A Stochastic source model for the 2015 Mw 7.9 Gorkha, Nepal, Earthquake using Multi-Dimensional Ensemble Empirical Mode Decomposition technique

The present study aims at developing a new strategy to model the spatial variability of slip on the rupture plane using multi-dimensional ensemble empirical mode decomposition (MEEMD) technique. Here, the earthquake slip distribution is split into finite number of empirical modes of oscillation called the intrinsic mode functions (IMFs). This help in identifying the fluctuation component and trend in the slip data. The trend is positive and characterizes the nonstationary mean of the slip distribution. The fluctuation component can be modelled as a stationary random field using an exponential power spectral density function. The trend can be modeled as an elliptic patch. This new technique is demonstrated for the slip distribution of the recent Nepal Earthquake, 2015. It is observed that the new model can be used to simulate the spatial complexity of slip distribution of any earthquake

Modeling near-field tsunami observations to improve finite-fault slip models for the 11 March 2011 Tohoku earthquake

The massive tsunami generated by the 11 March 2011 Tohoku earthquake (M_w 9.0) was widely recorded by GPS buoys, wave gauges, and ocean bottom pressure sensors around the source. Numerous inversions for finite-fault slip time histories have been performed using seismic and/or geodetic observations, yielding generally consistent patterns of large co-seismic slip offshore near the hypocenter and/or up-dip near the trench, where estimated peak slip is ~60 m. Modeling the tsunami generation and near-field wave processes using two detailed rupture models obtained from either teleseismic P waves or high-rate GPS recordings in Japan allows evaluation of how well the finite-fault models account for the regional tsunami data. By determining sensitivity of the tsunami calculations to rupture model features, we determine model modifications that improve the fit to the diverse tsunami data while retaining the fit to the seismic and geodetic observations

Dynamics of earthquake nucleation process represented by the Burridge-Knopoff model

Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional Burridge-Knopoff (BK) model obeying the rate- and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the nucleation process, including the quasi-static initial phase, the unstable acceleration phase and the high-speed rupture phase or a mainshock. Two kinds of nucleation lengths L_sc and L_c are identified and investigated. The nucleation length L_sc and the initial phase exist only for a weak frictional instability regime, while the nucleation length L_c and the acceleration phase exist for both weak and strong instability regimes. Both L_sc and L_c are found to be determined by the model parameters, the frictional weakening parameter and the elastic stiffness parameter, hardly dependent on the size of an ensuing mainshock. The sliding velocity is extremely slow in the initial phase up to L_sc, of order the pulling speed of the plate, while it reaches a detectable level at a certain stage of the acceleration phase. The continuum limits of the results are discussed. The continuum limit of the BK model lies in the weak frictional instability regime so that a mature homogeneous fault under the RSF law always accompanies the quasi-static nucleation process. Duration times of each stage of the nucleation process are examined. The relation to the elastic continuum model and implications to real seismicity are discussed.Comment: Title changed. Changes mainly in abstract and in section 1. To appear in European Physical Journal

Depth-varying rupture properties of subduction zone megathrust faults

Subduction zone plate boundary megathrust faults accommodate relative plate motions with spatially varying sliding behavior. The 2004 Sumatra-Andaman (M_w 9.2), 2010 Chile (Mw 8.8), and 2011 Tohoku (M_w 9.0) great earthquakes had similar depth variations in seismic wave radiation across their wide rupture zones – coherent teleseismic short-period radiation preferentially emanated from the deeper portion of the megathrusts whereas the largest fault displacements occurred at shallower depths but produced relatively little coherent short-period radiation. We represent these and other depth-varying seismic characteristics with four distinct failure domains extending along the megathrust from the trench to the downdip edge of the seismogenic zone. We designate the portion of the megathrust less than 15 km below the ocean surface as domain A, the region of tsunami earthquakes. From 15 to ∼35 km deep, large earthquake displacements occur over large-scale regions with only modest coherent short-period radiation, in what we designate as domain B. Rupture of smaller isolated megathrust patches dominate in domain C, which extends from ∼35 to 55 km deep. These isolated patches produce bursts of coherent short-period energy both in great ruptures and in smaller, sometimes repeating, moderate-size events. For the 2011 Tohoku earthquake, the sites of coherent teleseismic short-period radiation are close to areas where local strong ground motions originated. Domain D, found at depths of 30–45 km in subduction zones where relatively young oceanic lithosphere is being underthrust with shallow plate dip, is represented by the occurrence of low-frequency earthquakes, seismic tremor, and slow slip events in a transition zone to stable sliding or ductile flow below the seismogenic zone

