RELAX  Git Revision b018706373a1d4278e2038ff1ad474b28eadfa4f
RELAX
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RELAX Documentation

program relax


PURPOSE: The program RELAX computes nonlinear time-dependent viscoelastic deformation with powerlaw rheology and rate-strengthening friction in a cubic, periodic grid due to coseismic stress changes, initial stress, surface loads, and/or moving faults.

ONLINE DOCUMENTATION: generate html documentation from the source directory with the doxygen (http://www.stack.nl/~dimitri/doxygen/index.html) program with command:

doxygen .doxygen

DESCRIPTION: Computation is done semi-analytically inside a cartesian grid. The grid is defined by its size sx1*sx2*sx3 and the sampling intervals dx1, dx2 and dx3. rule of thumb is to allow for at least five samples per fault length or width, and to have the tip of any fault at least 10 fault widths away from any edge of the computational grid.

Coseismic stress changes and initial coseismic deformation results from the presence of dislocations in the brittle layer. Fault geometry is prescribed following Okada or Wang's convention, with the usual slip, strike, dip and rake and is converted to a double-couple equivalent body-force analytically. Current implementation allows shear fault (strike slip and dip slip), dykes, Mogi source, and surface traction. Faults and dykes can be of arbitrary orientation in the half space.


METHOD: The current implementation is organized to integrate stress/strain- rate constitutive laws (rheologies) of the form

\[ \dot{\epsilon} = f(\sigma) \]

as opposed to epsilon^dot = f(sigma,epsilon) wich would include work- hardening (or weakening). The time-stepping implements a second-order Runge-Kutta numerical integration scheme with a variable time-step. The Runge-Kutta method integrating the ODE y'=f(x,y) can be summarized as follows:

\[ y_(n+1) = y_n + k_2 k_1 = h * f(x_n, y_n) k_2 = h * f(x_n + h, y_n + k_1) \]

where h is the time-step and n is the time-index. The elastic response in the computational grid is obtained using elastic Greens functions. The Greens functions are applied in the Fourier domain. Strain, stress and body-forces are obtained by application of a finite impulse response (FIR) differentiator filter in the space domain.


INPUT: Static dislocation sources are discretized into a series of planar segments. Slip patches are defined in terms of position, orientation, and slip, as illustrated in the following figure:

                 N (x1)
                /
               /| Strike
   x1,x2,x3 ->@---------------------—      (x2)
              |\        p .            \ W
              :-\      i .              \ i
              |  \    l .                \ d
              :90 \  S .                  \ t
              |-Dip\  .                    \ h
              :     . | Rake                 !!              |      ----------------------—