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software:relax:man_page [2014/01/06 18:46] (current)
emheien created
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 +  man(1) relax man page man(1)
 +  ​
 +  ​
 +  ​
 +  NAME
 +         relax - Evaluates the deformation due to fault slip, surface loading or
 +         ​inflation and the time series of postseismic ​ relaxation ​ that  follows
 +         due to fault creep or viscoelastic flow.
 +  ​
 +  SYNOPSIS
 +         ​relax ​ [-h]  [--dry-run] ​ [--help] [--no-grd-output] [--no-proj-output]
 +         ​[--no-relax-output] [--no-stress-output] ​ [--no-txt-output] ​ [--no-vtk-
 +         ​output] [--no-xyz-output]
 +  ​
 +  ​
 +  DESCRIPTION
 +         ​relax ​ computes nonlinear time-dependent viscoelastic deformation with
 +         ​powerlaw rheology and rate-strengthening friction in a half  space  due
 +         to coseismic stress changes, initial stress, surface loads, and/or mov-
 +         ing faults.
 +  ​
 +  ​
 +  OPTIONS
 +         ​-h ​    print a short message and abort calculation
 +  ​
 +         ​--dry-run
 +        write lightweigh geometry files and abort calculation
 +  ​
 +         ​--help print a short message and abort calculation
 +  ​
 +         ​--no-grd-output
 +        cancel output in GMT grd binary format
 +  ​
 +         ​--no-proj-output
 +        cancel output in geographic projection
 +  ​
 +         ​--no-relax-output
 +        cancel output of the postseismic contribution
 +  ​
 +         ​--no-stress-output
 +        cancel output of stress tensor in any format
 +  ​
 +         ​--no-txt-output
 +        cancel output in text format
 +  ​
 +         ​--no-vtk-output
 +        cancel output in Paraview VTK format
 +  ​
 +         ​--no-xyz-output
 +        cancel output in GMT xyz format
 +  ​
 +         ​--with-stress-output
 +        export stress tensor
 +  ​
 +         ​--with-vtk-output
 +        export output in Paraview VTK format
 +  ​
 +         ​--with-vtk-relax-output
 +        export relaxation to VTK format
 +  ​
 +  ​
 +  ENVIRONMENT
 +         The environment variable OMP_NUM_THREADS controls the number of threads
 +         used by OpenMP at execution. For example, the calls
 +  ​
 +         ​OMP_NUM_THREADS=4 ./relax
 +  ​
 +         and
 +  ​
 +         ​export OMP_NUM_THREADS=4
 +         relax
 +  ​
 +         ​produce the same output.
 +  ​
 +  ​
 +  INPUT PARAMETERS
 +         grid size (sx1,​sx2,​sx3)
 +        Defines ​ the number of samples in the three directions. sx1, sx2
 +        and sx3 must be powers of two for optimal efficiency of the Fast
 +        Fourier ​ Transform. sx3 must be even for internal memory manage-
 +        ment considerations.
 +  ​
 +     sx2
 +        +------------+
 +    1  /   /|
 +  x  / / |    x1 (north)
 +  s  / /  |    /
 +    /        / ​  ​|  ​ /
 +  +------------+ ​   + +------->​ x2 (east)
 +         s |       |   / |
 +         x |       |  / |
 +         3 |       | /      x3 (depth)
 +  |       |/
 +  +------------+
 +  ​
 +         ​sampling size, smoothing & nyquist (dx1,​dx2,​dx3,​beta,​nq)
 +        dx1,dx2,dx3 control the sampling size of the model and the  size
 +        of the computational domain.
 +  ​
 +        beta  is a  roll-off parameter (0 <= beta <= 0.5) that controls
 +        the tapering of the slip distribution ​ on  faults. ​ beta=0.2-0.3
 +        are recommended values.
