Abstract: The continuously increasing quantity and quality of seismic waveform data carry the potential to provide images of the Earth’s internal structure with unprecedented detail. Harnessing this rapidly growing wealth of information, however, constitutes a formidable challenge. While the emergence of faster supercomputers helps to accelerate existing algorithms, the daunting scaling properties of seismic inverse problems still demand the development of more efficient solutions. The diversity of seismic inverse problems – in terms of scientific scope, spatial scale, nature of the data, and available resources – precludes the existence of a silver bullet. Instead, efficiency derives from problem adaptation. Within this context, this chapter describes a collection of methods that are smart in the sense of exploiting specific properties of seismic inverse problems, thereby increasing computational efficiency and usable data volumes, sometimes by orders of magnitude. These methods improve different aspects of a seismic inverse problem, for instance, by harnessing data redundancies, adapting numerical simulation meshes to prior knowledge of wavefield geometry, or permitting long-distance moves through model space for Monte Carlo sampling.

Earth’s magnetic field as it is measured by satellite missions is mainly generated by the dynamo process in the liquid outer core of the Earth. Other sources that are also regarded as internal are the static lithospheric field due to crustal magnetisation, the induced field in the mantle, lithospheric and Oceanic induced fields. The latter are generated by secondary dynamo processes, where the motion of conductive seawater in an ambient magnetic field induces a magnetic field. External fields originate in Earth’s magnetosphere and ionosphere. All these individual source fields differ in their strength, they spatially overlap and vary on similar time scales. These characteristics are challenging in resolving the processes that are related to these sources. The aim of this article is to provide a brief review of current geomagnetic field modelling techniques, which are based on measurements of Earth’s magnetic field at satellite altitude. Furthermore, we discuss different applications of the field modelling techniques and their limitations.