FSA: Fault & Stress Analysis software

Ongoing development           Current stable version: 36.5

• Purpose
• Status and documentation
• Data
• Procedures
• References
  • How to refer to this program
  • References
• Installation
• Revision history
  • Program versions
  • Revisions of this file 2017-03-05

Purpose

• faults: faults, fault and slip, or earthquake focal mechanisms,
• stress, and
• the relationship between fault and slip and the state of stress.

Status and documentation

• This software is continuously evolving, as applications suggest new features.
• A tragic but inevitable consequence of this is that the documentation below typically lags behind development.
• A user's manual is being (too) slowly assembled. To keep its links active, it is recommended to preserve its folder structure after downloading.
• Fsa versions ≥ 19 are a complete rewrite of based on a new flexible data structure of the previous Fsa18 version, that remains available for comparisons and for its last feature not yet ported.
  • New functions introduced since Fsa18
    • Fault data rotation around an horizontal axis
    • Representation of fault data without slip indicators, such as those observed in boreholes
    • Handling of both nodal planes of fault plane solutions
    • Stress tensor representation (histograms, stereos, and Frohlich's triangular diagrams)
    • Slip sense only inversion (as in Lisle, 2001)
    • Stress directions mapping
    • Stress & fault analysis detailed output file
  • Last function in Fsa18 not yet available in Fsa28
    • Synthetic fault and slip generation
  • Stress and fault data files can be exchanged between Fsa18 and current versions of Fsa.

Data

Internal Representation

• Fault data
  • The basic fault data type is represented by 4 numbers:
    • 3 real numbers: strike, dip and rake (α, δ, λ) defined as in (Aki & Richard, 1980, page 106)
    • 1 integer number: the fault identification number, either read in the input file or generated, depending on formats.
  • Other fault data type are derived from the basic data type
    • either by including additional information such as
      • bedding orientation (to correct for tilting)
      • location given by 1 or 3 coordinates
      • second nodal plane of fault plane solutions
      • rake range when slip is only constrained to belong to a sector
    • or by restricting information such as
      • no slip information: fault plane only
• Stress data
  • The basic stress data type is represented by 5 numbers:
    • 3 real numbers: the Euler's angles θ, φ and ψ, that define the orientation of the principal stress direction in the geographical frame. These angles are defined as in (Celerier,1988, Fig 2) after replacing e₁, e₂, e₃ by North, East and Down.
    • 1 real number: the stress tensor aspect ratio defined as in (Celerier,1988; Celerier,1995) :
      r₀ = (σ₁ - σ₂)/(σ₁ - σ₃) where σ₁ ≥ σ₂ ≥ σ₃
      
    • 1 integer number: the stress data identification number, either read in the input file or generated, depending on formats.
  • Other stress data type are derived from the basic data type
    • by including additional information such as
      • projection of principal stress directions into the horizontal plane (for mapping)
      • location given by 2 or 3 coordinates

Input and Output Files

Input can be either fault or stress data. Output can also be either fault or stress data. That means one can invert stress from fault data (input = fault, output = stress), generate fault compatible with a stress state (input = stress, output = fault), or analyse the relationship between fault and stress (input = stress AND fault).

The various types and formats of input fault and stress data files are detailed in the user's manual.

Note that conversion between formats can be achieved by reading data from an input file in one format and writing them into an output file in a different format.

Procedures

Actions affecting fault data only

• Read fault and slip data in various formats.
• Write fault and slip data in various formats.
  Combined with the read function, this provide a way to convert data between formats.
• Graphical representation of data
  • Most plot parameters (scaling, line width, polygon fill, colors, symbols) can be altered interactively.
  • Stereographic projection
    • The stereographic projection can be either
      • equal area (Schmidt, default) or
      • conformal (Wulff).
    • Available stereographic projections include those of
      • planes and slip vectors
      • poles of planes
      • slip vectors
  • Histograms of
    • strike
    • dips
    • rake
  • Rake versus strike plot, designed to be overlain by Breddin's graph, to graphically assess the tectonic regime (Célérier & Séranne, 2001)
• Fault data rotation around an horizontal axis. Old documentation in: fsa.guide.jpb