Dynamical system analysis and forecasting of deformation produced by an earthquake fault

We present a method of constructing low-dimensional nonlinear models describing the main dynamical features of a discrete 2D cellular fault zone, with many degrees of freedom, embedded in a 3D elastic solid. A given fault system is characterized by a set of parameters that describe the dynamics, rheology, property disorder, and fault geometry. Depending on the location in the system parameter space we show that the coarse dynamics of the fault can be confined to an attractor whose dimension is significantly smaller than the space in which the dynamics takes place. Our strategy of system reduction is to search for a few coherent structures that dominate the dynamics and to capture the interaction between these coherent structures. The identification of the basic interacting structures is obtained by applying the Proper Orthogonal Decomposition (POD) to the surface deformations fields that accompany strike-slip faulting accumulated over equal time intervals. We use a feed-forward artificial neural network (ANN) architecture for the identification of the system dynamics projected onto the subspace (model space) spanned by the most energetic coherent structures. The ANN is trained using a standard back-propagation algorithm to predict (map) the values of the observed model state at a future time given the observed model state at the present time. This ANN provides an approximate, large scale, dynamical model for the fault.Comment: 30 pages, 12 figure

Model of deep non-volcanic tremor part I: ambient and triggered tremor

There is evidence of triggering of tremor by seismic waves emanating from distant large earthquakes. The frequency contents of triggered and ambient tremor are largely identical, suggesting that tremor does not depend directly on the nature of the source. We show here that the model of plate dynamics developed earlier by us is an appropriate tool for describing the onset of tremor. In the framework of this model, tremor is an internal response of a fault to a failure triggered by external disturbances. The model predicts generation of radiation in a frequency range defined by the fault parameters. Other specific features predicted are: the upper limit of the size of the emitting area is a few dozen km; tremor accompanies earthquakes and aseismic slip; the frequency content of tremor depends on the type of failure. The model also explains why a tremor has no clear impulsive phase, in contrast to earthquakes. A comparatively small effective normal stress (hence a high fluid pressure) is required to make the model consistent with observed tremor parameters. Our model indicates that tremor is not necessarily a superposition of low frequency earthquakes, as commonly assumed, although the latter may trigger them. The approach developed complements the conventional viewpoint which assumes that tremor reflects a frictional process with low rupture speed. Essentially our model adds the hypothesis that resonant-type oscillations exist inside a fault. This addition may change our understanding of the nature of tremor in general, and the methods of its identification and location in particular.Comment: 32 pages, 16 figures. arXiv admin note: text overlap with arXiv:1202.091

Seismic Radiation From Simple Models of Earthquakes

We review some basic features of shear wave generation and energy balance for a 2D anti plane rupture. We first study the energy balance for a flat fault, and for a fault that contains a single localized kink. We determine an exact expression for the partition between strain energy flow released from the elastic medium surrounding the fault, radiated energy flow and energy release rate. This balance depends only on the rupture speed and the residual stress intensity factor. When the fault contains a kink, the energy available for fracture is reduced so that the rupture speed is reduced. When rupture speed changes abruptly, the radiated energy flow also changes abruptly. As rupture propagates across the kink, a shear wave is emitted that has a displacement spectral content that decreases like ω^(-2) at high frequencies. We then use spectral elements to model the propagation of an antiplane crack with a slip-weakening friction law. Since the rupture front in this case has a finite length scale, the wave emitted by the kink is smoothed at very high frequencies but its general behavior is similar to that predicted by the simple sharp crack model. A model of a crack that has several kinks and wanders around a mean rupture directions, shows that kinks reduce the rupture speed along the average rupture direction of the fault. Contrary to flat fault models, a fault with kinks produces high frequency waves that are emitted every time the rupture front turns at a kink. Finally, we discuss the applicability of the present results to a 3D rupture model

Rupture characteristics of major and great (M_w ≥ 7.0) megathrust earthquakes from 1990 to 2015: 1. Source parameter scaling relationships