 +  ​
 +        nyquist ​ controls ​ how  the slip distribution is evaluated: is a
 +        fault patch dimension is smaller than  nyquist*dx, ​ then it ​ is
 +        evaluated ​ using the Okada'​s equations; otherwise, fault slip is
 +        represented by equivalent body forces, which  leads  to  a  much
 +        faster calculation.
 +  ​
 +        The   ​extent ​  ​of ​  ​the computational grid ​ is  exported ​ to
 +        wdir/​cgrid.vtp for visualization in Paraview.
 +  ​
 +  ​
 +         ​origin position & rotation (xo,yo,rot)
 +        Indicates the coordinates (xo,yo) and orientation of the compu-
 +        tational coordinate system. Use 0 0 0.
 +  ​
 +  ​
 +         ​observation depths for displacements and stress
 +        Indicates ​ depths ​ at which map views of displacement and stress
 +        are exported in GMT.
 +  ​
 +  ​
 +         ​output directory (wdir)
 +        All output files are written to the specified directory.
 +  ​
 +  ​
 +         ​elastic parameters and the buoyancy wavelength (lambda, mu, gamma)
 +        The uniform Lame parameter (lambda), shear modulus (mu) and  the
 +        buoyancy wavelength ​ (gamma=(1-nu)*rho*g/​mu),​ where nu is Pois-
 +        son's ration, rho is the density of the crust, g is the  gravity
 +        acceleration. ​ For  the  Earth, ​ typical values are lambda=mu=30
 +        GPa, and gamma = 8.33e-7 /m = 8.33e-4 /km
 +  ​
 +  ​
 +         ​integration time and output time parameters (T,dt,a)
 +        Integration time (T) refers to the duration of  the  calculation
 +        in  physical ​ units. dt is the time step of output files (dt<T).
 +        Negative integer values for dt indicates output tied  to inter-
 +        nally  optimized time steps: -1 corresponds to output every time
 +        step, -2 to output every other time steps. Scaling ​ parameter ​ a
 +        modifies the internally evaluated time step. 0 < a < 1 improves
 +        the accuracy of the time evolution. a > 1 reduces ​ the  accuracy
 +        of  the explicit time integration but speeds up the calculation.
 +  ​
 +  ​
 +         ​number of observation planes (nop)
 +        Observation planes are planar surface of arbitrary ​ orientation
 +        where displacement and stress are exported in ASCII and GMT .grd
 +        format for visualization. Integer nop indicates ​ the  number ​ of
 +        such planes. If nop > 0 then relax asks for the geometry of each
 +        planes, with one line per plane, as follows:
 +  ​
 +        # nb x1 x2 x3 length width strike dip
 +  ​
 +        where nb is an index running from 1 to nop, x1, x2  and  x3  are
 +        the  reference coordinates,​ length and width, and strike and dip
 +        are the dimension and the orientation of the observation plane.
 +        These parameters are defined in Section FAULT GEOMETRY.
 +  ​
 +  ​
 +         ​number of observation points (np)
 +        Observation ​ points ​ are locations where displacement and stress
 +        are exported as time series in ASCII. Integer no indicates ​ the
 +        number ​ of  such points. If np > 0 then relax asks for the name
 +        and location of each point, with one line per point, as follows:
 +  ​
 +        # nb NAME x1 x2 x3
 +  ​
 +        where  nb is an index running from 1 to np, NAME is a four-char-
 +        acter name used to identify the output file, x1, x2 and  x3  are
 +        the point coordinates. Time series of displacement and stress at
 +        these points are written to file NAME.txt, ​ where  NAME  is  the
 +        user-provided name.
