[cig-commits] r12188 - in short/3D/PyLith/trunk/doc/userguide: . boundaryconditions
brad at geodynamics.org
brad at geodynamics.org
Fri Jun 13 12:44:28 PDT 2008
Author: brad
Date: 2008-06-13 12:44:28 -0700 (Fri, 13 Jun 2008)
New Revision: 12188
Modified:
short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
short/3D/PyLith/trunk/doc/userguide/userguide.lyx
Log:
Updated fault section to include discussion of multiple kinematic ruptures and new slip time functions (constant rate and step function).
Modified: short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx 2008-06-13 19:24:24 UTC (rev 12187)
+++ short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx 2008-06-13 19:44:28 UTC (rev 12188)
@@ -1611,11 +1611,12 @@
each time step.
Table
\begin_inset LatexCommand ref
-reference "tab:fault:output"
+reference "tab:fault:kin:output"
\end_inset
- lists the fields available for output.
+ lists the fields available for output for a fault with kinematic (prescribed)
+ earthquake rupture.
The fault coordinate system is shown in Figure
\begin_inset LatexCommand ref
reference "fig:fault:slip:motions"
@@ -1700,7 +1701,170 @@
e shear modulus and condition the equations for faster convergence rates.
\end_layout
+\begin_layout Subsection
+Kinematic Earthquake Rupture
+\end_layout
+
\begin_layout Standard
+Kinematic earthquake ruptures specify the slip as a function of time on
+ the fault surface.
+ Slip may evolve simultaneously over the fault surface instantaneously in
+ a single time step (as is usually done in quasi-static simulations) or
+ propagate over the fault surface over hundreds and up to thousands of time
+ steps (as is usually done in a dynamic simulation).
+\end_layout
+
+\begin_layout Subsubsection
+Governing Equations
+\end_layout
+
+\begin_layout Standard
+The insertion of cohesive cells into the finite-element mesh has the effect
+ of decoupling the motion of the two sides of the fault surface.
+ In order to impose the desired relative motion, we must adjust the governing
+ equations.
+ PyLith employs Lagrange multiplier constraints to do this.
+ Typically, the additional degrees of freedom associated with the Lagrange
+ multipliers results in a complex implementation.
+ However, the use of Lagrange multiplier constraints with cohesive cells
+ makes this very easy; we simply add the additional degrees of freedom associate
+d with the Lagrange multipliers to the cohesive cells as shown in Figure
+
+\begin_inset LatexCommand ref
+reference "fig:fault:cohesive:quad4:kin"
+
+\end_inset
+
+.
+ As a result, the fault implementation is completely confined to the cohesive
+ cell.
+ Furthermore, the Lagrange multiplier constraints correspond to forces required
+ to impose the relative motions, so they are related to the change in stress
+ on the fault surface associated with fault slip.
+ If we write the governing equations in the form
+\begin_inset Formula \begin{equation}
+\underline{A}\overrightarrow{u}=\overrightarrow{b}\,,\end{equation}
+
+\end_inset
+
+then inserting the Lagrange multiplier constraints results in
+\begin_inset Formula \begin{equation}
+\left[\begin{array}{cc}
+\underline{A} & \underline{C}^{T}\\
+\underline{C} & 0\end{array}\right]\left[\begin{array}{c}
+\overrightarrow{u}\\
+\overrightarrow{L}\end{array}\right]=\left[\begin{array}{c}
+\overrightarrow{b}\\
+\overrightarrow{D}\end{array}\right]\,,\end{equation}
+
+\end_inset
+
+where
+\begin_inset Formula $\underline{C}$
+\end_inset
+
+ is a matrix of direction cosines relating the relative motion across the
+ fault to the vector of fault slip,
+\begin_inset Formula $\overrightarrow{D}$
+\end_inset
+
+, and
+\begin_inset Formula $\overrightarrow{L}$
+\end_inset
+
+ is the vector of Lagrange multipliers.
