Earthquake statistics inferred from plastic events in soft-glassy materials

We propose a new approach for generating synthetic earthquake catalogues based on the physics of soft glasses. The continuum approach produces yield-stress materials based on Lattice-Boltzmann simulations. We show that, if the material is stimulated below yield stress, plastic events occur, which have strong similarities with seismic events. Based on a suitable definition of displacement in the continuum, we show that the plastic events obey a Gutenberg-Richter law with exponents similar to those for real earthquakes. We further find that average acceleration, energy release, stress drop and recurrence times scale with the same exponent. The approach is fully self-consistent and all quantities can be calculated at all scales without the need of ad hoc friction or statistical laws. We therefore suggest that our approach may lead to new insight into understanding of the physics connecting the micro and macro scale of earthquakes.Comment: 13 pages, 7 figure

Finite-Frequency SKS Splitting: Measurement and Sensitivity Kernels

Splitting of SKS waves caused by anisotropy may be analyzed by measuring the splitting intensity, i.e., the amplitude of the transverse signal relative to the radial signal in the SKS time window. This quantity is simply related to structural parameters. Extending the widely used cross-correlation method for measuring travel-time anomalies to anisotropic problems, we propose to measure the SKS-splitting intensity by a robust cross-correlation method that can be automated to build large high-quality datasets. For weak anisotropy, the SKS-splitting intensity is retrieved by cross-correlating the radial signal with the sum of the radial and transverse signals. The cross-correlation method is validated based upon a set of Californian seismograms. We investigate the sensitivity of the SKS-splitting intensity to general anisotropy in the mantle based upon a numerical technique (the adjoint spectral-element method) considering the full physics of wave propagation. The computations reveal a sensitivity remarkably focused on a small number of elastic parameters and on a small region of the upper mantle. These fundamental properties and the practical advantages of the measurement make the cross-correlation SKS-splitting intensity particularly well adapted for finite-frequency imaging of upper-mantle anisotropy

Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods

We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by ‘banana–doughnut’ kernels which exhibit large, path-dependent variations and even sign changes. P-wave travel-times appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation travel-time anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation travel-time anomaly, and the second a generalized ‘splitting intensity’. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver

Probabilistic point source inversion of strong-motion data in 3-D media using pattern recognition: A case study for the 2008 M w 5.4 Chino Hills earthquake

Despite the ever increasing availability of computational power, real-time source inversions based on physical modeling of wave propagation in realistic media remain challenging. We investigate how a nonlinear Bayesian approach based on pattern recognition and synthetic 3-D Green's functions can be used to rapidly invert strong-motion data for point source parameters by means of a case study for a fault system in the Los Angeles Basin. The probabilistic inverse mapping is represented in compact form by a neural network which yields probability distributions over source parameters. It can therefore be evaluated rapidly and with very moderate CPU and memory requirements. We present a simulated real-time inversion of data for the 2008 Mw 5.4 Chino Hills event. Initial estimates of epicentral location and magnitude are available ∼14 s after origin time. The estimate can be refined as more data arrive: by ∼40 s, fault strike and source depth can also be determined with relatively high certainty

Earthquake statistics inferred from plastic events in soft-glassy materials

We propose a new approach for generating synthetic earthquake catalogues based on the physics of soft glasses. The continuum approach produces yield-stress materials based on Lattice-Boltzmann simulations. We show that, if the material is stimulated below yield stress, plastic events occur, which have strong similarities with seismic events. Based on a suitable definition of displacement in the continuum, we show that the plastic events obey a Gutenberg-Richter law with exponents similar to those for real earthquakes. We further find that average acceleration, energy release, stress drop and recurrence times scale with the same exponent. The approach is fully self-consistent and all quantities can be calculated at all scales without the need of ad hoc friction or statistical laws. We therefore suggest that our approach may lead to new insight into understanding of the physics connecting the micro and macro scale of earthquakes

Discovery and analysis of topographic features using learning algorithms: A seamount case study

Identifying and cataloging occurrences of particular topographic features are important but time-consuming tasks. Typically, automation is challenging, as simple models do not fully describe the complexities of natural features. We propose a new approach, where a particular class of neural network (the “autoencoder”) is used to assimilate the characteristics of the feature to be cataloged, and then applied to a systematic search for new examples. To demonstrate the feasibility of this method, we construct a network that may be used to find seamounts in global bathymetric data. We show results for two test regions, which compare favorably with results from traditional algorithms

Direct observations of causal links in plastic events and relevance to earthquake seismology

Earthquakes are complex physical processes driven by stick-slip motion on a sliding fault. After the main event, a series of aftershocks is usually observed. The latter are loosely defined as earthquakes that follow a parent event and occur within a prescribed space-time window. In seismology, it is currently not possible to establish an unambiguous causal relation between events, and the nearest-neighbor metric is commonly used to distinguish aftershocks from independent events. Here, we employ a soft-glass model as a proxy for earthquake dynamics, previously shown to be able to correctly reproduce the phenomenology of earthquakes, together with a technique that allows us to clearly separate independent and triggered events. We show that aftershocks in our plastic event catalog follow Omori's law with slopes depending on the triggering mode, an observation possibly useful for seismology. Finally, we confirm that the nearest-neighbor metric is indeed effective in separating independent events from aftershocks

Self Similar Properties of Avalanche Statistics in a Simple Turbulent Model

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterised by two well defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time $t_w$ followed by abrupt avalanche-like energy drops of sizes $S$ due to strong intermittent fluctuations of energy dissipation. We study the probability distribution $P[t_w]$ and $P[S]$ which both exhibit a quite well defined scaling behaviour. Although $t_w$ and $S$ are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events.Comment: 12 pages, 10 figure

Self-similar properties of avalanche statistics in a simple turbulent model

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time tw followed by abrupt avalanche-like energy drops of sizes S due to strong intermittent fluctuations of energy dissipation. We study the probability distribution P[tw] and P[S] which both exhibit a quite well-defined scaling behaviour. Although tw and S are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events

Azimuthal anisotropy of Rayleigh-wave phase velocities in the east-central United States

We explore the Rayleigh-wave phase velocity structure of the east-central US in a broad period range (10-200 s). Using a recent implementation of the two-stations method, we first measure interstation dispersion curves of Rayleigh-wave phase velocities along 60 paths. We then invert our collection of dispersion curves for isotropic and azimuthally anisotropic (2Ψ and 4Ψ) phase-velocity maps. The inversion is performed by a damped, smoothed LSQR, and the output model is parametrized on a triangular grid of knots with a 140 km grid spacing. Using the isotropic component of the phase velocity maps to constrain regional variations in shear velocity and Moho-depth, we observe that over the upper-middle crust depth range (z 1 per cent), and the azimuth of the fast-propagation direction is uniform over the entire region and equal to 54°. Our results suggest that azimuthal anisotropy beneath the east-central US is vertically distributed in three distinct layers, with a different geodynamic origin for each of the