The behavior of a lithospheric magnetization and magnetic field model

1.   Introduction

In modern navigational systems, the geomagnetic field provides information on spatial location on the Earth. The Earth’s magnetic field has both an internal source that arises in the core of the earth, and, to a lesser extent, external sources. The Earth’s magnetic field is not constant but varies with time, and can be portrayed usefully only by geomagnetic field models that are based on data from observatories and satellite measurements. The lithospheric magnetic field has two major sources: (1) induced magnetization, i.e., the magnetization that is induced in the lithosphere from the Earth’s magnetic field; and (2) remanent (residual) magnetization of the rocks themselves. The lithospheric magnetic anomaly field can be used in studying the structure and composition of the lithosphere, the lithosphere’s thermal history, and as an aid in mineral exploration. Currently, the seventh generation lithospheric magnetic field model (MF7) is one of the more widely used lithospheric field models. The MF model series, unlike other series, focuses only on the lithospheric field (e.g. Maus et al., 2002; 2007; Maus, 2010a). Examples of other global lithospheric models are those developed by Stockmann et al. (2009), Kother et al. (2015), Thébault et al. (2016), and Olsen et al. (2017). Another class of lithosphere-based field models considers multi-sources; prominent examples are the comprehensive model (CM) series (e.g. Sabaka et al., 2002), the British Geological Survey (BGS) models (e.g. Thomson and Lesur, 2007; Thomson et al., 2010), the GeoForschung Zentrum (GFZ) Reference Internal Magnetic Model (GRIMM) (e.g. Lesur et al., 2008; 2015), and the CHAOS models (e.g. Olsen et al., 2006; Finlay et al., 2016). Some of these latter models are being updated constantly with high-resolution data that continue to become available, and refined by improved processing methods. Updated models include: (1) the CM series of field model, updated from the first generation CM1 model (Sabaka et al., 2002) to the sixth generation CM6 model (Sabaka et al., 2020); (2) the CHAOS series, from CHAOS-1 (Olsen et al., 2006) to CHAOS-7 (Finlay et al., 2020); and (3) the MF series models, from MF1 (Maus et al., 2002) to MF7 (Maus, 2010a).

Models of the lithospheric magnetic field have employed different regularization schemes for the radial magnetic field (B_r). These include: L1 normal regularization (Morschhauser et al., 2014; Olsen et al., 2017), L2 normal regularization (Maus, 2010a), and maximum entropy regularization (Stockmann et al., 2009; Kother et al., 2015). Model parametrization choice is one of important aspects in constructing lithospheric models, and a variety of model parametrizations has been adopted. These are harmonic splines (Langel and Whaler, 1996), spherical caps (e.g. Haines, 1985; Thébault, 2006), spherical triangle tessellations (Stockmann et al., 2009), equivalent dipole sources (e.g. Mayhew, 1979; Olsen et al., 2017), and equivalent source methods involving monopoles (O'Brien and Parker, 1994; Kother et al., 2015).

Although different methods of regularization and parametrization may result in models that can be distinguished from one another, method choice does not have a decisive effect on a model’s ability to obtain a high-resolution field. Key to the success of any model is the quality of its data sources, which depend not only on observation means, but on data selection criteria. Criteria for temporal and environmental selection have been improved over the past decades; Thébault et al. (2017) reviewed identification methods commonly used for geomagnetic field data, and proposed a spatial data correction scheme for modeling the lithospheric magnetic field. Other studies that discuss data selection are provided by Olsen et al. (2017), Finlay et al. (2020), and Sabaka et al. (2020).

It is worth noting that means of observation play a key role in collecting global magnetic field data. The CHAMP satellite flew in a near-polar orbit with an inclination of 87.3° (angle between satellite orbit and equator); Swarm A and C fly at an inclination of 87.35°, and Swarm B at 87.75°. These near-polar orbit satellites have collected large quantities of data along North−South tracks. To further our understanding of the dynamics and structure of Earth’s magnetic field, data from satellites flying at lower inclinations are essential. Unfortunately, there are currently no low-inclination satellite missions that collect magnetic data. For this reason, the MSS-1 mission, scheduled to be launched at the beginning of 2023, has been designed to have an orbit inclination i = 41°. The low inclination orbit will be valuable in refining structural features that trend East−West, which is necessary in the construction of a reliable field model of the Earth’s lithosphere that can be used for quantitative studies of lithospheric composition and structure, and even guide future resource exploration.