+ Note that by using the direction cosines to relate the relative motion
+ across the fault, the slip vector and Lagrange multipliers (forces required
+ to impose the slip) are in the local fault coordinate system (lateral motion,
+ reverse motion, and fault opening).
+ Because the solution vector now mixes displacements,
+\begin_inset Formula $\overrightarrow{u}$
+\end_inset
+
+, and forces,
+\begin_inset Formula $\overrightarrow{L}$
+\end_inset
+
+, the matrix on the left-hand side is ill-conditioned.
+ In order to improve the conditioning we scale the direction cosines in
+ the upper right portion of the matrix by an amount necessary to reduce
+ the forces in the solution vector to within a few orders of magnitude of
+ the displacements, resulting in
+\begin_inset Formula \begin{equation}
+\left[\begin{array}{cc}
+A & a\underline{C}^{T}\\
+\underline{C} & 0\end{array}\right]\left[\begin{array}{c}
+\overrightarrow{u}\\
+\frac{1}{a}\overrightarrow{L}\end{array}\right]=\left[\begin{array}{c}
+\overrightarrow{b}\\
+\overrightarrow{D}\end{array}\right]\,.\end{equation}
+
+\end_inset
+
+While the matrix on the left-hand side is now nonsymmetric, the solution
+ converges very quickly.
+ Future releases of PyLith may use alternative conditioning algorithms to
+ retain the symmetry of the matrix, thereby reducing storage requirements.
+\end_layout
+
+\begin_layout Subsubsection
+Arrays of Kinematic Rupture Components
+\end_layout
+
+\begin_layout Standard
+Multiple earthquake ruptures can be specified on a single fault surface.
+ This permits repeatedly rupturing the same portion of a fault or combining
+ earthquake rupture on one subset of the fault surface with steady aseismic
+ slip on another subset (the two subsets may overlap in both time and space).
+ A dynamic array of kinematic earthquake rupture components associates a
+ name (string) with each kinematic rupture.
+ The default dynamic array contains a single earthquake rupture,
+\begin_inset Quotes eld
+\end_inset
+
+rupture
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The eq_srcs is the FaultCohesiveKin facility for thie dynamic array.
+ An example of setting the array of kinematic rupture components in a .cfg
+ file:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+eq_srcs = [earthquake,creep] ; Array of kinematic earthquake ruptures
+\end_layout
+
+\begin_layout Standard
+The output manager includes generic fault information (orientation) as well
+ as the final slip or slip rate (as in the case of the constant slip rate
+ slip time function) and slip initiation time for each kinematic rupture.
+ The name of the slip and slip initiation time vertex fields are of the
+ form
+\family typewriter
+final_slip_NAME
+\family default
+ and
+\family typewriter
+slip_time_NAME
+\family default
+, respectively, where
+\family typewriter
+NAME
+\family default
+ refers to the name used in the dynamic array of kinematic ruptures,
+\family typewriter
+eq_srcs
+\family default
+.
+\end_layout
+
+\begin_layout Standard
\begin_inset Float table
placement H
wide false
@@ -1784,7 +1948,7 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
@@ -1815,7 +1979,7 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
@@ -1846,7 +2010,7 @@
\end_inset
</cell>
</row>
-<row topline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
@@ -1862,7 +2026,7 @@
\begin_layout Standard
\family typewriter
-final_slip
+final_slip_NAME
\end_layout
\end_inset
@@ -1871,13 +2035,13 @@
\begin_inset Text
\begin_layout Standard
-Vector of final slip (in fault coordinate system)
+Vector of final slip (in fault coordinate system) in meters
\end_layout
\end_inset
</cell>
</row>
-<row topline="true" bottomline="true">
+<row bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
@@ -1894,6 +2058,11 @@
\family typewriter
slip_time
+\family default
+_
+\family typewriter
+\noun on
+NAME
\end_layout
\end_inset
@@ -1902,13 +2071,13 @@
\begin_inset Text
\begin_layout Standard
-Time at which slip begins
+Time at which slip begins in seconds
\end_layout
\end_inset
</cell>
</row>
-<row bottomline="true">
+<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
@@ -1935,7 +2104,7 @@
\begin_inset Text
\begin_layout Standard
-Slip vector at time step (in fault coordinate system)
+Slip vector at time step (in fault coordinate system) in meters
\end_layout
\end_inset
@@ -1966,7 +2135,7 @@
\begin_inset Text
\begin_layout Standard
-Change in fault tractions (in fault coordinate system)
+Change in fault tractions (in fault coordinate system) in Pa
\end_layout
\end_inset
@@ -1985,7 +2154,7 @@
\begin_layout Standard
Fields available in output of fault information.
