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Mars has a magnetic field originating in its strongly magnetized crust that holds clues to the planet's interior. We apply vector spherical harmonic decomposition to simple candidate magnetic structures to separate the parts responsible for the anomalies from those that remain invisible. A uniform magnetic layer produces no anomalies: spatial variations are essential although secondary magnetization does produce a weak field that might reflect the primordial dynamo field. A hemispheric layer produces anomalies confined to the equator rather than the observed hemispheric difference. A uniformly magnetized crust with variable thickness determined from gravity and topography produces a crustal field with large anomalies at the major impact crater sites that are not observed. These anomalies are not present if the magnetic layer lies deeper than the crater floor. We conclude that decomposing magnetizations in this way is a useful tool in the interpretation of Martian magnetic anomalies. Plain Language Summary: Four billion years ago Mars had a magnetic field generated by a dynamo operating in its liquid core, as Earth has today. It cooled faster than Earth and dynamo action ceased but not before it had magnetized the planet's crust. This study is made topical by the arrival of the Chinese rover Zhurong, which is capable of carrying out a ground magnetic survey. The lander InSight recorded a magnetic field some 10 times stronger than expected from measurements made by satellite in orbit. Here we use a relatively new technique to separate proposed magnetic structures into their "invisible" and "visible" parts. We show this while the magnetic field is stronger in the Southern Hemisphere than the North, this does not imply one hemisphere is more strongly magnetized than the other. Strong ground measurements can be explained by a strongly magnetized, invisible, shell that has been broken up into smaller, visible, fragments. Larger impact craters have no magnetic anomaly, an observation often attributed to removal of the original magnetized material; we show the anomaly remains if the surrounding crust is strongly magnetized and propose the source of the anomalies lies deeper than the bottom of these craters. Key Points: Vector spherical harmonic analysis can help elucidate magnetic structures in Mars' crustSecondary magnetization in a uniform shell produces a magnetic anomaly that reflects the original dynamo fieldAbsence of anomalies at large impact craters cannot be explained by simply excavating magnetized crust [ABSTRACT FROM AUTHOR]

Most subduction zones have associated long‐wavelength anomalies in the lithospheric magnetic field observed at satellite altitude. We model the 13 subduction zones defined by seismicity and seismic tomography using vertically integrated magnetizations that are increasing, level, or decreasing away from the trench. These mimic end members of a magnetized mantle wedge, a uniform layer, and a magnetized dipping lithospheric slab. They are added to a global model of vertically integrated magnetization based on continental and oceanic geology. We find the dipping slab places the anomaly too close to the trench, while the other two fit the data equally well and use the level model in the main part of the study. Anomalies at the Sunda, Aleutians, Cascadia, Central American, and Kamchatka‐Japan zones are well modeled by uniform magnetization of differing susceptibilities and spatial extents. We show the South American anomaly is weak because the magnetization lies mainly in the null space that produces no external potential magnetic field. There is no anomaly associated with the Ryukyu system, possibly because the present subduction started too recently for magnetization to have formed. The magnetic anomaly stretching down the Baja California peninsula is not present in the prediction because there is no seismicity on which to base a slab geometry, but recent tomography suggests a fossil slab there and we propose historic subduction as the origin of the Baja magnetic anomaly. Finally, we discuss the mineralogical origins of the magnetization and favor serpentinization of the region above the subducted plate. Key Points: Many subduction zones are associated with long‐wavelength magnetic anomaliesThe anomalies are unlikely to be explained by magnetization solely in the subducting slabModeling supports the hypothesis of magnetized serpentinite in the mantle wedge [ABSTRACT FROM AUTHOR]

The problem of understanding how Earth's magnetic field is generated is one of the foremost challenges in modern science. It is believed to be generated by a dynamo process, where the complex motions of an electrically conducting fluid provide the inductive action to sustain the field against the effects of dissipation. Current dynamo simulations, based on the numerical approximation to the governing equations of magnetohydrodynamics, cannot reach the very rapid rotation rates and low viscosities (i.e. low Ekman number) of Earth due to limitations in available computing power. Using a pseudospectral method, the most widely used method for simulating the geodynamo, computational requirements needed to run simulations in an 'Earth-like' parameter regime are explored theoretically by approximating operation counts, memory requirements and communication costs in the asymptotic limit of large problem size. Theoretical scalings are tested using numerical calculations. For asymptotically large problems the spherical transform is shown to be the limiting step within the pseudospectral method; memory requirements and communication costs are asymptotically negligible. Another limitation comes from the parallel implementation, however, this is unlikely to be threatened soon and we conclude that the pseudospectral method will remain competitive for the next decade. Extrapolating numerical results based upon the code analysis shows that simulating a problem characterizing the Earth with Ekman number E = 10 would require at least 13 000 days per magnetic diffusion time with 54 000 available processors, a formidable computational challenge. At E = 10 an allocation of around 350 million CPU hours would compute a single diffusion time, many more CPU hours than are available in current supercomputing allocations but potentially reachable in the next decade. Exploration of the 10⩽ E⩽10 regime could be performed at the present time using a substantial share of national supercomputing facilities or a dedicated cluster. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]