Actions affecting stress tensors data only

• Read stress tensor data in various formats.
• Write stress tensor data in various formats.
  Combined with the read function, this provide a way to convert data between formats.
• Graphical representation of data
  • Most plot parameters (scaling, line width, polygon fill, colors, symbols) can be altered interactively.
  • Principal stress axis s₁, s₂, s₃ representations:
    • Stereographic projection that can be either
      • equal area (Schmidt, default) or
      • conformal (Wulff).
    • Histograms of
      • azimuth
      • plunges
    • Frohlich's (1992, 2001) triangular diagrams

Actions affecting stress tensors and using fault data

• Optimal tensor:
  Compute for each fault plane the Euler's angle of the stress tensor best oriented to reactivate the fault plane, assuming a friction law and using the friction angle φ₀. The geometry can be found in (Compton, 1966; Etchecopar, 1984; Celerier, 1988 Fig. 6; Tajima and Celerier, 1989; Celerier, 2008 Fig. 1)
• Random tensor search:
  Monte Carlo approach to search a stress tensor that best explains the slip directions. This mainly follows the method proposed by Etchecopar et al. (1981) and Etchecopar (1984).
  • In a first step, stress tensor data are generated by using a random variable X within [0,1] as follows:
    • θ = X * 360
    • φ = Arccos(X)
    • ψ = X * 180
    • r₀ = X
    So that the orientations are uniformly distributed in space.
    Note: to obtain a reasonable estimate, a minimum of 1000 random tensors need to be generated.
  • In a second step, for each tensor, the fault plane error, E(i), that measures the difference between predicted and observed parameters for each fault slip data is computed.
  • In a third step, for each tensor, the global error, F, that measures its compatibility with respect to the global fault and slip data set, is computed
  • In a fourth step the tensors are ranked by increasing value of F and only the n first tensors are retained (n can be adjusted).
  • Inversion parameters allow to choose among a few fault plane error, E(i), and global error, F, depending on data type.
• Tensor optimisation.
  In this approach one of the 4 parameters (θ, φ, ψ, r₀) defining the stress tensor is varied while the others are kept constant. The global error, F, is computed as in the random search. The tensor with the lowest F value is retained. This can be used to refine solutions found by random search.

Actions using stress tensors and fault data: analysis of the relationship

• Global plot: all the stress tensors and the fault data. Stereoplots + histogram of Ftm. Each tensor gives one count in the histogram.
• One plot per stress tensor:
  • Histogram of the angular misfit on each fault plane. Each fault data gives one count
  • Angular misfit as a function of the fault data rank. Note that the fault data rank are contiguous and correspond to the line number in the data file (i.e. the order in which the data are read) NOT NECESSARY the fault data identification numbers that do not need to be contiguous
  • Value of s₀ to activate each fault plane as a function of the fault data rank.
    s₀ = (σ₁ - σ₃)/σ₁ is defined as in (Celerier, 1988; Tajima and Celerier, 1989)
  • Mohr circle where the data are shown with the identification number

References

How to refer to this program

1. the random search method:
   • Etchecopar, Vasseur, & Daignieres (1981)
2. descriptions of the methods implemented in Fsa with examples of application:
   • Heuberger et al. (2010) or Burg et al. (2005)
3. the software version and its location:
   • Celerier, B., YYYY, FSA: Fault & Stress Analysis software, version XX.X, http://www.bcelerier.univ-montp2.fr/software/dcmt/fsa/fsa.html
     where YYYY and XX.X are the year and version that are displayed when the program starts;
     they can also be found in the revision history chapter of the manual.

• For the random search method:
  • Etchecopar, Vasseur, & Daignieres (1981)
  • Etchecopar (1984)
• For the definition of s₀ = (σ₁ - σ₃)/σ₁:
  • Celerier (1988; 2008)
  • Tajima and Celerier (1989)
• For the original definition of Φ = (σ₂-σ₃)/(σ₁-σ₃):
  • Angelier (1975)
• For the definition of r₀ = (σ₁ - σ₂)/(σ₁ - σ₃) used in Fsa:
  • Celerier (1988; 1995; 2008)
  • Tajima and Celerier (1989)
• For the geometry of optimal stress tensor:
  • Compton (1966)
  • Etchecopar (1984)
  • Celerier (1988; 2008)
• For the triangular representation of stress tensor axes:
  • Frohlich & Apperson (1992)
  • Frohlich (1992; 2001)
  • Celerier (2008: Appendix B; 2010)
• For the evaluation of friction condition:
  • Appendix A of Burg et al. (2005)
• For slip sense inversion (note that, whereas the general idea originates from these papers, the inversion method used in fsa is different from that proposed in these papers):
  • Lisle et al. (2001)
  • Orife et al. (2002)
• For a quality criteria in the case of polyphased data:
  • Appendix A of Heuberger et al. (2010)
• Work that used Fsa:
  • De Larouzière et al. (1999)
  • Zeilinger et al. (2000)
  • Célérier & Séranne (2001)
  • Provost & Houston (2001, 2003a, 2003b)
  • Célérier et al. (2002)
  • Louvel et al. (2002)
  • Titus et al. (2002)
  • Burg et al. (2005)
  • Célérier (2008)
  • Federico et al. (2009)
  • Heuberger et al. (2010)