\begin_inset LatexCommand label
-name "tab:fault:output"
+name "tab:fault:kin:output"
\end_inset
@@ -2002,122 +2171,686 @@
\end_layout
-\begin_layout Subsection
-Kinematic Earthquake Source
+\begin_layout Subsubsection
+Kinematic Earthquake Rupture Parameters
\end_layout
\begin_layout Standard
-Kinematic earthquake sources specify the slip as a function of time on the
- fault surface.
- Slip may evolve simultaneously over the fault surface instantaneously in
- a single time step (as is usually done in quasi-static simulations) or
- propagate over the fault surface over hundreds and up to thousands of time
- steps (as is usually done in a dynamic simulation).
+The kinematic rupture parameters include the origin time and slip time function.
+ The slip initiation time in the slip time function is relative to the origin
+ time (default is 0).
+ This means that slip initiates at a point at a time corresponding to the
+ sum of the kinematic rupture's origin time and the slip initiation time
+ for that point.
+ An example of specifying the kinematic earthquake rupture properties and
+ components in a .cfg file:
\end_layout
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+eq_srcs = [earthquake,creep]
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.earthquake]
+\end_layout
+
+\begin_layout LyX-Code
+origin_time = 0.0*s ; default origin time
+\end_layout
+
+\begin_layout LyX-Code
+slip_function = pylith.faults.BruneSlipFn ; default slip time function
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.creep]
+\end_layout
+
+\begin_layout LyX-Code
+origin_time = 10.0*year ; start creep at 10.0 years
+\end_layout
+
+\begin_layout LyX-Code
+slip_function = pylith.faults.ConstRateSlipFn ; switch to constant slip rate
+ slip function
+\end_layout
+
\begin_layout Subsubsection
-Governing Equations
+Slip Time Function
\end_layout
\begin_layout Standard
-The insertion of cohesive cells into the finite-element mesh has the effect
- of decoupling the motion of the two sides of the fault surface.
- In order to impose the desired relative motion, we must adjust the governing
- equations.
- PyLith employs Lagrange multiplier constraints to do this.
- Typically, the additional degrees of freedom associated with the Lagrange
- multipliers results in a complex implementation.
- However, the use of Lagrange multiplier constraints with cohesive cells
- makes this very easy; we simply add the additional degrees of freedom associate
-d with the Lagrange multipliers to the cohesive cells as shown in Figure
+The current release of PyLith supports specification of the evolution of
+ fault slip using analytical expressions for the slip time history at each
+ point where the parameters for the slip time function may vary over the
+ fault surface.
+ Currently, three slip time functions are available: (1) a step-function
+ for quasi-static modeling of earthquake rupture, (2) a constant slip rate
+ time function for modeling steady aseismic slip, and (3) the integral of
+ Brune's far-field time function
+\begin_inset LatexCommand cite
+key "Brune:1970"
+
+\end_inset
+
+ for modeling the dynamics of earthquake rupture.
+ Additional slip time functions will likely be available in future releases.
