Earthquake Cycle Model Research Articles

Viscoelastic earthquake cycle models with deep stress‐driven creep along the San Andreas fault system

We develop a two‐dimensional boundary element earthquake cycle model including deep interseismic creep on vertical strike‐slip faults in an elastic lithosphere coupled to a viscoelastic asthenosphere. Uniform slip on the upper part of the fault is prescribed periodically to represent great strike‐slip earthquakes. Below the coseismic rupture the fault creeps in response to lithospheric shear stresses within a narrow linear viscous fault zone. The model is applied to the GPS contemporary velocity field across the Carrizo Plain and northern San Francisco Bay segments of the San Andreas fault, as well as triangulation measurements of postseismic strain following the 1906 San Francisco earthquake. Previous analysis of these data, using conventional viscoelastic coupling models without stress‐driven creep [Segall, 2002], shows that it is necessary to invoke different lithosphere‐asthenosphere rheology in northern and southern California in order to explain the data. We show that with deep stress‐driven interseismic creep on the San Andreas fault, the data can be explained with the same rheology for northern and southern California. We estimate elastic thickness in the range 44–100 km (95% confidence level), fault zone viscosity per unit width of 0.5–8.2 × 1017Pa s/m, and asthenosphere relaxation time of 24–622 years (0.1–2.9 × 1020Pa s) for northern and southern California. We estimate a slip rate of 21–27 mm/yr and recurrence time of 188–315 years for the northern San Francisco Bay San Andreas fault and slip rate of 32–42 mm/yr with recurrence time of 247–536 years for the Carrizo Plain.

Earthquake cycles and physical modeling of the process leading up to a large earthquake

A thorough discussion is made on what the rational constitutive law for earthquake ruptures ought to be from the standpoint of the physics of rock friction and fracture on the basis of solid facts observed in the laboratory. From this standpoint, it is concluded that the constitutive law should be a slip-dependent law with parameters that may depend on slip rate or time. With the long-term goal of establishing a rational methodology of forecasting large earthquakes, the entire process of one cycle for a typical, large earthquake is modeled, and a comprehensive scenario that unifies individual models for intermediate- and short-term (immediate) forecasts is presented within the framework based on the slip-dependent constitutive law and the earthquake cycle model. The earthquake cycle includes the phase of accumulation of elastic strain energy with tectonic loading (phase II), and the phase of rupture nucleation at the critical stage where an adequate amount of the elastic strain energy has been stored (phase III). Phase II plays a critical role in physical modeling of intermediate-term forecasting, and phase III in physical modeling of short-term (immediate) forecasting. The seismogenic layer and individual faults therein are inhomogeneous, and some of the physical quantities inherent in earthquake ruptures exhibit scale-dependence. It is therefore critically important to incorporate the properties of inhomogeneity and physical scaling, in order to construct realistic, unified scenarios with predictive capability. The scenario presented may be significant and useful as a necessary first step for establishing the methodology for forecasting large earthquakes.

GeoFEM Kinematic Earthquake Cycle Simulation in Southwest Japan

— We construct a viscoelastic FEM model with 3-D configuration of the subducting Philippine Sea plate in Southwest Japan to simulate recent 300-year kinematic earthquake cycles along the Nankai-Suruga-Sagami trough, based on the kinematic earthquake cycle model. This 300-year simulation contains a series of three great interplate earthquakes. The inclusion of viscoelasticity produces characteristic velocity field during earthquake cycles regardless of the assumed constant plate coupling throughout the interseismic period. Just after the occurrence of interplate earthquakes, the viscoelastic relaxation creates the seaward motion in the inland region. In the middle period, the seaward motion gradually decreases, and the resultant velocity field is similar to the elastic one. Later, just before the next interplate earthquake, displacements due to the interplate coupling in the viscoelastic material are distributed more broadly in the forearc region than in the purely elastic one, since the viscoelastic relaxation due to the previous earthquake mostly disappears. The effects of such interplate earthquake cycles on five major inland faults in southwest Japan, where large intraplate earthquakes occurred during this period, are quantitatively evaluated using the Coulomb failure function (CFF). The calculated change in CFF successfully predicts the occurrence of the 1995 Kobe earthquake (M∼7). The occurrence of other inland earthquakes, however, cannot be explained by the calculated changes in CFF, and especially the 1891 Nobi earthquake (M∼8), the largest inland earthquake in Japan, which occurred at the time close to the local minimum of CFF. This implies that further improvements are necessary for our FEM modeling, such as the modeling of steady east-west compressive force and stress interactions between the inland faults.

