After the Earth's hot magma emerges from volcanoes and when the ambient temperature decreases below the Curie temperature, crustal magnetization takes place with the amplitude and direction of the core dynamo field being frozen in the cooling rock at that instant of geologic time. Magnetic signatures of the Earth's lithosphere recorded in rock magnetization can thus unveil the slow movement of Earth's continents and are usually employed in interpreting and understanding large-scale geological processes such as plate tectonics. Profiles of lithospheric magnetization have played an essential role in untangling the history of the Earth's tectonics in various geological epochs, offering a unique magnetic fingerprint deployed to define and study polar wonder, seafloor spreading, and plate movement. Earth's lithospheric magnetization is of two different types: remanent and induced. Earth's crustal magnetization in its continents is primarily induced while oceanic lithospheric magnetization in the ridge regions is mainly remanent. There exists a broad spatial spectrum of the lithospheric magnetic field: at the large scale O(1000) km, it overlaps with the core dynamo field; at the intermediate scale O(100) km which is predominant, it can be measured by the high-precision geomagnetic satellites; and at the small scale O(10) km, it cannot be accurately measured at the satellite altitude of about 400-500 km where the existing satellites usually orbit.
The lithospheric magnetic field modeling requires nearer surface measurements such as lower-altitude-perigee satellites together with ground, marine and airborne magnetic surveys. The new geomagnetic constellation is particularly suitable for the studies of intermediate or small scales of geomagnetic anomalies of the lithospheric origin. Constructing an accurate global lithospheric magnetic model, however, remains a highly challenging task. One of the main difficulties stems from the Runcorn theorem which states that a constant magnetic susceptibility in a spherical shell does not produce visible external magnetic field signatures for an inducing dipole field internal to the shell, suggesting that there exists a large null space of the inverse problem. Moreover, the lithospheric magnetic field is characterized by many sharp discontinuities and, consequently, it is numerically difficult to use the standard spherical harmonic expansion to model it.
Below is a brief description of our progress on lithospheric magnetic field. Magnetic minerals, which are distributed in rocks that make up the lithosphere, are the source of the lithospheric field. The part of the Earth’s magnetic field that originates in the lithosphere consists of a superposition of magnetic anomalies with a broad spectrum of sizes and intensities, which arise from geological and tectonic features. Based on the vertically integrated magnetization model, we compute the lithospheric magnetic field at an expected 400 km altitude. The model forwarding indicates that the amplitude of the lithospheric anomalies (Br) is between -14.8 nT and 18.2 nT at 400 km altitude. This information is useful because it provides a reference for the lithospheric source of the Earth’s magnetic field that contributes to the magnetic measurements from satellite. The lithospheric magnetic anomaly field can be used in studying of structure and composition of lithosphere, thermal history, and aid in mineral exploration.

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