+\end_layout
+
+\begin_layout Paragraph
+Step-Function Slip Time Function
+\end_layout
+
+\begin_layout Standard
+This slip function prescribes a step in slip at a given time at a point:
-\begin_inset LatexCommand ref
-reference "fig:fault:cohesive:quad4:kin"
+\end_layout
+\begin_layout Standard
+\begin_inset Formula \begin{gather*}
+D(t)=\left\{ \begin{array}{cc}
+0 & t<t_{r}\\
+D_{final} & t\ge t_{r}\end{array}\right.\,,\end{gather*}
+
\end_inset
+where
+\begin_inset Formula $D(t)$
+\end_inset
+
+ is slip at time
+\begin_inset Formula $t$
+\end_inset
+
+,
+\begin_inset Formula $D_{final}$
+\end_inset
+
+ is the final slip, and
+\begin_inset Formula $t_{r}$
+\end_inset
+
+ is the slip initiation time (time when rupture reaches the location).
+ The slip is specified independently for each of the component of slip,
+ and the slip and slip starting time may vary over the fault surface.
+\end_layout
+
+\begin_layout Description
+final_slip Spatial database of slip (
+\begin_inset Formula $D_{final})$
+\end_inset
+
.
- As a result, the fault implementation is completely confined to the cohesive
- cell.
- Furthermore, the Lagrange multiplier constraints correspond to forces required
- to impose the relative motions, so they are related to the change in stress
- on the fault surface associated with fault slip.
- If we write the governing equations in the form
-\begin_inset Formula \begin{equation}
-\underline{A}\overrightarrow{u}=\overrightarrow{b}\,,\end{equation}
+\end_layout
+\begin_layout Description
+slip_time Spatial database of slip initiation times (
+\begin_inset Formula $t_{r}$
\end_inset
-then inserting the Lagrange multiplier constraints results in
-\begin_inset Formula \begin{equation}
-\left[\begin{array}{cc}
-\underline{A} & \underline{C}^{T}\\
-\underline{C} & 0\end{array}\right]\left[\begin{array}{c}
-\overrightarrow{u}\\
-\overrightarrow{L}\end{array}\right]=\left[\begin{array}{c}
-\overrightarrow{b}\\
-\overrightarrow{D}\end{array}\right]\,,\end{equation}
+).
+\end_layout
+\begin_layout Standard
+An example of setting these parameters in a
+\family typewriter
+.cfg
+\family default
+ file is:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.rupture]
+\end_layout
+
+\begin_layout LyX-Code
+slip_function = pylith.faults.StepSlipFn
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.rupture.slip_function]
+\end_layout
+
+\begin_layout LyX-Code
+final_slip.iohandler.filename = final_slip.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+slip_time.iohandler.filename = sliptime.spatialdb
+\end_layout
+
+\begin_layout Standard
+The spatial database files for the slip time function specify the spatial
+ variation in the parameters for the slip time function.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<column alignment="left" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" leftline="true" rightline="true" width="2.5in">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\series bold
+Database
+\end_layout
+
\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+\begin_layout Standard
+
+\series bold
+Value
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\series bold
+Description
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+final_slip
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+left-lateral-slip
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Amount of left-lateral final slip in meters.
+ Use negative values for right-lateral slip.
+ Applies to faults in 2D and 3D only.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+reverse-slip
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Amount of reverse slip in meters.
+ Use negative values for normal slip.
+ Applies to faults in 3D only.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+fault-opening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Amount of fault opening in meters.