This study reviews, first, our current knowledge of the geological and tectonic structures of the lithosphere and how they contribute to the lithospheric magnetic field. Next is a brief summary of the magnetic behavior of rocks whose induced fields (which are dependent on their susceptibility) and whose remanent magnetization, both contribute to the lithospheric field. Finally, we concentrate on the magnetic field contribution from the lithosphere as it will be observed from the MSS-1 mission. Based on the vertically integrated magnetization model presented herein, we compute the lithospheric magnetic field at an expected 400 km altitude of MSS-1. We analyze the effect of the low inclination attitude of satellite orbit on the sensitivity with which lateral variations of the lithospheric magnetic field, and thus structural features, can be resolved. This geology-based prior information can provide a useful reference for establishing an improved satellite-data-derived lithospheric field model based on the new observations collected by the MSS-1 mission.

2.   Structure of the Lithosphere

The Earth’s lithosphere is an outermost layer that consists of the crust and the uppermost portion of the solid mantle. Since the discovery of seafloor spreading (Dietz, 1961; Hess, 1962), it has become clear that the lithosphere can be divided into different tectonic plates (Wilson 1965), which are bounded by mid-oceanic ridges, subduction zones, and/or transform faults. Plate tectonics, in this new spatial framework of the lithosphere, comprises the motions of many plates with respect to each other over the Earth’s surface, in which the motion of each plate is treated as that of a rigid body. Continents, which are part of the plates, often have a rigid part that has been stable over long geological time spans. These are known as cratons.

Figure 1 presents the present-day major global plates with isochron coloring that indicates age distribution of oceanic crust. Note that many plate boundaries are longitudinal in orientation. The cratons of the continents consist of Precambrian (>540 Ma) rocks, indicating that the cratons have been largely stable in the evolution of the lithosphere. These include, but are not limited to, the Eurasian, African, North American, South American, Pacific Ocean, and Australian plates (Goodwin, 1996). As we will see below, magnetic anomalies that originate in the lithosphere are mainly linked to geological regions covered by Precambrian rocks, including both exposed parts and parts that are overlain by younger Phanerozoic cover.

Figure  1.  Global plate reconstruction at present-day (Seton et al., 2012). Colors (see basemap) indicate ages of oceanic crust. Black lines denote mid-ocean ridges and transform faults. Black arrows denote the absolute velocity vectors of plate. Subduction zones are indicated by red lines. Plate name abbreviations include: AFR = Africa, ARA = Arabia, CAP = Capricorn, CAR = Caribbean, COC = Cocos, LB = Lau Basin, NAZ = Nazca, NFB = North Fiji Basin, PAC = Pacific, PS = Philippine Sea, SCO = Scotia Sea, and SOM = Somalia. For more detailed information see (Seton et al., 2012).

DownLoad: Full-Size Img PowerPoint

Plate tectonic features and other geologic structures are key factors in establishing models of lithospheric remanent magnetization and magnetic susceptibility. On the basis of plate tectonic structure (Goodwin, 1991, 1996), susceptibility of rocks (Clark and Emerson, 1991; Hunt et al., 1995), and thickness of the crust, Hemant and Maus (2005) built a vertically integrated susceptibility model (VIS). A model of the lithospheric magnetic field can be obtained by combining the modeling described above with the oceanic crust remanent magnetization model that was based on seafloor isochron information (Müller et al., 1997) and rotation models of the plates (Royer et al., 1992). Combining the VIS model with the global remanent magnetization model allows calculation of the magnetic field of the lithosphere at different altitudes above the Earth’s surface, which in turn can be compared with satellite measurements.

3.   Magnetic Characteristics of the Lithosphere

3.1   Properties of Magnetic Minerals

Magnetic minerals, such as iron oxides, iron sulfides, and iron hydroxides, are commonly found in terrestrial rocks and are the sources of the lithospheric magnetic field. They include the titanomagnetite series (Fe₃O₄−Fe₂TiO₄), titanohematite series (αFe₂O₃− FeTiO₃), magnetite-maghemite series (Fe₃O₄−γFe₂O₃), and other minerals, such as pyrrhotite (Fe₇S₈ −Fe₁₁S₁₂), greigite (Fe₃S₄), and goethite (αFeOOH). These ferromagnetic minerals are capable of remanent magnetization. Depending on mineral composition and grain size, the remanent magnetization carried by particles can be very stable over geologic time.