 +  ​
 +  ​
 +         ​number of stress observation segments (nsp)
 +        Stress ​ observation ​ segments ​ are  fault  patches ​ where stress
 +        (shear, normal, dip-shear, strike-shear,​ Coulomb stress) evalu-
 +        ated  and  exported ​ in GMT and VTK formats. This is how Coulomb
 +        and other time-dependent stress calculations are carried out  in
 +        relax. ​ Integer nsp indicates the number of such patches. If nsp
 +        > 0 then relax asks for the definition of each fault patch, with
 +        one line per patch, as follows:
 +  ​
 +        # nb x1 x2 x3 length width strike dip friction
 +  ​
 +        where  nb is an index running from 1 to nsp, x1, x2, x3, length,
 +        width, strike and dip are the position, dimension ​ and  orienta-
 +        tion  of the fault patches and friction is the friction coeffi-
 +        cient (usually chosen at 0.6) used to  compute ​ Coulomb ​ stress.
 +        The geometry parameters are defined in section FAULT GEOMETRY.
 +  ​
 +        All receiver faults for Coulomb stress calculations are exported
 +        in wdir/​rfaults-dsigma-0000.vtp for visualization in Paraview.
 +  ​
 +  ​
 +         ​number of pre-stress interface (npsi)
 +        Pre-stress interfaces specify at what depth and how  pre stress
 +        changes. If npsi > 0, then relax requires the depths and stress
 +        values at each interface, one line per interface, as follows:
 +  ​
 +        # nb depth sigma11 sigma12 sigma13 sigma22 sigma23 sigma33
 +  ​
 +        where nb is an index running from 1 to npsi, depth is the  depth
 +        where  pre-stress ​ changes, ​ and sigma11, 12, 13, 22, 23, and 33
 +        and the components of the symmatric stress tensor.
 +  ​
 +  ​
 +         ​number of linear viscous interfaces (nlvi)
 +        Viscous interfaces specify at what depth and how the ​ viscosity
 +        changes ​ in  the Earth, and define the background 1-D viscosity
 +        model that can be subsequently modified using ductile zones. ​ If
 +        nlvi > 0, then relax requires the depths and viscosity and cohe-
 +        sion values at each interface, one line per interface, ​ as  fol-
 +        lows:
 +  ​
 +        # nb depth gammadot0 cohesion
 +  ​
 +        where  nb is an index running from 1 to nlvi, depth is the depth
 +        where cohesion and gammadot0 change, gammadot0 is  the  fluidity
 +        (defined as ​ gammadot0 = mu / eta, where eta is the viscosity),
 +        the reciprocal of the Maxwell relaxation time, and  cohesion ​ is
 +        the minimum value of stress to drive viscoelastic flow. The def-
 +        inition of the 1-D model is explained in Section DEPTH-DEPENDENT
 +        STRUCTURE.
 +  ​
 +        All  viscous interface are exported to wdir/​linearlayer-nb.vtp ,
 +        where nb is the interface index, for visualization in  Paraview.
 +  ​
 +        The definition of the 1-D depth-dependent model is followed by:
 +  ​
 +        number of linear ductile zones (nldz)
 +  ​
 +        Ductile ​ zones  are  volumes ​ where  the background viscosity is
 +        ammended. If nldz > 0, then relax requires the list  of  ductile
 +        zones, defined as
 +  ​
 +        # nb dgammadot0 x1 x2 x3 length width thickness strike dip
 +  ​
 +        where  nb  is an index running from 1 to nldz, dgammadot0 is the
 +        modifier to the background fluidity, x1, x2, x3, length,​ width,​
 +        thickness, strike and dip are the position, dimension and orien-
 +        tation of the rectangular volume. The  fluidity ​ used  to  drive
 +        viscoelastic ​ flow  is  gammadot0+dgammadot0. If gammadot0+dgam-
 +        madot0<​=0,​ no flow occurs. ​ Therefore, ​ setting ​ large  negative
 +        values ​ of  dgammadot0 ​ makes  the region elastic. The geometric
 +        parameters are defined in Section LATERAL VARIATIONS OF  VISCOUS
 +        PROPERTIES.
 +  ​
 +        All  ductile zones are exported to wdir/​weakzones-linear.vtp for
 +        visualization in Paraview, including when computation is aborted
 +        with the --dry-run option.
