Crustal stress and faulting

Introduction

Stress is, by definition, the cause of deformation. Yet, if deformation and displacements are routinely measured and even monitored, measuring stress is always an indirect process. In the brittle part of the crust it is the cause of fault movements and earthquakes. Conversely, these fault movements give some constraint on the ambient state of stress. This relationship between fault movement and state of stress is the focus of the research activity described in this page. This relationship is investigated through 4 approaches: theoretical developments, developments of analytical methods, software development, and case studies.

Theory

• Question: how much does slip on a single fault plane constrain the stress tensor ?
  • Mathematical formulation: inverse problem for a single fault plane with friction and rake constraints
  • Results:
    • Analytical solutions
    • Graphical representations
  • Publications: detailed analysis in Célérier (1988a) and main results in Célérier (1988b)
  
  
• Question: can a single stress tensor explain seismic ruptures with double focal mechanisms ?
  • Mathematical formulation: inverse problem for two fault planes with friction and rake constraints
  • Simplifying assumptions: search only stress tensors either with a vertical principal stress direction or that are optimally oriented with respect to the initial focal mechanism
  • Results:
    • Analytical solutions
    • Graphical representations:
  • Publication: Tajima & Célérier (1989)
  
  
• Question: what is the distribution of slip rakes of faults reactivated in a common tectonic regime ?
  • Mathematical formulation: direct problem with rake constraint only
  • Results:
    • Analytical solutions
    • Graphical representations
      • Faulting style as a function of tectonic regime
      • Typical fault slip in various tectonic regimes
      • Rake level curves in various tectonic regimes
  • Publication: Célérier (1995)
  
  
• Question: how accurate are estimates of extension derived from fault heave ?
  • Approach: geometrical analysis
  • Result: error range as a function of fault block rotation
  • Publication: Sclater & Célérier (1988)
  
  
• Question: what is the relationship between the tectonic regime, the rake of the slip vectors, the dip of the nodal planes, and the plunges of the P, B, and T axes of earthquake focal mechanisms ?
  • Approach: geometrical analysis
  • Results: level curves of rake and dip as a function of P, B, and T plunges
  • Publication: Célérier (2010)

Methods

• Graphical stress inversion from fault slip data in the case of vertical principal stress
  • Approach: geometrical analysis
  • Result: Breddin's graph
  • Publication: Célérier & Séranne (2001)
  
  
• Evaluation of friction conditions for solutions of stress inversion from fault slip data
  • Approach: Mohr's circles
  • Result: importance of the stress ratio s₀ = (σ₁ - σ₃)/σ₁
  • Publication: Appendix A of Burg et al. (2005)
  
  
• Evaluation of the quality of stress tensor solutions in the case of multi-phase fault slip data
  • Approach: compare with random results
  • Result: define the minimal number of fitting data required for a significant solution tensor
  • Publication: Appendix A of Heuberger et al. (2010)

Software

• Stress inversion from fault slip data or focal mechanism, stress analysis
  • Fsa : Fault & Stress Analysis, stress inversion from fault slip data.
  • Other stress inversion software available on the web.
  
  
• Focal mechanisms catalogue extraction:
  • RexGCMT : REad and EXtract Global Centroid Moment Tensor.
  • RexFPS : REad and EXtract FPFIT or HASH data.
  
  
• Stereographic plotting:
  • BasicStereo : plots data on stereos and produces stereonets
  
  
• True dip from apparent dips:
  • App2truedip : computes true dip from two apparent dips.
  • App2truedipG : computations as in App2truedip with additional graphic output.

Case studies

• How frequent is Anderson's faulting in world seismicity ?
  • Approach: analysis of the Global Centroid Moment Tensor catalog.
  • Result: data in the 0-30 km depth range are consistent with Anderson's faulting being the most frequent case, but they do not require it.
  • Publication: Célérier (2008)
  
  
• Fault slip data
  • Pakistan fold-and-thrust belt (Burg et al., 2005).
  • Karakoram-Kohistan suture zone (Heuberger et al., 2010).
  • Miocene extension in Greece (Faucher et al., 2021)
  • Eocene limestones West of Montpellier (Ballas et al., 2022)
  
  
• Subduction zones earthquakes focal mechanisms
  • Chile, Kurile and Santa Cruz (Tajima & Célérier, 1989)
  • Betic Cordillera (Ruiz-Constán et al., 2011)
  
  
• Borehole fault data
  • Alboran Sea, ODP Site 976 (De Larouzière et al., 1999).

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