Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling
Abstract
In present paper, authors examine the dynamics of a spring-slider model, considered as a phenomenological setup of a geological fault motion. Research is based on an assumption of delayed interaction between the two blocks, which is an idea that dates back to original Burridge-Knopoff model. In contrast to this first model, group of blocks on each side of transmission zone (with delayed interaction) is replaced by a single block. Results obtained indicate predominant impact of the introduced time delay, whose decrease leads to transition from steady state or aseismic creep to seismic regime, where each part of the seismic cycle (co-seismic, post-seismic and inter-seismic) could be recognized. In particular, for coupling strength of order 10 2 observed system exhibit inverse Andronov-Hopf bifurcation for very small value of time delay, tau approximate to 0.01, when long-period (T = 12) and high-amplitude oscillations occur. Further increase of time delay, of order 10(-1), induces an occ...urrence of a direct Andronov-Hopf bifurcation, with short-period (T = 0.5) oscillations of approximately ten times smaller amplitude. This reduction in time delay could be the consequence of the increase of temperature due to frictional heating, or due to decrease of pressure which follows the sudden movement along the fault. Analysis is conducted for the parameter values consistent with previous laboratory findings and geological observations relevant from the seismological viewpoint.
Keywords:
Spring-block model / Time delay / Rate-and-state dependent friction law / Seismic cycleSource:
Chaos Solitons & Fractals, 2018, 106, 310-316Publisher:
- Pergamon-Elsevier Science Ltd, Oxford
Funding / projects:
- Magmatism and geodynamics of the Balkan Peninsula from Mesozoic to present day: significance for the formation of metallic and non-metallic mineral deposits (RS-MESTD-Basic Research (BR or ON)-176016)
DOI: 10.1016/j.chaos.2017.11.037
ISSN: 0960-0779
WoS: 000418932800040
Scopus: 2-s2.0-85037533755
Collections
Institution/Community
PharmacyTY - JOUR AU - Kostić, Srdan AU - Vasović, Nebojša AU - Todorović, Kristina AU - Franović, Igor PY - 2018 UR - https://farfar.pharmacy.bg.ac.rs/handle/123456789/3204 AB - In present paper, authors examine the dynamics of a spring-slider model, considered as a phenomenological setup of a geological fault motion. Research is based on an assumption of delayed interaction between the two blocks, which is an idea that dates back to original Burridge-Knopoff model. In contrast to this first model, group of blocks on each side of transmission zone (with delayed interaction) is replaced by a single block. Results obtained indicate predominant impact of the introduced time delay, whose decrease leads to transition from steady state or aseismic creep to seismic regime, where each part of the seismic cycle (co-seismic, post-seismic and inter-seismic) could be recognized. In particular, for coupling strength of order 10 2 observed system exhibit inverse Andronov-Hopf bifurcation for very small value of time delay, tau approximate to 0.01, when long-period (T = 12) and high-amplitude oscillations occur. Further increase of time delay, of order 10(-1), induces an occurrence of a direct Andronov-Hopf bifurcation, with short-period (T = 0.5) oscillations of approximately ten times smaller amplitude. This reduction in time delay could be the consequence of the increase of temperature due to frictional heating, or due to decrease of pressure which follows the sudden movement along the fault. Analysis is conducted for the parameter values consistent with previous laboratory findings and geological observations relevant from the seismological viewpoint. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - Chaos Solitons & Fractals T1 - Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling VL - 106 SP - 310 EP - 316 DO - 10.1016/j.chaos.2017.11.037 ER -
@article{ author = "Kostić, Srdan and Vasović, Nebojša and Todorović, Kristina and Franović, Igor", year = "2018", abstract = "In present paper, authors examine the dynamics of a spring-slider model, considered as a phenomenological setup of a geological fault motion. Research is based on an assumption of delayed interaction between the two blocks, which is an idea that dates back to original Burridge-Knopoff model. In contrast to this first model, group of blocks on each side of transmission zone (with delayed interaction) is replaced by a single block. Results obtained indicate predominant impact of the introduced time delay, whose decrease leads to transition from steady state or aseismic creep to seismic regime, where each part of the seismic cycle (co-seismic, post-seismic and inter-seismic) could be recognized. In particular, for coupling strength of order 10 2 observed system exhibit inverse Andronov-Hopf bifurcation for very small value of time delay, tau approximate to 0.01, when long-period (T = 12) and high-amplitude oscillations occur. Further increase of time delay, of order 10(-1), induces an occurrence of a direct Andronov-Hopf bifurcation, with short-period (T = 0.5) oscillations of approximately ten times smaller amplitude. This reduction in time delay could be the consequence of the increase of temperature due to frictional heating, or due to decrease of pressure which follows the sudden movement along the fault. Analysis is conducted for the parameter values consistent with previous laboratory findings and geological observations relevant from the seismological viewpoint.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "Chaos Solitons & Fractals", title = "Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling", volume = "106", pages = "310-316", doi = "10.1016/j.chaos.2017.11.037" }
Kostić, S., Vasović, N., Todorović, K.,& Franović, I.. (2018). Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling. in Chaos Solitons & Fractals Pergamon-Elsevier Science Ltd, Oxford., 106, 310-316. https://doi.org/10.1016/j.chaos.2017.11.037
Kostić S, Vasović N, Todorović K, Franović I. Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling. in Chaos Solitons & Fractals. 2018;106:310-316. doi:10.1016/j.chaos.2017.11.037 .
Kostić, Srdan, Vasović, Nebojša, Todorović, Kristina, Franović, Igor, "Nonlinear dynamics behind the seismic cycle: One-dimensional phenomenological modeling" in Chaos Solitons & Fractals, 106 (2018):310-316, https://doi.org/10.1016/j.chaos.2017.11.037 . .