has been replaced by the average of that reading and the eight adjacent readings in a square window that is 0.5 m wide. While this window averaging creates very smooth contour lines, the amplitudes of the anomalies are reduced, and their widths are increased. This, plus the lower spatial resolution of this map, makes it unsuitable for a geophysical interpretation. Figure 34: Another simple but unsuitable correction. The faults in the magnetic map of Figure 32 are apparent only because of the bi-directional traverses that were made. If unidirectional traverses are used, the faults are still in the map, but they cannot be seen. The measurement traverses for Figure 32 alternated between north-going and south-going, and these lines were spaced by 0.25 m. This figure shows only the readings from the north-going traverses, now with a line spacing of 0.5 m. The patterns in this map have an error of location that is about 0.1 m; also, since it is inefficient to make unidirectional traverses, or to throw away measurements, this is not a good correction. Figure 35: The two errors in the magnetic map. This sketch shows how contour lines are affected by two faults. One fault is called heading error. This is caused by magnetic material moving with the magnetometer; on north-going lines of traverse the readings may all be increased slightly, and they may all be decreased on south-going lines. This error slightly broadens the anomaly highs on north-going traverses. The second fault is called a coordinate shift or a locational error. This fault does not change the values of the readings; instead, the locations of the readings are recorded with a systematic error. This fault may be caused by a lag in the display of the magnetometer, by averaging within the instrument, or by a parallax error created by the operator's estimate of the location of the sensor. Locational error is apparent on contour maps by an apparent shearing of the lines. While close study of the contour lines on a magnetic map will reveal the two errors that are indicated above, mathematical methods are better for distinguishing the two faults. Figure 36: A verification of the heading error. On north-going traverses, the average reading along each column was always higher than the average found on south-going traverses. While the difference is small, it was large enough to have a significant effect on the magnetic map. The moving iron that causes this heading error may have been in the clothing of either operator of the equipment; iron within the circuitry of the display console, or on the sensor cables or connectors, could also contribute; finally, a small amount of magnetic dust on the sensor could cause some of this heading error. Figure 37: After the correction for heading error. The striations in the magnetic map are reduced, although not eliminated. The improvement (compared to the original in Figure 32) is most apparent in the areas with faint anomalies. This correction was done by adding about 0.7 nT to all of the readings along south-going lines of traverse; this 0.7 nT is just the difference between the two curves in Figure 36. Figure 38: A verification of the locational error. These curves show that the north coordinates of all of the readings were shifted by about 0.08 m forward along the direction of traverse. This analysis was done with a cross-correlation between adjacent lines of traverse. While this allows for the best and most precise correction, one can also just estimate the average spatial amplitude of the undulations on the contour lines. Figure 39: After the correction for locational error. The regular undulations in the contour lines of the original map (Figure 32) have now been eliminated, although random undulations remain. This map has lost none of the information of the original readings, but is now much easier to view. The locational error was corrected by shifting the coordinates of the readings; the north-going traverses were shifted to the north by about 0.08 m, and the south-going traverses were shifted to the south, also by about 0.08 m. Data spike: Artifact from window averaging Data spike: Artifact from spline interpolation 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Measurement column spacing = 1 m Magnetic anomaly on the moon 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m North coordinate, -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 40: Errors that may be created by data processing. A large-amplitude anomaly may be detected with a single reading; this may be caused by a small and shallow object. If window averaging is applied to the measurements in order to smooth them, the one-point anomaly may be converted to a square or rectangle of the size of the averaging window; see panel A. In panel B, the grid of readings that were made at a broad interval has been interpolated to a fine interval with spline interpolation; this creates a "diffraction pattern" at each small-area anomaly. Panel C shows how a simple anomaly may be warped if widely-spaced lines of traverse are made. A magnetic survey on the moon would find no magnetic low; see panel D. 200 Ba(peak) = 200 * M / d3 Anomaly peak = Ba(peak) where M = magnetic moment, Am2 For an object with a mass of 1 kg: 160 M (steel) = 0.3 Am2 M (iron) = 0.03 Am2 M (fired earth) = 0.003 Am2 M (brick wall) = 0.0003 Am2

120

Half of peak Width, w = 1 m 80 Magnetic anomaly, nT anomaly, Magnetic 40

Zero level 0

Be = 57,000 nT Dipole source o Ie = 70 Depth, d = 1 m M = 1 Am2 -40 -4 -2 0 2 4 North coordinate, m

Figure 41: The analysis of a magnetic anomaly. This analysis may be applied to many anomalies, but particularly to those that are caused by objects whose diameter is less than their distance. The depth from the magnetic sensor to the middle of a compact feature is about equal to the width of the anomaly that it causes at half its peak amplitude. This is called the "half width rule", which is an abbreviation for "full width half amplitude", and which can be further summarized as d = w. Once this depth has been approximated, the mass of the object can be estimated from the anomaly peak with the aid of the equation in the figure; for this estimate, it is necessary to assume what type of material is underground. 100 A geometric calculation of the magnetic anomaly of a long feature with a rectangular cross-section

80 Anomaly from upper surface

60

Resultant total anomaly = 40 upper - lower

Anomaly from 20 lower surface

line of measurement 0 Magnetic anomaly, no units no anomaly, Magnetic

-20

Cross-section of Angular size of rectangular feature lower surface -40

-60 -5-4-3-2-1012345 North coordinate, m

Figure 42: The geometric calculation of an anomaly. This simple approximation can aid one's thinking about the anomalies from elongated objects. The magnetic anomaly that is caused by the upper surface of the rectangular prism is proportional to the angular size of that surface as it changes along the line of measurement; the same process applies to the anomaly from the lower surface. The difference of the two anomalies gives the resultant anomaly of the whole prism. If the magnetic field is vertical, there is no contribution to the anomaly from the sides of the prism. Total field - Vertical component 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

North component East component 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 43: Three perpendicular components of a magnetic anomaly. Some magnetometers (such as cesium and proton) measure the total field of the Earth; these instruments find anomalies like that in panel A. Fluxgate magnetometers measure one component of the total field; three perpendicular components are plotted in panels B - D. The vectorial sum of these three components is the total field, in panel A. Inclination angle, 0.01 degrees declination angle, 0.02 degrees 3 3 A B 2 2

1 1

0 0

-1 -1 North coordinate, m North coordinate, m -2 -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Northerly gradient, 5 nT/m Easterly gradient, 5 nT/m 3 3 C D 2 2

1 1

0 0

-1 -1 North coordinate, m coordinate, North -2 North coordinate, m -2

-3 -3 -3-2-10123 -3-2-10123 East coordinate, m East coordinate, m

Figure 44: Four more variations on a magnetic map. For the same dipolar anomaly that is mapped in Figure 43, different aspects of the magnetic field may be plotted. The direction of the magnetic field is mapped in the upper two panels; inclination angle is the dip angle below horizontal, and the declination angle is the angle east of grid north. While gradiometers typically have their two sensors along a vertical line, these sensors may also be placed along a horizontal line; the magnetic maps that could then be measured over compact objects are plotted in panels C and D.