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In earthquake dynamics there are two end member models of rupture: propagating cracks and self-healing pulses. These arise due to different properties of ruptures and have implications for seismic hazard; rupture mode controls near-field strong ground motions. Past studies favor the pulse-like mode of rupture, however, due to a variety of limitations, it has proven difficult to systematically establish their kinematic properties. Here we synthesize observations from a database of >150 rupture models of earthquakes spanning M7-M9 processed in a uniform manner and show the magnitude scaling properties (rise time, pulse width, and peak slip rate) of these slip pulses indicates self-similarity. Self similarity suggests a weak form of rupture determinism, where early on in the source process broader, higher amplitude slip pulses will distinguish between events of increasing magnitude. Indeed, we find by analyzing the moment rate functions that large (M7.5+) and very large (M8.5+) events are statistically distinguishable relatively early (at ~15 seconds) in the rupture process. This suggests that with dense regional geophysical networks the potential strong ground motions from a large rupture can be identified before their onset across the source region.

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The interesting question “Why do nominal compressional (P-wave) seismic energy sources generate so much shear (S-wave) energy?” arises in both explosion and exploration seismology. The relative amount of P vs S energy is an important, but not definitive, discriminant between explosive (chemical or nuclear) and earthquake (shear and/or tensile dislocation) seismic sources. A long-established (and over-simplified) model of a buried explosion is a spherical cavity subject to uniform radial surface traction (time-varying pressure). Spherically-symmetric and radially-polarized P-waves diverge from the source zone. The moment density tensor representation consists of three orthogonal force dipoles of equal magnitude, activated with same waveform. The tensor is isotropic, and is thus even in the mathematical sense. Many common seismic sources (double couple with no net moment) also lead to an even tensor. However, the same cavity subject to tangential (or twisting) traction about a symmetry axis radiates only S-waves. The moment tensor characterizing such a torque source is odd. These two source types are end members on a continuum between pure P and pure S generators. In this study, we derive a general 3×3 moment tensor with nine independent elements. Two important implications of an odd moment tensor pertain to forward modeling and inversion of seismic data. For forward modeling via the first-order coupled velocity-stress PDE system, even and odd parts constitute particular inhomogeneous (body source) terms, differentiated with respect to time and space, respectively. Most moment tensor inversion algorithms presently restrict consideration to symmetry, which biases results if the actual tensor has an odd part. Synthetic and field examples of data generated by “nominal P” sources containing clear S arrivals are given. Finally, we demonstrate construction of a dipole seismic source by superposing two point moment sources of opposite polarity, with infinitesimal separation.

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Volcanic earthquakes are controlled by a wide range of physical parameters. The relative importance of such parameters, and how they are connected, can be difficult to discern, due to limited observations. However, large eruptions are outstanding opportunities for studying those parameters, since the magnitude seismicity could be unusually large, such as the Holuhraun fissure eruption due to Bardarbunga caldera collapse. The fissure eruption in Holuhraun in September 2014, due to the laterally propagating dike that connects this lava field with the Bárdarbunga caldera, was coincident in time with the subsidence of approximate 70 m in the caldera (Guðmundsson et al., 2016). Some of the earthquakes associated with the caldera subsidence exhibit large non-double-couple components (NDCC) in their seismic moment tensors. This could be due to one of several phenomena, including intrusive processes like dikes or sills (Kanamori et al 1993, Riel et al 2014) as well as geometric effects due slip on a curved fault (Nettles & Ekström, 1998). Historically, the largest earthquakes in Bardarbunga before the 2014-2015 caldera collapse had shown large NDCC in their moment tensors (1976-1996, Nettles and Ekström, 1998), similarly to the 2014-2015 seismicity. However, the ancient focal mechanisms were reverse, completely opposed to the 2014-2015 ones. Currently, some of the seismic activity that continues in Bárdarbunga after the eruption and caldera collapse, exhibits waveforms with reverse polarity, compared to the ones registered during the eruption (Jónsdóttir, et al., 2017). In addition, for the largest recent events, we have inverted seismic moment tensors and as a result, we have found large NDCC with the reverse focal mechanism, similarly to the 1976-1996 seismicity. The historical changes in the moment tensors and the inversions in the polarity could indicate that the slip on the ring fault is now going in the opposite direction and that the caldera is now inflating. We have inverted seismic moment tensor for intermediate magnitude earthquakes (4.0 <= Mw. <= 4.8) during the 2014-2015 eruption and caldera collapse, as result, we have observed a systematic increase in the NDCC component with magnitude. This finding would provide key insights regarding the main mechanism that originates the NDCC moment tensors.

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A moment tensor is a symmetric matrix that expresses the source for a seismic event. The fundamental lune of eigenvalues is a certain subset of the unit sphere whose points represent the source types for all moment tensors. Familiar source types such as double couple or pure isotropic have natural locations on the lune. Although the lune consists only of source types, it gives a useful, if incomplete, picture of moment tensor space as a whole. For each subset B of the lune we therefore consider the associated set BU of unit moment tensors that have their source types in B. We then wish to get a sense of BU from looking at B. We succeed in calculating both the volume and the angular diameter of BU. We also calculate the angular diameter and the volume of the set LambdaU of unit moment tensors that have source type Lambda, and we plot the results as contours on the lune. We show that great circle arc lengths on the lune are closely related to angles between moment tensors, and that arc length on the lune gives a natural measure of difference in source type. We show how to calculate volume elements for a variety of moment tensor coordinates. Volumes are relevant in part because we equate fractional volume with the probability that expresses randomness. We thus can find the probability that a random moment tensor have its source type in a given subset of the lune. These insights could be useful for characterizing uncertainties for individual events and for distinguishing source types among a set of events. Additional challenges of uncertainty characterization are expected if additional source parameters are considered, such as magnitude, hypocenter, origin time and source-time function.

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