Faulting and frictional plastic deformation

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FAULTING AND FRICTIONAL PLASTIC DEFORMATION

thus earthquake magnitude (Hanks and Kanamori, 1979), is limited by the frictional strength of the upper-crust. Upward-directed fault slip along the footwall scarp during an earthquake causes an increase in elevation at the surface, but also a component of horizontal displacement away from the fault plane. During the brief seismic slip-events, displacements at the side boundaries of the model are approximately zero, and thus coseismic fault displacements result in a horizontal compression of the crust. This elastic deformation lowers the differential stress in the near-surface of the footwall and at depths less than 500 m, the compression is so great that the horizontal stress exceeds the vertical, i.e., |σxx| > |σzz|, and the stress regime is compressional (see hatched regions in Figure 3.2(a-b)). The shallow extent of these zones is principally a reflection of the low lithostatic vertical stress at shallow depths, which is exceeded by only a modest horizontal compression.

Extension budget

The extension rate of the modelled rift, which is applied as a velocity boundary condition at the lateral boundaries, must be accommodated within the crust by some combination of the available means of deformation, i.e., by fault slip, or the accumulation of elastic, frictional plastic, or viscous strain. The relative contribution of each to the total extension of the crust during a single seismic cycle comprises the extension budget. For instance, if during a single seismic cycle tectonic extension of 2.64 m is comprised of 0.66 m of horizontal elastic strain, 0.66 m of horizontal frictional-plastic strain, and 1.32 m horizontal component of fault slip, then the relative contribution of each component is 0.25, 0.25 and 0.5, respectively. Depending on the means of deformation available, the extension budget will vary with both depth (e.g., viscous strain does not accumulate in the upper-crust) and time (e.g., fault slip occurs only during the seismic period). Figure 3.4 shows a representative extension budget with depth for the (a) interseismic and (b) seismic periods, and (c) a full seismic cycle, where each component is normalised against the total extension (2.64 m) during the full cycle.

FAULTING AND FRICTIONAL PLASTIC DEFORMATION

component of vertical movement, and thus a correspondingly larger earthquake, at steeper angles of fault dip. A reduction in the fault-slip component of the extension budget must be compensated by an increase in other components, which for an upper-crust at dynamic equilibrium must be frictional-plastic strain. This result is largely independent of the elastic properties of the crust, and the partitioning of upper-crustal extension between the accumulation of frictional-plastic strain and episodic fault slip appears to be controlled principally by the geometry of the system.

Fault listricity

A fault geometry in which the dip angle shallows with depth has been proposed to account for observations of reverse drag in the hanging wall stratigraphy (e.g., Janecke et al., 1998). Such listric normal faults typically dip at steep angles (70 − 80◦ ) near the surface but are inferred to shallow in regions where overpressured pore fluids are encountered (Bruce, 1984), or where viscosity contrasts rotate the principal stresses (Bradshaw and Zoback, 1988). In the TVZ, faults dip steeply at the surface, however, seismological observations (Beanland et al., 1990) and kinematic arguments (Villamor and Berryman, 2001) suggest that fault dip shallows to 45−60◦ at seismogenic depths. In this section, the effect of fault listricity on distributions of frictional-plastic strain is considered.

FAULTING AND FRICTIONAL PLASTIC DEFORMATION

(Figure 3.6). Coseismic displacements at the surface of the model are qualitatively similar to the planar fault geometry (Figure 2.3), exhibiting uplift of the footwall and subsidence of the hanging wall. As the interseismic period is 220 years in length for both geometries, comparisons can be made between the two profiles. Surface displacements for the listric geometry are significantly less than for the shallow planar fault, which indicates that extension applied for a given period is producing a smaller slip event. This is consistent with Figure 3.5(b) showing fault slip as a diminishing proportion of the extension budget with increased dip angle. Fault parallel dip-slip profiles are also qualitatively similar to their planar counterparts (Figure 2.4), but again at a reduced magnitude reflecting the smaller slip event.

Contents :

• 1 The Taupo Volcanic Zone
  • 1.1 Introduction
  • 1.2 Location and definition
  • 1.3 Tectonism
    • 1.3.1 The Taupo Fault Belt and Paeroa Fault
    • 1.3.2 Seismicity
  • 1.4 Volcanism and magmatism
    • 1.4.1 Heat flux of the TVZ
    • 1.4.2 Stratigraphy of the TVZ
    • 1.4.3 Magmatic intrusion
  • 1.5 Geothermal activity
    • 1.5.1 Convective cells
    • 1.5.2 Distribution of geothermal fields
    • 1.5.3 Hydrothermal alteration
  • 1.6 Thesis outline
• 2 Mechanical model of the crust
  • 2.1 The deforming crust
    • 2.1.1 Principal axes
    • 2.1.2 Plane-strain
    • 2.1.3 Stress decomposition
  • 2.2 Frictional plastic deformation
  • 2.3 Viscous deformation
  • 2.4 Computational model
    • 2.4.1 Fault friction
  • 2.5 Deformation during the seismic cycle
    • 2.5.1 Surface displacement
    • 2.5.2 Strain
  • 2.6 Summary of models
• 3 Faulting and frictional plastic deformation
  • 3.1 Introduction
    • 3.1.1 Previous numerical experiments
  • 3.2 Distribution of frictional plasticity
    • 3.2.1 Frictional plastic yield shadow
  • 3.3 Extension budget
    • 3.3.1 Fault listricity
  • 3.4 Fault plane rotation
  • 3.5 Evolution of a normal fault system
  • 3.6 Chapter summary
• 4 Energetics of extension and fault rupture
  • 4.1 Elastic rebound
  • 4.2 Extension, energy and crustal stress
    • 4.2.1 Strain energy calculations
  • 4.3 Energy conservation and work balance
    • 4.3.1 Fault block energy budgets
  • 4.4 Spatial distribution of energy flow
    • 4.4.1 Anelastic interseismic dissipation of energy
    • 4.4.2 EE and GPE exchange
  • 4.5 Interpretation of hanging wall displacement
  • 4.6 Chapter summary
  • Circulation model of the crust
• 5 Circulation model of the crust
  • 5.1 Introduction
  • 5.2 Heat and mass transport
  • 5.3 Finite Element Heat and Mass transfer (FEHM)
  • 5.4 General procedure for model construction
    • 5.4.1 Computational domain and meshing
    • 5.4.2 Boundary conditions
    • 5.4.3 Initial conditions
  • 5.5 Distribution of permeability
    • 5.5.1 Heterogeneity and anisotropy
    • 5.5.2 Coupled porosity and permeability
  • 5.6 Summary of models
• 6 Rift-scale models
• 7 Silica deposition in geothermal systems
• 8 Seismic perturbation of geothermal systems
• 9 Summary and conclusions

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Numerical models of tectonism and geothermal circulation with application to the Taupo Volcanic Zone, New Zealand