References

• Aki, K. and Richards, P., 1980. Quantitative seismology, theory and methods, Freeman, Vol I, 557p.
  
  
• Angelier, J., 1975, Sur l'analyse des mesures dans les sites failles: l'utilite d'une confrontation entre les methodes dynamiques et cinematiques, C. R. Acad. Sc. Paris 281 Serie D, 1805-1808
  
  
• Burg, J. P., Célérier, B., Chaudhry, N. M., Ghazanfar, M., Felix Gnehm, F. & Schnellmann, M., 2005, Fault analysis and paleostress evolution in large strain regions: methodological and geological discussion of the southeastern Himalayan fold-and-thrust belt in Pakistan, Journal of Asian Earth Sciences , 24, 445-467 doi:10.1016/j.jseaes.2003.12.008.
  
  
• Célérier, B.,  1988, Constraint on stress tensor from slip on a single fault plane., University of Texas at Austin, Institute for Geophysics, Technical report nb 73, 88p.
  
  
• Célérier, B.,  1988, How much does slip on a reactivated fault plane constrain the stress tensor ? , Tectonics, 7, 1257-1278, doi:10.1029/TC007i006p01257.
  
  
• Célérier, B., 1995, Tectonic regime and slip orientation of reactivated faults, Geophysical Journal International, 121, 143-191, doi:10.1111/j.1365-246X.1995.tb03517.x, and Erratum, Geophysical Journal International, 122, 703, doi:10.1111/j.1365-246X.1995.tb07021.x.
  
  
• Célérier, B., 2008, Seeking Anderson's faulting in seismicity: a centennial celebration , Reviews of Geophysics, 46, RG4001, 1-34, doi:10.1029/2007RG000240.
  
  
• Célérier, B., 2010, Remarks on 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, Tectonophysics, 482, 42-49, doi:10.1016/j.tecto.2009.03.006.
  
  
• Célérier, B. & Séranne, M., 2001, Breddin's graph for tectonic regimes, Journal of Structural Geology, 23, 789-801, doi:10.1016/S0191-8141(00)00140-1, and Erratum Journal of Structural Geology , 23, 1487, doi:10.1016/S0191-8141(01)00058-X
  
  
• Célérier, B., Louvel, V., Le Gall, B., Gardien, V. & Huchon, P., 2002, Presentation and structural analysis of FMS electrical images in the northern margin of the Woodlark Basin , In: Taylor, B., Huchon, P. and Klaus, A. (Eds), Proceedings of the Ocean Drilling Program, Scientific Results, 180 , Ocean Drilling Program, College Station, Texas, 1-159, doi:10.2973/odp.proc.sr.180.177.2002.
  
  
• Compton, 1966, Analyses of Pliocene-Pleistocene deformation and stresses in northern Santa Lucia range, California, Geological Society of America Bulletin, 77, 1361-1380.
  
  
• De Larouzière, F. D., Pézard, P. A., Comas, M. C., Célérier, B. & Vergniault, C., 1999, Structure and tectonic stresses in metamorphic basement, Site 976, Alboran sea , In: Zahn, R., Comas, M. C. and Klaus, A. (Eds), Proceedings of the Ocean Drilling Program, Scientific Results, 161 , Ocean Drilling Program, College Station, Texas, 319-329 doi:10.2973/odp.proc.sr.161.212.1999.
  
  
• Etchecopar, A. 1984, Etude des etats de contrainte en tectonique cassante et simulations de deformations plastiques (approche mathematique). These d'Etat, Universite des Sciences et Techniques du Languedoc.
  
  
• Etchecopar, A., Vasseur, G. & Daignieres, M. 1981. An inverse problem in microtectonics for the determination of stress tensors from fault striation analysis. J. Struct. Geol. 3, 51-65, doi: 10.1016/0191-8141(81)90056-09.
  