Simulation of the Transition of Earthquake Rupture from Quasi-static Growth to Dynamic Propagation

We have simulated a rupture transition from quasi-static growth to dynamic propagation using the boundary integral equation method. In order to make a physically reasonable model of earthquake cycle, we have to evaluate the dynamic rupture propagation in the context of quasi-static simulation. We used a snapshot of the stress distribution just before the earthquake in the quasi-static simulation. The resultant stress will be fed back to the quasi-static simulation. Since the quasi-static simulation used the slip-and time-dependent constitutive relation, the friction law itself evolves with time. Thus, we used the slip-weakening constitutive relation for dynamic rupture propagation consistent with that used for the quasi-static simulation. We modeled a San Andreas type strike-slip fault, in which two different size asperities existed.

3-D Viscoelastic FEM Modeling of Crustal Deformation in Northeast Japan

As a first step toward establishing a standard earthquake cycle model in Japan, we simulate the crustal deformation during the past 100 years in northeast Japan, using a 3-D FEM based on the kinematic model. Then, we compare the computed results with the observed long-term leveling data and the recent GPS data. On the whole, although the effect of the subducting PAC is dominant, coseismic deformation of the interplate earthquakes can be clearly seen in the inland. Moreover, the postseismic deformation of the earthquakes due to the viscoelastic upper mantle seriously affects the inland movements, and continues for a few decades. Our modeling, including the effects of the interplate earthquakes and the three-dimensional viscoelastic inhomogeneity, reasonably explains the observed movement. Finally, we stress that the viscoelastic effect should be taken into consideration in the analyses, even if no earthquakes occur in the analyzed period.

Stress on the seismogenic and deep creep plate interface during the earthquake cycle in subduction zones

The deep creep plate interface extends from the down-dip edge of the seismogenic zone down to the base of the overlying lithosphere in subduction zones. Seismogenic/deep creep zone interaction during the earthquake cycle produces spatial and temporal variations in strains within the surrounding elastic material. Strain observations in the Nankai subduction zone show distinct deformation styles in the co-seismic, post-seismic, and inter-seismic phases associated with the 1946 great earthquake. The most widely used kinematic model to match geodetic observations has been a 2-D Savage-type model where a plate interface is placed in an elastic half-space and co-seismic slip occurs in the upper seismogenic portion of the interface, while inter-seismic deformation is modeled by a locked seismogenic zone and a constant slip velocity across the deep creep interface. Here, I use the simplest possible 2-D mechanical model with just two blocks to study the stress interaction between the seismogenic and deep creep zones. The seismogenic zone behaves as a stick-slip interface where co-seismic slip or stress drop constrain the model. A linear constitutive law for the deep creep zone connects the shear stress (σ) to the slip velocity across the plate interface (s′) with the material property of interface viscosity (ζ ) as: σ = ζ s′. The analytic solution for the steady-state two-block model produces simple formulas that connect some spatially-averaged geodetic observations to model quantities. Aside from the basic subduction zone geometry, the key observed parameter is τ, the characteristic time of the rapid post-seismic slip in the deep creep interface. Observations of τ range from about 5 years (Nankai and Alaska) to 15 years (Chile). The simple model uses these values for τ to produce estimates for ζ that range from 8.4 × 1013 Pa/m/s (in Nankai) to 6.5 × 1014 Pa/m/s (in Chile). Then, the model predicts that the shear stress acting on deep creep interface averaged over the earthquake cycle ranges from 0.1 MPa (Nankai) to 1.7 MPa (Chile). These absolute stress values for the deep creep zone are slightly smaller than the great earthquake stress drops. Since the great earthquake recurrence time ( T recur) is much larger than τ for Nankai, Alaska, and Chile, the model predicts that rapid post-seismic creep should re-load the seismogenic zone to about (1/3) of the co-seismic change; geodetically observed values range from about (1/10) to more than (1/2). Also, for the case of (Trecur/τ) ≫1, the model predicts that the slip velocity across the deep creep interface during the inter-seismic phase should be about (2/3) the plate tectonic velocity (R). Thus the deep creep velocity used in Savage-type models should be less than R. Even complex 3-D models with non-linear creep laws should make a similar prediction for inter-seismic deep creep rates. At present, it seems that geodetic observations at Nankai and other subduction zones are more consistent with a deep creep rate of R rather than (2/3) R. This discrepancy is quite puzzling and is difficult to explain in the context of a 2-D steady-state earthquake cycle model. Future observational and modeling studies should examine this apparent discrepancy to gain more understanding of the earthquake cycle in subduction zones.

