It has been known since the early 1950s that rocks and sediments display a magnetic anisotropy when constituent mineral grains have a preferred orientation (Graham, 1954; Hargraves, 1959). Magnetic fabric is usually described by the anisotropy of magnetic susceptibility (AMS), measured in weak applied fields. With this method all minerals in a rock or sediment contribute to the susceptibility. Therefore, the observed anisotropy is the sum of the individual mineral components, their specific susc\eptibility anisotropy and their preferred alignment. Since nonferromagnetic matrix minerals often make up the bulk composition of a rock or sediments, the low‐field susceptibility of these minerals can dominate the measured signal. The anisotropy of magnetic remanence (AMR) is only dependent on the ferromagnetic grains (s.l.) in a rock. Since the number of different ferromagnetic phases is more limited, the source of the AMR is easier to distinguish, and the degree of anisotropy is less sensitive to mineral variation (Jackson, 1991).
In early studies several authors noted that certain rocks that display AMS also have natural remanent magnetizations (NRMs) that are shallowly inclined toward the plane of high susceptibility (Howell et al., 1958; Hargraves, 1959; Fuller, 1960). This observation promoted the first studies examining the anisotropy of remanent magnetization. Since then numerous investigations have used the anisotropy of remanent magnetization to determine if the ferromagnetic minerals are preferentially aligned, which may in turn affect the characteristic remanent magnetization (ChRM) of a rock.
The physical theory of magnetization and the magnetic behavior of minerals is given elsewhere in this volume. Detailed coverage on the theory of AMS and AMR is available in several textbooks and review papers (Jackson, 1991; Rochette et al., 1992; Tarling and Hrouda, 1993; Borradaile and Henry, 1997; Tauxe, 2002). A cursory description necessary to understand the basis of anisotropy of remanent magnetization follows.
where χ is the susceptibility, a material constant that can be described by a tensor of second order, and H is the inducing field. The remanent magnetization is the magnetization that remains after the material is removed from an applied magnetic field and is carried by ferrimagnetic minerals.
It can be represented geometrically by an ellipsoid with principal axes parallel to the eigenvectors of k r and lengths equal to the corresponding eigenvalues, where k r1 ≥ k r2 ≥ k r2. It must be noted that M r should be both linearly dependent on the intensity of the inducing field and reversible.
In a rock or sediments, we are interested in the total contribution of all ferrimagnetic minerals to the observed signal. If a material is isotropic, i.e., the minerals show no preferred orientation, then M i will be along the direction of the applied field and M r will be in the direction of the field that produced the remanence. If, however, the minerals in a rock or sediment have a preferred orientation then the acquired magnetization will lie between the applied field direction and the direction of the easy axis of magnetization. The easy axis of magnetization may be related to the shape of the grain, as is the case for ferrimagnetic spinel. Minerals that display shape anisotropy have a high spontaneous magnetization and a slight departure from equidimensional habit leads to the magnetization being preferentially aligned along the long axis of a grain. Crystallography may also control the direction of magnetization, due to the geometric distribution of atoms within the crystallographic lattice. The ferrimagnetic minerals, hematite and pyrrhotite, are controlled by magnetocrystalline anisotropy. Compared to the value along the c‐axis, the susceptibility in the basal plane is two orders of magnitude higher in hematite and three orders of magnitude higher in pyrrhotite. Stress within a mineral may also lead to an anisotropic acquisition of magnetization, known as magnetostriction. It arises from the strain dependence of the anisotropy constants and has been observed in titanomagnetite.
Types of remanent magnetization
A rock or sediment can acquire different types of remanent magnetizations. Some types of remanence are acquired by natural processes, whereas other types are imparted under laboratory conditions. When rocks form from molten lava or sediments are deposited, the magnetic moments of ferromagnetic minerals align statistically with the prevailing Earth's magnetic field and receive a remanent magnetization, known as the NRM.
The NRM that is found in rocks that are formed from molten lava is called a thermal remanent magnetization (TRM). When individual ferrimagnetic minerals cool through their Curie temperature or Néel temperature, the ferrimagnetic grains take on the magnetization of the ambient magnetic field. TRM is very stable over time. Sediments acquire their remanent magnetization as they are deposited. The ferrimagnetic grains align statistically in the ambient field as they settle and the acquired magnetization is called a detrital remanent magnetization (DRM). As the grains are cemented in the matrix of the sediment, the resulting magnetization is a postdetrital remanent magnetization (pDRM).