  
• Federico, L., Spagnolo, C., Crispini, L., Capponi, G. 2009, Fault-slip analysis in the metaophiolites of the Voltri Massif: constraints for the tectonic evolution at the Alps/Apennine boundary, Geological Journal, 44, 225-240.
  
  
• Frohlich, C., 1992, Triangle diagrams: ternary graphs to display similarity and diversity of earthquake focal mechanisms, Physics of the Earth and Planetetary Interiors, 75, 193-198.
  
  
• Frohlich, C., 2001, Display and quantitative assessment of distributions of earthquake focal mechanisms, Geophysical Journal International, 144, 300-308.
  
  
• Frohlich, C. & Apperson, K.D., 1992, Earthquake focal mechanisms, moment tensors, and the consistency of seismic activity near plate boundaries, Tectonics, 11, 279-296.
  
  
• Heuberger, S., Célérier, B., Burg, J. P., Chaudhry, N. M., Dawood, H., Hussein, S., 2010, Paleostress regimes from brittle structures of the Karakoram-Kohistan Suture Zone and surrounding areas of NW Pakistan, Journal of Asian Earth Sciences, 38, 307-335, doi:10.1016/j.jseaes.2010.01.004.
  
  
• Lisle, R., Orife, T. & Arlegui, L., 2001, A stress inversion method requiring only fault slip sense, J. Geophys. Res., 106, 2281-2289.
  
  
• Louvel, V., Le Gall, B., Célérier, B., Gardien, V. & Huchon, P., 2002, Structural analysis of the footwall fault block of the Moresby detachment (Woodlark rift basin) from borehole images , In: Taylor, B., Huchon, P. and Klaus, A. (Eds), Proceedings of the Ocean Drilling Program, Scientific Results, 180 , Ocean Drilling Program, College Station, Texas, 1-43.
  
  
• Orife, T., Arlegui, L. & Lisle, R., 2002, DIPSLIP: a QuickBasic stress inversion program for analysing sets of faults without slip lineations, Computers & Geosciences, 28, 775-781.
  
  
• Provost, A.-S. & Houston, H., 2001, Orientation of the stress field surrounding the creeping section of the San Andreas Fault: evidence for a narrow mechanically-weak fault zone, J. Geophys. Res., 106, 11373-11386.
  
  
• Provost, A.-S. & Houston, H., 2003a, Constraints from stress orientations on the evolution of frictional strength along the San Andreas plate boundary system, J. Geophys. Res., 108, 10.1029/2001JB001123.
  
  
• Provost, A.-S. & Houston, H., 2003b, Investigation of temporal variations in stress orientations before and after four major earthquakes in California, Phys. Earth Planet. Inter., 139, 255-267.
  
  
• Tajima, F. & Célérier, B., 1989, Possible focal mechanism change during reactivation of a previously ruptured subduction zone, Geophysical Journal International, 98, 301-316, doi:10.1111/j.1365-246X.1989.tb03354.x.
  
  
• Titus, S.J., Fossen, H., Pedersen, R.B., Vigneresse, J.L. & Tikoff, B., 2002, Pull-apart formation and strike-slip partitioning in an obliquely divergent setting, Leka Ophiolite, Norway, Tectonophysics, 354, 101-119.
  
  
• Zeilinger, G., Burg, J.P., Chaudhry, N., Dawood, H. & Hussain, S., 2000, Fault systems and Paleo-stress tensors in the Indus Suture Zone (NW Pakistan), Journal of Asian Earth Sciences, 18, 547-559.
  
  

Installation

System dependent: 3 files

System	MacOS.9 (68k - PPC)	MacOS.X (PPC - i86)	MS-Windows (i86)	SunOS (Sparc)
General information to download and read first	MacOS classic versions	MacOS X versions	MS-Windows versions	SunOS versions
Screen graphic application	The Quickdraw (-qd-) application	The Quartz (-qtz-) application	No screen application yet	The GKS (-gks-) application
File graphic application	The PostScript (-ps-) application	The PostScript (-ps-) application	The PostScript (-ps-) application	The PostScript (-ps-) application
WARNINGS	These applications require classic MacIntosh (CR) end of line input files. Choose an application compatible with your system	These applications require Unix (LF) end of line input files. Choose an application compatible with your system	These applications require Windows (CRLF) end of line input files. Choose an application compatible with your system	These applications require Unix (LF) end of line input files. Choose an application compatible with your system

Revision history

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