Source parameter scaling for major and great thrust-faulting events on circum-Pacific megathrusts is examined using uniformly processed finite-fault inversions and radiated energy estimates for 114 M_w ≥ 7.0 earthquakes. To address the limited resolution of source spatial extent and rupture expansion velocity (V_r) from teleseismic observations, the events are subdivided into either group 1 (18 events) having independent constraints on V_r from prior studies or group 2 (96 events) lacking independent V_r constraints. For group 2, finite-fault inversions with V_r = 2.0, 2.5, and 3.0 km/s are performed. The product V_r^3Δσ_E, with stress drop Δσ_E calculated for the slip distribution in the inverted finite-fault models, is very stable for each event across the suite of models considered. It has little trend with M_w, although there is a baseline shift to low values for large tsunami earthquakes. Source centroid time (T_c) and duration (T_d), measured from the finite-fault moment rate functions vary systematically with the cube root of seismic moment (M_0), independent of assumed V_r. There is no strong dependence on magnitude or Vr for moment-scaled radiated energy (E_R/M_0) or apparent stress (σ_a). Δσ_E averages ~4 MPa, with direct trade-off between V_r and estimated stress drop but little dependence on M_w. Similar behavior is found for radiation efficiency (η_R). We use V_r^3Δσ_E and T_c/M_0^(1/3) to explore variation of stress drop, V_r and radiation efficiency, along with finite-source geometrical factors. Radiation efficiency tends to decrease with average slip for these very large events, and fracture energy increases steadily with slip

Introduction to the Special Issue on the 2011 Tohoku Earthquake and Tsunami

The 11 March 2011 Tohoku earthquake (05:46:24 UTC) involved a massive rupture of the plate‐boundary fault along which the Pacific plate thrusts under northeastern Honshu, Japan. It was the fourth‐largest recorded earthquake, with seismic‐moment estimates of 3–5×10^(22)  N•m (M_w 9.0). The event produced widespread strong ground shaking in northern Honshu; in some locations ground accelerations exceeded 2g. Rupture extended ∼200  km along dip, spanning the entire width of the seismogenic zone from the Japan trench to below the Honshu coastline, and the aftershock‐zone length extended ∼500  km along strike of the subduction zone. The average fault slip over the entire rupture area was ∼10  m, but some estimates indicate ∼25  m of slip located around the hypocentral region and extraordinary slip of up to 60–80 m in the shallow megathrust extending to the trench. The faulting‐generated seafloor deformation produced a devastating tsunami that resulted in 5–10‐km inundation of the coastal plains, runup of up to 40 m along the Sanriku coastline, and catastrophic failure of the backup power systems at the Fukushima Daiichi nuclear power station, which precipitated a reactor meltdown and radiation release. About 18,131 lives appear to have been lost, 2829 people are still missing, and 6194 people were injured (as reported 28 September 2012 by the Fire and Disaster Management Agency of Japan) and over a half million were displaced, mainly due to the tsunami impact on coastal towns, where tsunami heights significantly exceeded harbor tsunami walls and coastal berms

Earthquake Size Distribution: Power-Law with Exponent Beta = 1/2?

We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter beta of the power-law distribution of earthquake sizes. In particular, we find that estimated beta-values may be inflated by 1-3% because relative moment uncertainties decrease with increasing earthquake size. Moreover, earthquake clustering greatly influences the beta-parameter. If clusters (aftershock sequences) are taken as the entity to be studied, then the exponent value for their size distribution would decrease by 5-10%. The complexity of any earthquake source also inflates the estimated beta-value by at least 3-7%. The centroid depth distribution also should influence the beta-value, an approximate calculation suggests that the exponent value may be increased by 2-6%. Taking all these effects into account, we propose that the recently obtained beta-value of 0.63 could be reduced to about 0.52--0.56: near the universal constant value (1/2) predicted by theoretical arguments. We also consider possible consequences of the universal beta-value and its relevance for theoretical and practical understanding of earthquake occurrence in various tectonic and Earth structure environments. Using comparative crystal deformation results may help us understand the generation of seismic tremors and slow earthquakes and illuminate the transition from brittle fracture to plastic flow.Comment: 46 pages, 2 tables, 11 figures 53 pages, 2 tables, 12 figure