The five common types of remanent paleomagnetizations are thermoremanent magnetization, chemical remanent magnetization, detrital remanent magnetization, viscous remanent magnetization, and thermoviscous remanent magnetization. A sixth type, isothermal remanent magnetization, describes magnetization acquired in a direct current (DC) applied field, and is not common in nature. In the presence of a magnetic field, a rock can acquire a thermal remanent magnetization when cooling through its Curie temperature. Above the Curie temperature, the magnetization is paramagnetic; individual magnetic moments are free to fluctuate in the rock. Curie temperature plays a key role in the acquisition of remanent magnetization. Coercivity is a measure of the ability of ferromagnetic material to withstand an ambient field without becoming demagnetized. Table 1 shows three types of magnetic properties for common magnetic minerals. The ability and stability of minerals carrying remanent magnetization are related to these magnetic parameters.

Table  1.  Summary of magnetic properties of common ferromagnetic minerals in rock.^a

Mineral	Composition	Ms (kA/m)	Tc (°C)	Bc (mT)
Magnetite	Fe3O4	480	580	0.1–34.3
Hematite	αFe2O3	~2.5	680	4.0–520.0
Maghemite	γFe2O3	380	590–675	6.4–9.0
Titanohematite	Fe2.4Ti0.6O4	125	150	2.0–158.0
Goethite	αFeOOH	~2	127	25–890.0
Pyrrhotite	Fe7S8	~80	320–325	9.8–97.2
Greigite	Fe3S4	~125	~330	10.0–71.3
aMs = Saturation magnetization, Tc = Curie or Néel temperature, Bc = Coercivity.

 | Show Table

DownLoad: CSV

3.2   Susceptibility Model

The magnetic anomaly field of the Earth’s lithosphere is closely associated with geological structures and composition of the planet’s crustal rocks. For the magnetic distribution of the continental crust, Precambrian units are often more strongly magnetized in comparison to the Phanerozoic crust. In the construction of a global susceptibility model, geological units are assigned an average value of susceptibility, based on laboratory measurements performed on samples of typical rock types. Because in many regions of the world, Precambrian basement underlies younger geological provinces, a higher value of susceptibility is assigned to the lower crust in a susceptibility model. The Archean (>2,500 Ma) lower crust is assigned a susceptibility 1.2 times larger than that for its corresponding upper crust. In the case where the craton rock is post-Archean, the susceptibility of the lower crust is assumed to be 1.6 times larger. For example, when a susceptibility value of 0.01 SI is assigned to younger Phanerozoic provinces, 0.016 SI is the mean value assigned to the lower crust of such a Phanerozoic province. More detailed information on the susceptibility distributions for different geological units is provided in the systematic work of Hemant (2003).

To establish a vertically integrated susceptibility (VIS) model over the oceanic crust, a three-layered model is used (White et al., 1992). The stratum thickness of each layer within the vertical column is multiplied by that layer’s susceptibility. For more details about how the model is established see Hemant and Maus (2005). Figure 2 presents a global VIS model that is based on comprehensive information from geological and rock magnetism studies.

Figure  2.  VIS (vertically integrated susceptibility) map of the world (Hemant and Maus, 2005). High susceptibility, which coincides with cratons, is shown in warm colors; low susceptibility is indicated with cooler colors.

DownLoad: Full-Size Img PowerPoint

A vertically integrated magnetization (VIM) model, derived from VIS and remanent magnetization models, was employed by Gubbins et al. (2011) to analyze the lithospheric magnetization in terms of vector spherical harmonics. Note that the VIM is comprised of two parts: (i) induced magnetization and (ii) remanent magnetization. Here the induced magnetization is derived from a global VIS model (Hemant and Maus, 2005). The remanent magnetization for the oceanic lithosphere is generated from an isochron map of the ocean floor and rotation of the plate reconstruction models (Masterton, 2010). Applying vector spherical harmonics to the global VIM model, Gubbins et al. (2011) decomposed lithospheric magnetization into three parts. These are: (i) the part that yields a potential magnetic field that is observable outside the shell, (ii) the part that yields a magnetic field inside the shell, and (iii) a part, known as toroidal, that yields no magnetic field at all.