An IRM is acquired in a strong DC field (H IRM, generally >10 mT) of known intensity and direction. All ferrimagnetic grains with a coercivity less than or equal to H IRM will be remagnetized. Since IRM is a strong‐field remanence the imparted magnetization is not linearly related to H IRM. If the applied field is below saturation and if only the first‐order terms are considered, a symmetric matrix can be assumed for constant H IRM (Cox and Doell, 1967; Stephenson et al., 1986; Jackson, 1991). Saturation IRM also shows a grain‐size dependence for (titano‐)magnetite, hematite, and pyrrhotite (Figure M56b).
Measurement of the anisotropy of magnetic remanence
where RMS is the root mean squared residuals normalized to k mean. The expression is an estimate of how well the anisotropy ellipsoid is resolved. The ellipsoid can be considered well resolved for GoF values under 10%; typically values are on the order of a few percent.
Stephenson et al. (1986) suggested an alternative method to obtain the ellipsoid of anisotropy of remanence. They measured the individual diagonal and off‐diagonal matrix elements directly. Here a laboratory remanent magnetization is applied along the sample x‐axis and the three components of the magnetization are measured. The sample is demagnetized and the same field is next applied along the sample y‐axis and all the three components of the magnetization are measured. After demagnetization the field is now applied along the sample z‐axis and the magnetization is measured. This yields nine values that overdefine the tensor and yield a measure of the precision of fit. This method is probably reliable for IRM, since the imparted remanence is relatively large, allowing for accurate determination of the magnetization components oriented normal to the applied field direction. It is less reliable for ARM and TRM where imparted remanences are relatively weak.
Anisotropy of anhysteretic remanent magnetization (AARM)
The anisotropy of ARM has also been called the anisotropy of anhysteretic susceptibility (AAS), since normalizing the magnetization by the field strength converts it to a pseudosusceptibility. An ARM is acquired from the DC bias field, often on the order of 0.05–0.1 mT, superimposed on the AC field. The strength of the bias field is on the order of one to two times that of the Earth's magnetic field. The intensity of the AC field can be chosen as desired, but is generally less than 300 mT, due to limits of commercially available AF demagnetizing units. This limitation means that an ARM can only be imparted to minerals with low coercivity, such as (titano‐)magnetite or pyrrhotite. A detailed description of the measurement procedure is outlined above and has been given in McCabe et al. (1985).
Since the coercivity of ferromagnetic minerals, particularly magnetite and titanomagnetite, is dependent on grain size, it is possible to impart an ARM to a particular grain‐size fraction during demagnetization in the DC bias field. This is accomplished by switching on the DC bias field in a specific AC field range or coercivity window during demagnetization. The imparted magnetization is known as a partial ARM (pARM). Jackson et al. (1988) demonstrated that the method can be used to distinguish if a specific grain‐size fraction is responsible for the observed AARM. For example, a high coercivity window (e.g., 80–150 mT) will only magnetize single‐domain magnetite, whereas a low coercivity window (e.g., 0–30 mT) would magnetize larger multidomain grains (see “Geological Applications” sections for a practical example).
Anisotropy of isothermal remanent magnetization (AIRM)
The advantage of AIRM is that a relatively strong DC field is applied to the sample, such that higher coercivity phases may also be magnetized. As stated above, IRM is not linearly related to the applied field; however, a symmetric matrix can be assumed if only the first‐order terms are considered. Jelinek (1996) proposed a nonlinear AIRM model that more precisely describes the magnetization phenomena, in which the anisotropy is also described by a symmetric second‐order tensor. The typical strength of the applied field is between 5 and 60 mT (Tarling and Hrouda, 1993). Cox and Doell (1967), who proposed the method originally, used an applied field of 700 mT, which is above the saturation of the ferromagnetic phases. The measurement procedure is the same as outlined above. The main difficulty with their method is the complete demagnetization between each imparted magnetization step. If lower fields are used, it should be possible to demagnetize with alternating field (AF) demagnetization. Cox and Doell (1967) rotated their samples in the 700 mT field of an electromagnet to randomize the magnetization, since complete randomization of magnetic domains is reversible.
where J r is the measured remanent magnetization, which is produced in the field H, and J m is the mean amplitude of a set of J r vectors averaged over all the results from the different directions of the applied field. This gives a set of D(H′) for each value of the alternating field demagnetization (H′).
