Since their development in the 1960s, seismic arrays have given a new impulse to seismology. Recordings from many uniform seismometers in a well‐defined, closely spaced configuration produce high‐quality and homogeneous data sets, which can be used to study the Earth's structure in great detail. Apart from an improvement of the signal‐to‐noise ratio due to the simple summation of the individual array recordings, seismological arrays can be used in many different ways to study the fine‐scale structure of the Earth's interior. They have helped to study such different structures as the interior of volcanos, continental crust and lithosphere, global variations of seismic velocities in the mantle, the core‐mantle boundary and the structure of the inner core. For this purpose many different, specialized array techniques have been developed and applied to an increasing number of high‐quality array data sets. Most array methods use the ability of seismic arrays to measure the vector velocity of an incident wave front, i.e., slowness and back azimuth. This information can be used to distinguish between different seismic phases, separate waves from different seismic events and improve the signal‐to‐noise ratio by stacking with respect to the varying slowness of different phases. The vector velocity information of scattered or reflected phases can be used to determine the region of the Earth from whence the seismic energy comes and with what structures it interacted. Therefore seismic arrays are perfectly suited to study the small‐scale structure and variations of the material properties of the Earth. In this review we will give an introduction to various array techniques which have been developed since the 1960s. For each of these array techniques we give the basic mathematical equations and show examples of applications. The advantages and disadvantages and the appropriate applications and restrictions of the techniques will also be discussed. The main methods discussed are the beam‐forming method, which forms the basis for several other methods, different slant stacking techniques, and frequency–wave number analysis. Finally, some methods used in exploration geophysics that have been adopted for global seismology are introduced. This is followed by a description of temporary and permanent arrays installed in the past, as well as existing arrays and seismic networks. We highlight their purposes and discuss briefly the advantages and disadvantages of different array configurations.

The thermal structure of the Earth's lowermost mantle--the D'' layer spanning depths of approximately 2,600-2,900 kilometres--is key to understanding the dynamical state and history of our planet. Earth's temperature profile (the geotherm) is mostly constrained by phase transitions, such as freezing at the inner-core boundary or changes in crystal structure within the solid mantle, that are detected as discontinuities in seismic wave speed and for which the pressure and temperature conditions can be constrained by experiment and theory. A recently discovered phase transition at pressures of the D'' layer is ideally situated to reveal the thermal structure of the lowermost mantle, where no phase transitions were previously known to exist. Here we show that a pair of seismic discontinuities observed in some regions of D'' can be explained by the same phase transition as the result of a double-crossing of the phase boundary by the geotherm at two different depths. This simple model can also explain why a seismic discontinuity is not observed in some other regions, and provides new constraints for the magnitude of temperature variations within D''.

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Broadband seismic shear waves are analyzed to investigate the fine‐velocity structure in the lowermost mantle beneath the Cocos plate, a region where previous studies have indicated the presence of a shear velocity increase about 200–300 km above the core‐mantle boundary. Data from 14 South American earthquakes recorded at California broadband networks provide dense ray path sampling of the lowermost mantle in an approximately 700 km long north‐south corridor, roughly 150 km wide. Application of a simplified seismic migration method that uses a homogeneous background velocity model suggests topography of the previously imaged positive impedance jump, varying in depth from north to south by as much as 150 km, with a weakly reflecting transition zone in between. The migration approach enables examination of small‐scale spatial variations and out‐of‐plane scattering effects. Topography of the discontinuity may account for observed variations in the amplitude of reflected arrivals or there may be lateral variations in the velocity contrast across the boundary. Lateral variations of the shear velocity structure within the D″ layer may produce some apparent topography in the discontinuity image, but any such volumetric structure is not yet well enough determined to incorporate in the migration. A localized negative impedance contrast reflector or scatterer is imaged at depths about 100 km below the positive reflector in the northern portion of the study area. Several scenarios can explain these results, including (1) a slab that reaches the lowermost mantle, (2) the birth of an upwelling beneath a recumbent slab, or (3) chemical layering in this region.