4.   Lithospheric Magnetic Field Models

4.1   Global Models

The earliest models of the lithospheric magnetic field were based on airborne and shipborne measurements. Many countries conducted their own programs to construct magnetic maps (e.g., Bankey et al., 2002). These maps were able to capture geological features of relatively modest scale, ranging from several kilometers to hundreds of kilometers. Insight into the magnetic structure of the global lithosphere, however, began only in the late 1960s with the launch of the Pogo satellite mission (Regan et al., 1975), and continued with Magsat in the late 1970’s (Langel et al., 1982; Cain et al., 1989; Ravat et al., 1995). The precision of early global field models, however, was limited by inaccuracies, at that time, in determination of satellite attitudes and orbital altitudes.

The modern era of satellite magnetometry began with the launch of Danish satellite Ørsted on 23 February, 1999 (Sabaka et al., 2020), followed by satellite CHAMP (launched on 15 July, 2000), SAC-C (launched on 21 November, 2000), and the Swarm satellites (launched on 22 November, 2013). The orbital attitudes and altitudes of these more recent satellites were determined with vastly improved accuracy; date collected by these single satellites and/or satellite constellations have allowed construction of a variety of high-accuracy field models. The level of spatial resolution of these models differs from mission to mission. Table 2 displays, for selected models, the data source, spherical harmonic degree coverage, and corresponding resolution of each model.

Table  2.  Selected magnetic field models using data from satellite missions.

Model name	Year	Data source	Spherical degree	Resolution (km)	Reference
Oersted-05	2000	Oersted, CHAMP, SAC-C	14−44	800	(Olsen et al., 2000)
CM3	2002	POGO-MAGSAT, Orsted-CHAMP-SAC, ground magnetic surveys	15−65	600	(Sabaka et al., 2002)
CM4	2004	POGO-MAGSAT, Orsted-CHAMP-SAC, ground magnetic surveys	16−65	600	(Sabaka et al., 2004)
CM5	2015	Oersted, SAC-C, CHAMP, ground magnetic surveys	16−107	374	(Sabaka et al., 2015)
CM6	2020	Oersted, SAC-C, CHAMP, Swarm, ground surveys	16−120	330	(Sabaka et al., 2020)
MF5	2006	CHAMP	16−100	400	(Maus et al., 2007)
MF6	2007	CHAMP	16−120	330	(Maus et al., 2008)
MF7	2010	CHAMP	16−133	300	(Maus, 2010a)
NGDC-720	2010	Swarm, CHAMP marine, aeromagnetic & ground magnetic surveys	16−720	56	(Maus, 2010b)
EMAG2	2017	Swarm, CHAMP, marine, aeromagnetic & ground magnetic surveys	—	3.7	(Maus et al., 2009; Meyer et al., 2017)
LCS-1	2017	Swarm, CHAMP	16−185	225	(Olsen et al., 2017)

 | Show Table

DownLoad: CSV

Lithospheric magnetic field models can be constructed in various ways, including the merger of one model into another. For example, LCS-1, a lithospheric magnetic field model, is determined entirely from magnetic ‘gradient’ data (Olsen et al., 2017). CHAOS-7 is a multi-source model covering a period of 21 years, from 1999 to 2020 (Finlay et al., 2020). For CHAOS-7 above degree 25, its static internal field merges to the LCS-1 model with degree from 16 to 185.

4.2   Magnetic Anomaly Field of the Lithosphere

Today’s magnetic field models are based on data collected by satellites as well as on data from marine, aeromagnetic, and ground magnetic surveys. To obtain a map of magnetic field anomalies originating in lithospheric sources, one can forward model the lithospheric magnetic field from knowledge of lithospheric structures and the magnetic properties of the materials distributed in those structures. Here we compute such a forward model of the magnetic field of the lithosphere, based on the VIM model that was used in Gubbins et al. (2011).

The magnetic potential V at point r due to a distribution of magnetization M is (Blakely, 1995)

where ${\mu }_{0}=4\pi \times {10}^{-7}\;{\rm{N}/\rm{A}}^{2}$ is permeability of free space, r is the position of dv, and the integral is carried out over the magnetized region.

