An arbitrary square integrable real-valued function (or, equivalently, the associated Hardy function) can be conveniently analyzed into a suitable family of square integrable wavelets of constant shape, (i.e. Obtained by shifts and dilations from any one of them.) The resulting integral transform is isometric and self-reciprocal if the wavelets satisfy an “admissibility condition” given here. Explicit expressions are obtained in the case of a particular analyzing family that plays a role analogous to that of coherent states (Gabor wavelets) in the usual $L_2 $ -theory. They are written in terms of a modified $ Gamma $-function that is introduced and studied. From the point of view of group theory, this paper is concerned with square integrable coefficients of an irreducible representation of the nonunimodular $ax + b$-group.

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Reliable analysis of low-energy earthquakes (microseismic) depends on how accurately one can detect and pick the arrival times, which are strongly influenced by the noise content. The study of.

Large intraplate earthquakes in oceanic lithosphere are rare and usually related to regions of diffuse deformation within the oceanic plate. The 23 January 2018 M W 7.9 strike-slip Gulf of Alaska earthquake ruptured an oceanic fracture zone system offshore Kodiak Island. Bathymetric compilations show a muted topographic expression of the fracture zone due to the thick sediment that covers oceanic basement but the fracture zone system can be identified by offset N-S magnetic anomalies and E-W linear zones in the vertical gravity gradient. Back-projection from global seismic stations reveals that the initial rupture at first propagated from the epicenter to the north, likely rupturing along a weak zone parallel to the ocean crustal fabric.

The rupture then changed direction to eastward directed with most energy emitted on Aka fracture zone resulting in an unusual multi-fault earthquake. Similarly, the aftershocks show complex behavior and are related to two different tectonic structures: (1) events along N-S trending oceanic fabric, which ruptured mainly strike-slip and additionally, in normal and oblique slip mechanisms and (2) strike-slip events along E-W oriented fracture zones.

To explain the complex faulting behavior we adopt the classical stress and strain partitioning concept and propose a generalized model for large intra-oceanic strike-slip earthquakes of trench-oblique oriented fracture zones/ocean plate fabric near subduction zones. Taking the Kodiak asperity position of 1964 maximum afterslip and outer-rise Coulomb stress distribution into account, we propose that the unusual 2018 Gulf of Alaska moment release was stress transferred to the incoming oceanic plate from co- and post-processes of the nearby great 1964 M W 9.2 megathrust earthquake. Some of the world’s largest earthquakes occur in Alaska, such as the great 1964 M W 9.2 earthquake (Fig. ). Most major and great earthquakes are related to rupture of the subduction megathrust. In contrast, many major earthquakes that occur in the oceanic lithosphere near subduction zones are usually bending-related outer-rise normal faulting earthquakes (e.g.,).

Oceanic lithosphere strike-slip earthquakes near subduction zones are rare. Two major Pacific Plate N-S trending strike-slip earthquakes (Fig., upper right; M W 7.8/7.7 in 1987/1988) ruptured a composite length of ~250 km in the central Gulf of Alaska. This region has hosted a spatially persistent cluster of diffuse seismicity since then,, where complex N-S aftershock patterns dominate and additionally ENE – WSW trending aftershock clusters reactivated fracture zones (FZs). This cluster of seismicity resulted from a combination of enhanced tensional stress in the Pacific Plate following the 1964 great Alaska earthquake and compressional stress resulting from the collision of the Yakutat Terrane with North America.

Additionally, the rupture occurred in a zone of weakness in the crust inherited from processes of plate formation. Convergence of the Pacific Plate with the North America Plate is currently 60 mm/yr and almost trench-normal (Fig. ). However, ocean plate fabric trends N-S and magnetic anomalies are ~30–35° oblique to the Alaska Trench (Fig., inset). Overview of the Gulf of Alaska shown by GEBCO 2014 bathymetric map. Star marks the  M W 7.9 Alaska earthquake. Magenta circles mark aftershocks in 1964 and yellow circles mark 2018 aftershocks (2018: M W > 4 on oceanic plate).