 +  ​
 +  ​
 +         ​number of nonlinear viscous interfaces (nnlvi)
 +        Nonlinear ​ viscous ​ interfaces specify at what depth and how the
 +        power-law rheology parameters change in the  Earth, ​ and define
 +        the background 1-D viscosity model that can be subsequently mod-
 +        ified using ductile zones. Viscoelastic relaxation in relax  can
 +        have  ontributions from both linear and nonlinear rheologies. If
 +        nnlvi > 0, then relax requires the depths, viscosity, power  and
 +        cohesion at each interface, one line per interface, as follows:
 +  ​
 +        # nb depth gammadot0 power cohesion
 +  ​
 +        where nb is an index running from 1 to nnlvi, depth is the depth
 +        where cohesion and gammadot0 change, gammadot0 is the  reference
 +        fluidity, power is the power-law rheology power exponent (strain
 +        rate = gammadot0 ( tau / mu ) ^ power, where tau is the  coseis-
 +        mic stress change plus the prestress), and cohesion is the mini-
 +        mum value of stress to drive viscoelastic flow.
 +  ​
 +        The definition of the 1-D  depth-dependent ​ power-law ​ model  is
 +        followed by:
 +  ​
 +        number of nonlinear ductile zones (nnldz)
 +  ​
 +        Nonlinear ductile zones are volumes where the background nonlin-
 +        ear viscosity is ammended. If nnldz > 0, then relax requires the
 +        list of nonlinear ductile zones, defined as
 +  ​
 +        # nb dgammadot0 x1 x2 x3 length width thickness strike dip
 +  ​
 +        where  nb is an index running from 1 to nnldz, dgammadot0 is the
 +        modifier to the background fluidity, x1, x2, x3, length,​ width,​
 +        thickness, strike and dip are the position, dimension and orien-
 +        tation of the rectangular volume. The power exponent of the duc-
 +        tile zone is the same as in the background model.
 +  ​
 +        All  ductile ​ zones are exported to wdir/​weakzones-nonlinear.vtp
 +        for visualization in Paraview, ​ including ​ when  computation ​ is
 +        aborted with the --dry-run option.
 +  ​
 +  ​
 +         ​number of friction interfaces (nfi)
 +        Friction interfaces ​ define ​ the  variations ​ of fault friction
 +        properties with depth, using the framework of rate-strengthening
 +        friction. If nfi < 0, relax requires the depth, reference veloc-
 +        ity, strengthening parameter and cohesion ​ at  each  depth, ​ one
 +        line per interface, as follows:
 +  ​
 +        # nb depth gamma0 (a-b)sigma friction cohesion
 +  ​
 +        where  nb  is an index running from 1 to nfi, depth is the depth
 +        where friction properties change, (a-b)sigma ​ is the ​ reference
 +        stress ​ (typically of the order of 1 MPa), friction is the fric-
 +        tion coefficient (usually ​ 0.6) and ​ cohesion ​ is  the stress
 +        enveloppe. ​ If  nfi  >  0 the list of interface is followed by a
 +        definition of faults where stress-driven slip occurs:
 +  ​
 +        number of afterslip planes (nap)
 +  ​
 +        Afterslip planes are rectangular surfaces ​ where  stress-driven
 +        slip  occurs. ​ If  nap > 0, relax requires the list of afterslip
 +        planes, as follows:
 +  ​
 +        # nb x1 x2 x3 length width strike dip rake
 +  ​
 +        where nb is a index running from 1 to nap, x1, x2,  x3,  length,
 +        width, ​ strike ​ and dip are the position, dimension and orienta-
 +        tion of the fault plane and rake is a +-90 constrain on the rake
 +        of  afterslip. ​ If |rake| > 360, the constraint is ignored. Some
 +        of these parameters are defined in Section FAULT GEOMETRY.
