With regard to the separation and inversion of fault slip data:

        1) Fault-slip data (including seismic focal mechanisms) record
displacement on the fault surfaces; therefore the inversion of these
data directly gives information about the principal incremental strain
axes, NOT the stress. Assuming that the principal axes from the
inversion are stress axes, is equivalent to assuming that the brittle
crust behaves as a mechanically isotropic, rheologically linear
material (see Twiss, R.J., and Unruh, J.R., 1998, Analysis of fault
slip inversions: Do they constrain stress or strain rate?: Journal of
Geophysical Research, v. 103, p. 12,205-12,222.). Since these are
somewhat questionable assumptions, why not just interpret the results
in terms of strain? Structural geologists are certainly used to
obtaining strain data from other deformed rocks, and they do not feel
the need to try to equate those principal axes with stress. So I do
not understand the single-minded insistence that inverting fault-slip
data gives information about the stress axes! Moreover, strain is
easier to interpret than stress. It is a record of what has actually
happened to the rocks. With stress, interpretation is always separated
from the observations of the rocks by an unknown (or at best
poorly-known) constitutive relation.

        2) A very useful indication of where the principal axes are likely to
be, is to plot and contour the P and T axes for the data. Multiple
maxima of either or both sets of axes indicate a heterogeneous data
set, and the location of the different maxima are a good indication of
approximately where the solutions lie.
        I have separated out as many as four different solutions from a set of
seismic focal mechanisms in this way. Using the P and T axes maxima as
initial solutions, I calculate the misfit for all the data, to each
possible solution, separate the data into subsets according to which
solution gives a minimum misfit to each datum, and then calculate the
best-fit solution to each subset. This process can be iterated to a
relatively stable definition of the subsets. Unfortunately, I do not
have this process automated yet, but if you have a program that
calculates the misfits, and use some program like Excel to sort the
results, it is not too troublesome to do by hand.
        The P and T axes, by the way, are also local incremental strain axes,
despite what numerous geophysicists like to claim, because they are by
definition both at 45 degrees to the shear plane and lie in the plane
containing the normal to the shear plane and the slip direction (the
'movement plane'). That is the orientation of the principal
incremental strain axes for a simple shear, and slip on a shear plane
is a discrete simple shear. There's no telling where the stress axes
are, because we know many faults are activated in non-optimal,
non-Coulomb-fracture orientations.

        3) I and colleagues have developed a 'micropolar' model for a
continuum description of deformation by slip on discrete faults. Based
on that model, I have written a program called FLTSLP that will invert
both seismic focal mechanisms and shear-plane/slickenline data for the
instantaneous strain axes. If anyone is interested in using it, I am
happy to provide the source code PROVIDED you own a copy of "Numerical
Recipes" by W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T.
Vetterling. This proviso is necessary because of copyright
restrictions. I have used a number of subroutines from this book, and
copyright restrictions enjoin me from distributing the source code for
these subroutines. If, however, you own a copy of the book, you have
bought the right to use and modify those subroutines, so I am not
violating any restrictions by providing you the source code for some of
their subroutines in my program.
        Briefly, FLTSLP operates in this manner: For a given set of model
parameters (orientations and difference ratio of principal
instantaneous strains, relative vorticity parameter), FLTSLP uses a
conjugate gradient method to find the best-fit shear-plane/slip-line
pair for each datum (i.e. neither the shear-plane nor the slip-line
orientation is assumed a priori to be a correct fit), and a downhill
simplex method with random restarts to find the set of model parameters
that best-fit the full data set. At this time, it only searches for
one solution at a time; it cannot search for multiple solutions. It
uses bootstrap statistics to determine the confidence limits for the
model parameters. I have versions that run in the VAX/VMS and the UNIX
operating systems.

        Cheers,

Rob Twiss
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             Robert J. Twiss, Prof. Emeritus email:
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             Geology Department telephone:
(530) 752-0179
             University of California at Davis FAX:
(530) 752-0951
             One Shields Ave. website:
www.geology.ucdavis.edu/
             Davis, CA 95616-8605, USA
faculty/twiss.html

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