In spherical polar coordinates, the magnetic potential V can be described by a spherical harmonic expansion

where ${P}_{n}^{m}\left(\mathrm{cos}\theta \right)$ is the Schmidt normalized associated Legendre function, ${g}_{n}^{m}$ and ${h}_{n}^{m}$are Gauss coefficients, and r_E = 6371.2 km is a reference radius of Earth. For a given M, one can obtain Gauss coefficients (${g}_{n}^{m}$ and ${h}_{n}^{m}$) through combining Equations (1) and (2), and further obtain a forwarding magnetic field. The degree of spherical harmonic will be dependent on the wavelength of a feature that describes the potential of the magnetic field. Spherical harmonic degrees for n = 1 to 15, are considered to arise from the core of the Earth. For this reason, an anomaly map of the lithosphere considers n ≥ 16, which is the range that is resolvable from data collected by the satellite programs described in Table 2. The higher the resolution of the map, i.e., the ability of the dataset to resolve short wavelengths, the higher the spherical harmonic degree that needs to be processed.

In this study, we compute a lithospheric magnetic field adopting a given global magnetization model VIM, to illustrate the possible resolution that can be achieved by the Macau Science Satellite-1. Figure 3 displays the vertical component of the predicted forward model of the anomalous field for a satellite altitude of 400 km, and for spherical harmonic degree up to n = 256. The amplitude of the lithospheric anomalies is between −14.8 nT and 18.2 nT. Large scale geological features, such as cratons and subduction belts, correspond generally to positive anomalies on magnetic anomaly maps for crust, because of the enhanced susceptibility of the rock in these regions. Basins and abyssal plains, on the other hand, often are expressed as negative anomalies, which may be related to crustal thinning.

Figure  3.  Predicted vertical magnetic field (B_r) anomaly map at 400 km altitude, for spherical harmonic degree 256. Map view is centered on the 0 meridian, shaded by topography.

DownLoad: Full-Size Img PowerPoint

What is clear from Figure 3 is that there is a broad spectrum of wavelengths, depending on the particular geological feature that gives rise to each anomaly. Upper crustal sources are associated with some relatively long wavelength fields and are likely to be important contributors to long-wavelength parts (Hall, 1974; Pilkington and Percival, 1999). Comparison of predicted with observed anomaly maps shows that in some anomalies the maps generally agree well with each other; examples can be seen in the southeastern part of the African continent, and also in cratonic areas, such as the northern Indian shield, the Siberian Craton, the north Brazilian shield, and the northern and southern cratons of Greenland. However, some differences exist between model-predicted anomalies and actual observations. For example, observations reveal a distribution of near east−west anomalies over the Pacific Ocean, but this feature is absent in the predicted map. Other regions where model predictions do not match observations include northwestern continental and coastal regions of Greenland, and the Kola peninsula. These discrepancies are found in all models of the anomalous magnetic field of the lithosphere, as discussed by Hemant and Maus (2005) and Masterton et al. (2013). Considerations that need to be addressed in future models include crustal thickness, which affects the depth of the Curie isotherm, the contribution of remanent magnetization (Hemant and Maus, 2005), and also non-homogeneities in the magnetization of the upper mantle and the oceanic crust (Masterton et al., 2013). Addressing these unresolved scientific problems will be a part of the goals and tasks for MSS-1 mission.

5.   Conclusions

We have reviewed the behavior of models of lithospheric magnetization and the global magnetic field. The susceptibility of various rocks has a major influence on details of the lithospheric magnetic field and the anomalous field. Magnetic anomalies over continental crust are largely due to the inducing field, while anomalies over oceanic crust are attributed to both remanent and inducing magnetization. A VIM-model-based predicted lithospheric field shows that field anomalies measured at the 400 km altitude can be as large as 18.2 nT. The resolution of satellite-collected data should be sufficient to capture higher wavelength features originating in the lithosphere.

The low inclination orbit of the Macau Science Satellite-1 mission should also aid in resolving geological features that have a more East−West trend, thus allowing increased spatial precision. Furthermore, higher resolution anomalous maps of the lithosphere can be used to refine our understanding of the susceptibility and/or magnetization distribution within the lithosphere, to improve our knowledge of associated structural and dynamic behavior of the lithosphere, and possibly to guide mineral resource exploration.