 +  ​
 +        All afterslip planes are exported in wdir/​aplane-nb.vtp ,  where
 +        nb in the patch index, for visualization in Paraview.
 +  ​
 +  ​
 +         ​number of interseismic loading shear faults (nisf)
 +        Interseismic shear faults are faults that move at a user-defined
 +        constant rate. If nisf > 0, relax requires the list of faults.
 +  ​
 +  ​
 +         ​number of interseismic loading opening dykes (niod)
 +        Interseismic opening dykes are intrusions that open at  a  user-
 +        defined ​ constant ​ rate. If niod > 0, relax requires the list of
 +        dykes.
 +  ​
 +  ​
 +         ​number of events (ne)
 +        Events are moments in time when new internal or external forces
 +        act  of  the  system ​ (ne >= 1). If ne = 1, then a list of shear
 +        faults, opening dyke and surface tractions are required and  the
 +        change ​ occurs at t = 0. If ne > 1, then a list of shear faults,
 +        opening dyke and surface tractions are required for each event.
 +        The  first  event  occurs ​ at  time 0 and each new event is pre-
 +        scribed a time of occurrence. Having multiple events allows ​ the
 +        user  to model ​ the  effect of a sequence of earthquakes,​ or to
 +        prescribe time-dependent loads.
 +  ​
 +  ​
 +         ​number of shear dislocations (strike-slip and dip-slip faults) (nsd)
 +        Shear dislocations are rectangular slip patches. If ​ nsd  >  0,
 +        relax expects a list of such slip patches, as follows
 +  ​
 +        # nb slip x1 x2 x3 length width strike dip rake
 +  ​
 +        where  nb is an index running from 1 to nsd, x1, x2, x3, length,
 +        width, strike dip are the position, dimension and orientation of
 +        the  slip  patch; slip and rake are the slip amplitude and rake.
 +        For positive slip, rake = 0 indicates left-lateral slip, and for
 +        positive slip ​ and  shallow dip (dip &#60;= 90), rake = 90 indicate
 +        thrust motion. These parameters are  defined ​ in Section ​ FAULT
 +        GEOMETRY.
 +  ​
 +        All  faults ​ are exported to wdir/​rfaults-e.vtp , where e is the
 +        event  number, ​ for  visualization ​ in   ​Paraview. ​  ​Export ​  to
 +        wdir/​rfaults-e.xy allows visualization with GMT.
 +  ​
 +  ​
 +         ​number of tensile cracks (nts)
 +        Tensile ​ cracks are dykes with opening or closure of the elastic
 +        walls. If nts > 0, relax expects a list of cracks:
 +  ​
 +        # nb opening x1 x2 x3 length width strike dip
 +  ​
 +        where nb is an index running from 1 to nts, opening is the  nor-
 +        mal  motion ​ of  the  walls, and the other parameters define the
 +        position, orientation and dimension of the cracks.
 +  ​
 +  ​
 +         ​number of surface loads (nsl)
 +        Surface loads are surface tractions in  the  vertical ​ direction
 +        coming ​ from  the  loading ​ and  unloading of lakes, dams or the
 +        freezing or melting of ice. If nsl > 0, relax expects a list  of
 +        surface ​ loads, ​ defined with their geometry and weight, as fol-
 +        lows:
 +  ​
 +        # nb x1 x2 length width t3 T phi
 +  ​
 +        where nb is an index running from 1 to nsl, x1, x2,  length ​ and
 +        width  define ​ the  position and dimension of the load, t3 is in
 +        units of stress (force/​surface),​ positive down, and T can  be  a
 +        period (T > 0 implies stress=t3*sin(2 pi/T + phi) or not (T &#60;= 0
 +        implies stress = t3 H(t), with H(t) the Heaviside function).
 +  ​
 +  ​
 +         time of next event (te)
 +        If the computation includes several events (ne > 0), the second
 +        and  subsequent events are preceded by their time of occurrence.
