FSA: Fault & Stress Analysis software
Ongoing development
Current stable version: 36.5
Purpose
To analyse
 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 e_{1}, e_{2}, e_{3} by North, East and Down.
 1 real number: the stress tensor aspect ratio defined as in (Celerier,1988; Celerier,1995) :
r_{0} = (σ_{1}  σ_{2})/(σ_{1}  σ_{3}) where σ_{1} ≥ σ_{2} ≥ σ_{3}
 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
 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 s_{1}, s_{2}, s_{3} representations:
 Stereographic projection that can be either
 equal area (Schmidt, default) or
 conformal (Wulff).
 Histograms of
 Frohlich's (1992, 2001) triangular diagrams
Actions affecting stress tensors and using fault data
Input = fault and slip data Output = new stress tensor 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 φ_{0}.
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
 r_{0} = 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, r_{0})
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
Input = fault and slip data and stress tensor data
A first step computes for each tensor the fault plane error, E(i), for each fault slip data #i.
A second step computes the global error, F (noted Ftm in the program ouputs), for each tensor and ALL the fault data.
Note: E(i) and F are controlled by the Inversion parameters.
Then different graphical representations are available with extra computations
 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 s_{0} to activate each fault plane as a function of the fault data rank.
s_{0} = (σ_{1}  σ_{3})/σ_{1} 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
If you publish results obtained with this program, it would be appreciated
if you referred to:
 the random search method:
 Etchecopar, Vasseur, & Daignieres (1981)
 descriptions of the methods implemented in Fsa with examples of application:
 Heuberger et al. (2010) or Burg et al. (2005)
 the software version and its location:
Additional references depending on the subject discussed:
 For the random search method:
 Etchecopar, Vasseur, & Daignieres (1981)
 Etchecopar (1984)
 For the definition of s_{0} = (σ_{1}  σ_{3})/σ_{1}:
 Celerier (1988; 2008)
 Tajima and Celerier (1989)
 For the original definition of Φ = (σ_{2}σ_{3})/(σ_{1}σ_{3}):
 For the definition of r_{0} = (σ_{1}  σ_{2})/(σ_{1}  σ_{3}) 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, 18051808

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 foldandthrust belt in Pakistan,
Journal of Asian Earth Sciences
, 24, 445467
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, 12571278,
doi:10.1029/TC007i006p01257.

Célérier, B., 1995,
Tectonic regime and slip orientation of reactivated faults,
Geophysical Journal International, 121, 143191,
doi:10.1111/j.1365246X.1995.tb03517.x,
and Erratum,
Geophysical Journal International, 122, 703,
doi:10.1111/j.1365246X.1995.tb07021.x.

Célérier, B., 2008,
Seeking Anderson's faulting in seismicity: a centennial celebration
,
Reviews of Geophysics,
46, RG4001, 134,
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, 4249,
doi:10.1016/j.tecto.2009.03.006.

Célérier, B. & Séranne, M., 2001,
Breddin's graph for tectonic regimes,
Journal of Structural Geology,
23, 789801,
doi:10.1016/S01918141(00)001401,
and Erratum
Journal of Structural Geology
,
23, 1487,
doi:10.1016/S01918141(01)00058X
 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, 1159,
doi:10.2973/odp.proc.sr.180.177.2002.
 Compton, 1966,
Analyses of PliocenePleistocene deformation and stresses in northern Santa Lucia range,
California, Geological Society of America Bulletin, 77, 13611380.
 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, 319329
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, 5165,
doi: 10.1016/01918141(81)9005609.
 Federico, L., Spagnolo, C., Crispini, L., Capponi, G. 2009,
Faultslip analysis in the metaophiolites of the Voltri Massif: constraints for the tectonic evolution at the Alps/Apennine boundary,
Geological Journal, 44, 225240.
 Frohlich, C., 1992,
Triangle diagrams: ternary graphs to display similarity and diversity of earthquake focal mechanisms,
Physics of the Earth and Planetetary Interiors, 75, 193198.
 Frohlich, C., 2001,
Display and quantitative assessment of distributions of earthquake focal mechanisms,
Geophysical Journal International, 144, 300308.
 Frohlich, C. & Apperson, K.D., 1992,
Earthquake focal mechanisms, moment tensors, and the consistency of seismic activity near plate boundaries,
Tectonics, 11, 279296.

Heuberger, S., Célérier, B., Burg, J. P., Chaudhry, N. M., Dawood, H., Hussein, S., 2010,
Paleostress regimes from brittle structures of the KarakoramKohistan Suture Zone and surrounding areas of NW Pakistan,
Journal of Asian Earth Sciences,
38, 307335,
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, 22812289.
 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, 143.
 Orife, T., Arlegui, L. & Lisle, R., 2002,
DIPSLIP: a QuickBasic stress inversion program for analysing sets of faults without slip lineations,
Computers & Geosciences, 28, 775781.
 Provost, A.S. & Houston, H., 2001,
Orientation of the stress field surrounding the creeping section of the San Andreas Fault:
evidence for a narrow mechanicallyweak fault zone,
J. Geophys. Res., 106, 1137311386.
 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, 255267.

Tajima, F. & Célérier, B., 1989,
Possible focal mechanism change during reactivation of a previously ruptured subduction zone,
Geophysical Journal International, 98, 301316,
doi:10.1111/j.1365246X.1989.tb03354.x.
 Titus, S.J., Fossen, H., Pedersen, R.B., Vigneresse, J.L. & Tikoff, B., 2002,
Pullapart formation and strikeslip partitioning in an obliquely divergent setting, Leka Ophiolite, Norway,
Tectonophysics, 354, 101119.
 Zeilinger, G., Burg, J.P., Chaudhry, N., Dawood, H. & Hussain, S., 2000,
Fault systems and Paleostress tensors in the Indus Suture Zone (NW Pakistan),
Journal of Asian Earth Sciences, 18, 547559.
Installation
System dependent: 3 files
Revision history
Program versions
The versions of the program are detailed in the revision history chapter of the
manual.
Revisions of this file
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