プレート境界における応力の蓄積過程と大地震の繰り返しに伴う地殻変動サイクルのモデル化について

For long-term prediction of large earthquakes at plate boundaries, it is important to develop an earthquake cycle model which can numerically simulate the processes of crustal deformation and stress accumulation at and around plate boundaries. We developed a general earthquake cycle model applicable to transform fault zones, subduction zones, and collision zones on the basis of elastic dislocation theory. In this model we regard the periodic occurrence of interplale earthquakes as a perturbation of the hypothetical steady slip motion proceeding on the whole plate boundary. Then the crustal deformation associated with the periodic occurrence of interplate earthquakes is given by the superposition of viscoelastic responses to the steady slip on the whole plate boundary, the steady back slip on the seismic zone, and the sequence of periodic seismic slips. The important points in this earthquake cycle model are as follows. Interaction between adjacent plates can be naturally represented by the increase of discontinuity in tangential displacement across the plate boundary. Viscoelastic stress relaxation of the asthenosphere strongly affects the crustal deformation during interseismic period. Since the stress relaxation time of the lithosphere-asthenosphere system is several hundreds years, we must consider the viscoelastic effects due to a series of large events occurred for the past several hundreds years to estimate crustal deformation correctly. Crustal deformation and stress accumulation due to steady slip on the whole plate boundary can not be neglected.

A dislocation model for the earthquake cycle at convergent plate boundaries

SUMMARY A kinematic model for the earthquake cycle at convergent plate boundaries has been constructed on the basis of dislocation theory. We model the lithosphere-asthenosphere system by a stratified semi-infinite medium under gravity, consisting of an elastic surface layer, an intervening layer with Maxwell viscoelasticity, and an elastic substratum. The steady motion of plate convergence is naturally represented by uniform slip at a constant rate on the upper boundary of the descending oceanic plate. The occurrence of interplate earthquakes is regarded as a perturbation of the steady state plate motion, and represented by a periodic sequence of step slips on a finite seismic zone of the plate interface. Based on dislocation theory we can show that the steady slip on the interface deeper than the lithosphereasthenosphere boundary does not contribute to surface deformation in the steady state. Accordingly the surface deformation associated with the earthquake cycle is given by the superposition of viscoelastic responses to the steady slip on the interface shallower than the lithosphere-asthenosphere boundary, the steady backslip on the seismic zone, and the periodic sequence of seismic slips. We have computed cyclic patterns of vertical displacements at the free surface for two representative cases, taking account of gravity effects. The patterns of vertical displacements differ notably in the latter stage of the cycle depending on whether or not the seismic zone extends through the entire thickness of the lithosphere. After the completion of one earthquake cycle, our model yields a certain amount of permanent deformation resulting from the steady plate convergence. The pattern of the permanent deformation, that is characterized by steep uplift on the continental side, sharp subsidence at the plate boundary, and gentle uplift on the oceanic side, is irrespective of the cyclic process of stress accumulation and release repeated on the seismic zone. The earthquake cycle model developed here provides a possible explanation for the formation of earthquake-origin marine terraces.