 +  ​
 +  ​
 +  EXAMPLE INPUTS
 +         The line starting with the '#'​ symbol are comments.
 +  ​
 +  ​
 +         ​CALLING SEQUENCE
 +  ​
 +        relax &#60; input.dat
 +  ​
 +        or
 +  ​
 +        relax &#​60;&#​60;​EOF
 +        # this line is a comment
 +        `cat input.dat`
 +        EOF
 +  ​
 +  ​
 +         ​COSEISMIC DISPLACEMENT
 +        Computes coseismic displacements due to uniform fault slip:
 +  ​
 +        relax --no-proj-output &#​60;&#​60;​EOF
 +        # grid size (sx1,​sx2,​sx3)
 +        256 256 256
 +        # sampling size, smoothing & nyquist (dx1,​dx2,​dx3,​beta,​nq)
 +        0.05 0.05 0.05 0.2 0
 +        # origin position & rotation
 +        0 0 0
 +        # observation depths for displacements and stress
 +        0 0.5
 +        # output directory
 +        output_dir
 +        # elastic parameters and gamma = (1-nu) rho g / mu = 8.33e-7 /m = 8.33e-4 /km
 +        30 30 8.33e-4
 +        # integration time (t1)
 +        0 -1 1
 +        # number of observation planes
 +        0
 +        # number of observation points
 +        0
 +        # number of stress observation segments
 +        0
 +        # number of prestress interfaces
 +        0
 +        # number of linear viscous interfaces
 +        0
 +        # number of powerlaw viscous interfaces
 +        0
 +        # number of friction interfaces
 +        0
 +        # number of interseismic loading strike-slip and opening
 +        0
 +        0
 +        # number of coseismic events
 +        1
 +        # number of shear dislocations (strike-slip and dip-slip faults)
 +        1
 +        # index slip x1 x2 x3 length width strike dip rake
 +      1 1 -1  0  0 2     ​1 ​     0  90    0
 +        # number of tensile cracks
 +        0
 +        # number of dilatation sources (Mogi source)
 +        0
 +        # number of surface loads
 +        0
 +        EOF
 +  ​
 +  ​
 +  ​
 +         ​POSTSEISMIC VISCOELASTIC DEFORMATION
 +        Computes time-dependent postseismic ​ viscoelastic ​ deformation
 +        driven by stress induced by fault slip:
 +  ​
 +        relax --no-proj-output &#​60;&#​60;​EOF
 +        # grid size (sx1,​sx2,​sx3)
 +        512 512 512
 +        # sampling size, smoothing & nyquist (dx1,​dx2,​dx3,​beta,​nq)
 +        0.5 0.5 0.5 0.2 0
 +        # origin position & rotation
 +        0 0 0
 +        # observation depths for displacements and stress
 +        0 10
 +        # output directory
 +        viscoelastic
 +        # elastic parameters and gamma = (1-nu) rho g / mu = 8.33e-7 /m = 8.33e-4 /km
 +        30 30 8.33e-4
 +        # integration time (t1)
 +        10 -1 0.5
 +        # number of observation planes
 +        0
 +        # number of observation points
 +        0
 +        # number of stress observation segments
 +        0
 +        # number of prestress interfaces
 +        0
 +        # number of linear viscous interfaces
 +        1
 +        # nb depth gammadot0 cohesion
 +  1    20 1   0
 +        # number of linear ductile zones
 +        0
 +        # number of powerlaw viscous interfaces
 +        0
 +        # number of friction interfaces
 +        0
 +        # number of interseismic loading strike-slip and opening
 +        0
 +        0
 +        # number of coseismic events
 +        1
 +        # number of shear dislocations
 +        1
 +        # index slip  x1 x2 x3 length width strike dip rake
 +      1 1 -10 0  0 20    10      0  90 0
 +        # number of tensile cracks
 +        0
 +        # number of dilatation sources
 +        0
 +        # number of surface loads
 +        0
 +        EOF
 +  ​
 +  ​
 +  ​
 +  ​
 +  ​
 +  FAULT GEOMETRY
 +         ​Static dislocation sources are discretized into a series of planar seg-
 +         ​ments. Slip patches are defined in terms of position, orientation, ​ and
 +         slip, as illustrated in the following figure. For positive slip, a zero
 +         rake corresponds to left-lateral strike-slip motion ​ and  a  90 degree
 +         ​rake ​ corresponds ​ to  a  thrust ​ motion ​ (when dip is smaller than 90
 +         ​degrees).
