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

Isotropic source terms of San Jacinto fault zone earthquakes based on waveform inversions with a generalized CAP method

We analyse source tensor properties of seven M_w > 4.2 earthquakes in the complex trifurcation area of the San Jacinto Fault Zone, CA, with a focus on isotropic radiation that may be produced by rock damage in the source volumes. The earthquake mechanisms are derived with generalized ‘Cut and Paste’ (gCAP) inversions of three-component waveforms typically recorded by >70 stations at regional distances. The gCAP method includes parameters ζ and χ representing, respectively, the relative strength of the isotropic and CLVD source terms. The possible errors in the isotropic and CLVD components due to station variability is quantified with bootstrap resampling for each event. The results indicate statistically significant explosive isotropic components for at least six of the events, corresponding to ∼0.4–8 per cent of the total potency/moment of the sources. In contrast, the CLVD components for most events are not found to be statistically significant. Trade-off and correlation between the isotropic and CLVD components are studied using synthetic tests with realistic station configurations. The associated uncertainties are found to be generally smaller than the observed isotropic components. Two different tests with velocity model perturbation are conducted to quantify the uncertainty due to inaccuracies in the Green's functions. Applications of the Mann–Whitney U test indicate statistically significant explosive isotropic terms for most events consistent with brittle damage production at the source

Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a new and minimal method for achieving control of a chaotic system

Analysis of earthquake body wave spectra for potency and magnitude values: implications for magnitude scaling relations

We develop a simple methodology for reliable automated estimation of the low-frequency asymptote in seismic body wave spectra of small to moderate local earthquakes. The procedure corrects individual P- and S-wave spectra for propagation and site effects and estimates the seismic potency from a stacked spectrum. The method is applied to >11 000 earthquakes with local magnitudes 0 < M_L < 4 that occurred in the Southern California plate-boundary region around the San Jacinto fault zone during 2013. Moment magnitude M_w values, derived from the spectra and the scaling relation of Hanks & Kanamori, follow a Gutenberg–Richter distribution with a larger b-value (1.22) from that associated with the M_L values (0.93) for the same earthquakes. The completeness magnitude for the M_w values is 1.6 while for M_L it is 1.0. The quantity (M_w – M_L) linearly increases in the analysed magnitude range as M_L decreases. An average earthquake with M_L = 0 in the study area has an M_w of about 0.9. The developed methodology and results have important implications for earthquake source studies and statistical seismology

Internal structure of the San Jacinto fault zone at Blackburn Saddle from seismic data of a linear array

Local and teleseismic earthquake waveforms recorded by a 180-m-long linear array (BB) with seven seismometers crossing the Clark fault of the San Jacinto fault zone northwest of Anza are used to image a deep bimaterial interface and core damage structure of the fault. Delay times of P waves across the array indicate an increase in slowness from the southwest most (BB01) to the northeast most (BB07) station. Automatic algorithms combined with visual inspection and additional analyses are used to identify local events generating fault zone head and trapped waves. The observed fault zone head waves imply that the Clark fault in the area is a sharp bimaterial interface, with lower seismic velocity on the southwest side. The moveout between the head and direct P arrivals for events within ∼40 km epicentral distance indicates an average velocity contrast across the fault over that section and the top 20 km of 3.2 per cent. A constant moveout for events beyond ∼40 km to the southeast is due to off-fault locations of these events or because the imaged deep bimaterial interface is discontinuous or ends at that distance. The lack of head waves from events beyond ∼20 km to the northwest is associated with structural complexity near the Hemet stepover. Events located in a broad region generate fault zone trapped waves at stations BB04–BB07. Waveform inversions indicate that the most likely parameters of the trapping structure are width of ∼200 m, S velocity reduction of 30–40 per cent with respect to the bounding blocks, Q value of 10–20 and depth of ∼3.5 km. The trapping structure and zone with largest slowness are on the northeast side of the fault. The observed sense of velocity contrast and asymmetric damage across the fault suggest preferred rupture direction of earthquakes to the northwest. This inference is consistent with results of other geological and seismological studies