Dynamics of a zone of four parallel faults: A deterministic model

Abstract

We consider a two‐dimensional model for quasi‐static evolution of four parallel faults. The model is based on the physics of continuum, with slips along the faults, long‐range interactions, a distribution of barriers and asperities, a velocity dependent friction, healing and reactivation of cohesive forces, and a mutual causality between faulting and tectonic forces all taken into account. Both the long‐term time series of seismic activity and details of seismic and aseismic crustal deformations during each phase of the earthquake cycle are produced by the model. It is shown that the system whose evolution is described by a set of deterministic differential equations may exhibit periodic or quite irregular (despite its assumed symmetry) behavior, depending on model parameters.

Radiated energy estimations from finite‐fault earthquake slip models

“…Another characteristic, , measures rupture heterogeneity in time and space [ Senatorski , ]. The overdamped dynamics [ Senatorski , , ] and quasi‐dynamic [ Rice , ] approximations of the rupture process assume that stress signals propagate instantaneously. Such an approach enables us to interpret K in terms of the radiated seismic energy, E S ≈( μ /2 v S ) K = E O , where v S is the shear wave speed.…”

Apparent stress scaling for tectonic and induced seismicity: Model and observations

“…These two assumptions imply that the net stress at a given time and location on the fault plane, s − s F , can be represented as a functional of slip displacements measured at the same time. They also imply that the evolution equation for the slip displacements can be expressed as a gradient system,q ∝ s − s F = δE S /δq (Senatorski, 1995;, where the last term denotes the functional derivative of the seismic energy functional, see…”

“…On the other hand, evolution equations for the slip field can be expressed under the same overdamped dynamics approximation (assumption 1) as (e.g., Senatorski, 1995;cf. Cochard and Madariaga, 1996) …”

“…It consists of three steps. In the first step a microscopic model is formulated to describe details of the earthquake rupture process in terms of stress and slip fields defined over a fault plane (Senatorski, 1995;2006). The model allows us to express earthquake source parameters as spatial and temporal averages of these fields.…”

“…The driving stress reflects the rate of decrease of the total energy of the system (elastic energy plus the potential energy of the loading mechanism) approaching equilibrium (e.g., Eshelby, 1956). Consequently it can be defined as a functional derivative of the elastic energy release functional (e.g., Rundle, 1989;Senatorski, 1995). 3 URL, Strathona, and tsunami data excluded.…”