 +  ​
 +        N (x1)
 +       /
 +      /| strike
 +  x1,x2,x3 ->​@--------------------------  ​ E (x2)
 +     ​|\  ​    p .     \ w
 +     :​-\  ​   i .      \ i
 +     ​| ​ \    l .       \ d
 +     :90 \  s .        \ t
 +     ​|-dip\ ​ . \ h
 +     : \. | Rake \
 +     ​|  ​ --------------------------
 +     : l e n g t h
 +     Z (x3)
 +  ​
 +  ​
 +         Slip distributions are defined as a list of slip on individual patches,
 +         for example:
 +  ​
 +        # number of shear dislocations
 +        4
 +        # nb slip x1 x2 x3 length width strike dip rake
 +  1  0.4  0  0  0    1.3   ​2.3  ​ 18  57    0
 +  2  1.1  0  1  0    1.3   ​2.3  ​ 18  57    0
 +  3  2.7  0  0  2    1.3   ​2.3  ​ 18  57    0
 +  4  0.2  0  1  2    1.3   ​2.3  ​ 18  57    0
 +  ​
 +  ​
 +  DEPTH-DEPENDENT STRUCTURE
 +         ​Depth-dependent variations of properties is obtained from the  interpo-
 +         ​lation ​ of a series of tie points, following the method employed in the
 +         PREM model. For example, the 1-D model below
 +  ​
 +     ​@------------------------>​ (modulus)
 +     |.
 +     | .
 +     ​| ​ .
 +         ​z1 ​ |   + v1
 +     ​|  ​ .
 +     | v3      .
 +      z2,z3  |   ​+ ​ -  - + v2
 +     ​| ​  |
 +     ​| ​  |
 +     ​| ​  | v4
 +      z4,z5  |   ​+ ​ -  - -  -  -  +  v5
 +     | |
 +     | :
 +     | |
 +     | :
 +     |
 +     Z (x3)
 +  ​
 +  ​
 +         is specified as follows:
 +  ​
 +        # number of interfaces
 +        6
 +        # nb depth value
 +  1     ​0 ​    0
 +  2    z1    v1
 +  3    z2    v2
 +  4    z3    v3
 +  5    z4    v4
 +  6    z5    v5
 +  ​
 +  ​
 +         and the last value v5 is continued down to the bottom extension of  the
 +         ​computational grid.
 +  ​
 +  ​
 +  LATERAL VARIATIONS OF VISCOUS PROPERTIES
 +         ​Lateral variations of viscous properties can occur in rectangular vol-
 +         umes of arbitrary orientation and dimension. The geometry of the anoma-
 +         ​lous ​ ductile ​ zones is defined with the reference position (x1,x2,x3),
 +         ​length,​ width, thickness, strike and dip,  as  illustrated ​ below. ​ The
 +         ​final ​ value of the fluidity that controls viscoelastic flow is the sum
 +         of the background value defined in the depth-dependent ​ model  and  the
 +         value in the ductile zones.