Caution must also be exercised when measuring the AIRM in pyrrhotite‐bearing rocks. A study by de Wall and Worm (1993) demonstrated that the shape of the ellipsoid and degree of anisotropy are dependent on the applied field in rocks containing pyrrhotite. Although the orientations of the principal axes are not affected, they showed that the degree of anisotropy in a sample of isometric pyrrhotite ore varied between 3.8 and 1.05 for applied field strengths between 1.5 and 100 mT, respectively. The authors attributed this effect to the control of the observed anisotropy by magnetocrystalline anisotropy in low applied fields, and by magnetostatic anisotropy, which arises from the cylindrical sample shape, in strong fields. Jackson and Borradaile (1991) reported a similar dependence of AIRM and field strength in hematite‐bearing slates, but attributed the effect to different coercivity fractions in the rocks.
It has been noted by Tauxe et al. (1990) that following repeated application of an IRM, the coercivity of the specimen increased after exposure to the first high field, so that in spite of demagnetization to remove the previous magnetization, some grains affected by the first field application were no longer affected by subsequent field applications. The authors attributed this effect to hematite grains with metastable domains, which change domain state during the AIRM experiment.
Anisotropy of thermal remanent magnetization (ATRM)
Heating a sample above the Curie or Néel temperature of its ferromagnetic phases and cooling it in an applied field will produce a TRM. As outlined in the general procedure, the sample must be first demagnetized. This can be achieved either with AF demagnetization or by heating the rock above its Curie temperature (T C) or Néel temperature (T N), and cooling in zero field. The rock is then magnetized in the first field direction by reheating above T C or T N and cooling in a field of fixed intensity and rate of cooling. It is important that the field intensity and rate of cooling is the same in all heating runs. After measurement of the imparted TRM, the sample is again demagnetized. At least six independent heating steps are necessary to define the tensor, 12 if the sample cannot be demagnetized in alternating fields and must be reheated above the blocking temperature. It is important to control that no chemical alteration has occurred, which could produce new ferromagnetic minerals and affect the acquired TRM. Often a thermomagnetic curve is made on a small piece of the sample to check that the ferromagnetic mineralogy is thermally stable.
As for a pARM, a partial TRM (pTRM) can be acquired if the field applied during cooling is turned on only when cooling through a particular temperature range. This requires accurate monitoring of the temperature during cooling.
Several examples are presented below to illustrate how AMR can differ from AMS and the type of geologic information that can be obtained from remanent fabrics. The most common method used in examining AMR is AARM. The experimental method is relatively simple and this magnetization method avoids many problems that have been found in applying IRM or TRM. The method is suitable for magnetite‐ and possibly pyrrhotite‐bearing rocks, but not for high coercivity phases, such as hematite. In this case, AIRM and ATRM are more suitable methods. An example is given for AMR in hematite‐bearing rocks. In the examples below, the magnitudes of the principal axes of the anisotropy ellipsoids are defined as k 1 ≥ k 2 ≥ k 3.
AMS and AARM
If the same processes leading to grain orientation affect the ferromagnetic and paramagnetic minerals in a rock, one would expect that the magnetic fabric of both components should be similar. The orientation of the AARM ellipsoid is close to the AMS ellipsoid, and the main difference between the two fabrics is found in terms of the degree of anisotropy, lineation, and foliation. If the two mineral components formed at separate times in the history of the rock or if deformation mechanisms acting on the different mineral components varied, then it is possible that the susceptibility and remanence magnetic fabrics could be different.
Magnetite is the major ferromagnetic phase in both lithologies. Anisotropy of ARM was investigated using a 0.1 mT DC bias field with a 150 mT alternating field, and the measurement procedure of McCabe et al. (1985). The AARM of the limestones is similar to the AMS fabric both in the orientation of the principal axes and the shape of the ellipsoid (Figure M59). This suggests that the susceptibility and remanent fabrics in the limestone are both controlled by magnetite. The AARM in the shales, however, is characterized by prolate ellipsoids, in which k 1 is well‐grouped and subparallel to the pencil directions and k 2 and k 3 are distributed in a girdle in a plane with k 1 as its pole (Figure M59). This remanent fabric shows that the magnetite grains have been more strongly affected by the horizontal compaction. The difference between the AMS and AARM fabrics can be explained by the fact that paramagnetic clays and phyllosilicates dominate the AMS fabric, which is largely controlled by bedding compaction. The magnetite grains acted as rigid particles in a passive matrix during deformation, and were therefore quicker to respond to the horizontal compression.