dorsal/arxiv
View SchemaDynamical system analysis and forecasting of deformation produced by an earthquake fault
| Authors | Marian Anghel, Yehuda Ben-Zion, Ramiro Rico-Martinez |
|---|---|
| Categories | |
| ArXiv ID | physics/0305099 |
| URL | https://arxiv.org/abs/physics/0305099 |
| DOI | 10.1007/s00024-004-2547-9 |
Abstract
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.
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"abstract": "We present a method of constructing low-dimensional nonlinear models\ndescribing the main dynamical features of a discrete 2D cellular fault zone,\nwith many degrees of freedom, embedded in a 3D elastic solid. A given fault\nsystem is characterized by a set of parameters that describe the dynamics,\nrheology, property disorder, and fault geometry. Depending on the location in\nthe system parameter space we show that the coarse dynamics of the fault can be\nconfined to an attractor whose dimension is significantly smaller than the\nspace in which the dynamics takes place. Our strategy of system reduction is to\nsearch for a few coherent structures that dominate the dynamics and to capture\nthe interaction between these coherent structures. The identification of the\nbasic interacting structures is obtained by applying the Proper Orthogonal\nDecomposition (POD) to the surface deformations fields that accompany\nstrike-slip faulting accumulated over equal time intervals. We use a\nfeed-forward artificial neural network (ANN) architecture for the\nidentification of the system dynamics projected onto the subspace (model space)\nspanned by the most energetic coherent structures. The ANN is trained using a\nstandard back-propagation algorithm to predict (map) the values of the observed\nmodel state at a future time given the observed model state at the present\ntime. This ANN provides an approximate, large scale, dynamical model for the\nfault.",
"arxiv_id": "physics/0305099",
"authors": [
"Marian Anghel",
"Yehuda Ben-Zion",
"Ramiro Rico-Martinez"
],
"categories": [
"physics.geo-ph",
"physics.data-an"
],
"doi": "10.1007/s00024-004-2547-9",
"title": "Dynamical system analysis and forecasting of deformation produced by an earthquake fault",
"url": "https://arxiv.org/abs/physics/0305099"
},
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