 +  ​
 +        N (x1)
 +       /
 +      /| strike
 +  x1,x2,x3 ->​@-------------------------- E (x2)
 +     ​|\  ​   \ w +
 +     :​-\  ​    \ i       /
 +     ​| ​ \       \ d     / s
 +     :90 \        \ t   / s
 +     ​|-dip\ \ h / e
 +     : \ \ / n
 +     ​|  ​ -------------------------- ​ k
 +     : l e n g t h   /  c
 +     | /  i
 +     :​ / ​ h
 +     ​|  ​      / ​  t
 +     :​  ​     /
 +     ​|  ​    +
 +     Z (x3)
 +  ​
 +  ​
 +         The input is defined as follows:
 +  ​
 +        # number of ductile zones
 +        1
 +        # nb dgammadot0 x1 x2 x3 length width thickness strike dip
 +  1    ​-1 ​ 0  0  0     1   1     1    ​0 ​ 90
 +  ​
 +  ​
 +  SEE ALSO
 +         ​Rousset B.,​ S. Barbot, J.-P. Avouac and Y.-J. Hsu, "​Postseismic Defor-
 +         ​mation Following the 1999 Chi-Chi Earthquake, Taiwan: ​ Implication ​ for
 +         ​Lower-Crust Rheology",​ J. Geophys. Res., 2012
 +  ​
 +         ​Bruhat ​ L., S. Barbot and J.-P. Avouac, "​Contributions of Afterslip and
 +         ​Viscoelastic Flow Following the 2004 Parkfield Earthquake",​ J. Geophys.
 +         Res., v. 116, B08401, 11 PP., 2011, doi:​10.1029/​2010JB008073
 +  ​
 +         ​Barbot ​ S.  and Y. Fialko, "A Unified Continuum Representation of Post-
 +         ​seismic Relaxation Mechanisms: Semi-Analytic Models of Afterslip, Poro-
 +         ​elastic Rebound and Viscoelastic Flow", Geophys. J. Int., v. 182, 3, p.
 +         ​1124-1140,​ 2010, doi:​10.1111/​j.1365-246X.2010.04678.x
 +  ​
 +         ​Barbot S. and Y. Fialko, "​Fourier-Domain Green Function for an  Elastic
 +         ​Semi-Infinite ​ Solid under Gravity, with Applications to Earthquake and
 +         ​Volcano Deformation",​ Geophys. J. Int., v. 182,​ no. ​ 2,  pp.  568-582,
 +         2010, doi:​10.1111/​j.1365-246X.2010.04655.x
 +  ​
 +         ​Barbot ​ S.,  Y. Fialko, ​ Y.  Bock, "​Postseismic Deformation due to the
 +         Mw6.0 2004 Parkfield Earthquake: Stress-Driven Creep on a  Fault  with
 +         ​Spatially ​ Variable ​ Rate-and-State ​ Friction ​ Parameters",​ J. Geophys.
 +         Res., vol. 114, B07405, 2009, doi:​10.1029/​2008JB005748
 +  ​
 +  ​
 +  ​
 +  ​
 +  BUGS
 +         No known bugs.
 +  ​
 +  ​
 +  AUTHOR
 +         ​Sylvain Barbot (sbarbot@ntu.edu.sg)
 +  ​
 +  ​
 +  COPYRIGHT
 +         RELAX is free software: you can redistribute it and/or modify it  under
 +         ​the ​ terms  of  the GNU General Public License as published by the Free
 +         ​Software Foundation, either version 3  of  the  License, ​ or  (at  your
 +         ​option) any later version.
 +  ​
 +         ​RELAX ​ is  distributed ​ in the hope that it will be useful, but WITHOUT
 +         ANY WARRANTY; without even the implied warranty of  MERCHANTABILITY ​ or
 +         ​FITNESS FOR ​ A PARTICULAR PURPOSE. ​ See the GNU General Public License
 +         for more details.
 +  ​
 +         You should have received a copy of the GNU General Public License along
 +         with RELAX. ​ If not, see &#​60;​http://​www.gnu.org/​licenses/>​.
 +  ​
 +  ​
 +  ​
 +  1.0.3  ​ 02 Nov 2012 man(1)
 +  ​
software/relax/man_page.txt ยท Last modified: 2014/01/06 18:46 by emheien