+ Negative values imply penetration.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+slip_time
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+slip_time
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Slip initiation time (
+\begin_inset Formula $t_{t})$
+\end_inset
+
+ in seconds.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Caption
+
+\begin_layout Standard
+Values in spatial database used as parameters in the constant slip rate
+ slip time function.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Paragraph
+Constant Slip Rate Slip Time Function
+\end_layout
+
+\begin_layout Standard
+This slip function prescribes a constant slip rate for the evolution of
+ slip at a point:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{gather*}
+D(t)=\left\{ \begin{array}{cc}
+0 & t<t_{r}\\
+V(t-t_{r}) & t\ge t_{r}\end{array}\right.\,,\end{gather*}
+
+\end_inset
+
where
-\begin_inset Formula $\underline{C}$
+\begin_inset Formula $D(t)$
\end_inset
- is a matrix of direction cosines relating the relative motion across the
- fault to the vector of fault slip,
-\begin_inset Formula $\overrightarrow{D}$
+ is slip at time
+\begin_inset Formula $t$
\end_inset
-, and
-\begin_inset Formula $\overrightarrow{L}$
+,
+\begin_inset Formula $V$
\end_inset
- is the vector of Lagrange multipliers.
- Note that by using the direction cosines to relate the relative motion
- across the fault, the slip vector and Lagrange multipliers (forces required
- to impose the slip) are in the local fault coordinate system (lateral motion,
- reverse motion, and fault opening).
- Because the solution vector now mixes displacements,
-\begin_inset Formula $\overrightarrow{u}$
+ is the slip rate, and
+\begin_inset Formula $t_{r}$
\end_inset
-, and forces,
-\begin_inset Formula $\overrightarrow{L}$
+ is the slip initiation time (time when rupture reaches the location).
+ The slip rate is specified independently for each of the component of slip,
+ and the slip rate and slip starting time may vary over the fault surface.
+\end_layout
+
+\begin_layout Description
+slip_rate Spatial database of slip rate (
+\begin_inset Formula $V)$
\end_inset
-, the matrix on the left-hand side is ill-conditioned.
- In order to improve the conditioning we scale the direction cosines in
- the upper right portion of the matrix by an amount necessary to reduce
- the forces in the solution vector to within a few orders of magnitude of
- the displacements, resulting in
-\begin_inset Formula \begin{equation}
-\left[\begin{array}{cc}
-A & a\underline{C}^{T}\\
-\underline{C} & 0\end{array}\right]\left[\begin{array}{c}
-\overrightarrow{u}\\
-\frac{1}{a}\overrightarrow{L}\end{array}\right]=\left[\begin{array}{c}
-\overrightarrow{b}\\
-\overrightarrow{D}\end{array}\right]\,.\end{equation}
+.
+\end_layout
+\begin_layout Description
+slip_time Spatial database of slip initiation times (
+\begin_inset Formula $t_{r}$
\end_inset
-While the matrix on the left-hand side is now nonsymmetric, the solution
- converges very quickly.
- Future releases of PyLith may use alternative conditioning algorithms to
- retain the symmetry of the matrix, thereby reducing storage requirements.
+).
\end_layout
-\begin_layout Subsubsection
-Slip Time Function
+\begin_layout Standard
+An example of setting these parameters in a
+\family typewriter
+.cfg
+\family default
+ file is:
\end_layout
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.ruptures]
+\end_layout
+
+\begin_layout LyX-Code
+slip_function = pylith.faults.ConstRateSlipFn
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.ruptures.slip_function]
+\end_layout
+
+\begin_layout LyX-Code
+slip_rate.iohandler.filename = slip_rate.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+slip_time.iohandler.filename = sliptime.spatialdb
+\end_layout
+
\begin_layout Standard
-The current release of PyLith supports specification of the evolution of
- fault slip using an analytical expression for the slip time history at
- each point where the parameters for the slip time function may vary over
- the fault surface.
- We use an integral of Brune's far-field time function
+The spatial database files for the slip time function specify the spatial
+ variation in the parameters for the slip time function.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<column alignment="left" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" leftline="true" rightline="true" width="2.5in">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\series bold
+Database
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\series bold
+Value
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\series bold
+Description
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+slip_rate
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+left-lateral-slip
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Slip rate for left-lateral final slip in meters per second.
+ Use negative values for right-lateral slip.
+ Applies to faults in 2D and 3D only.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+reverse-slip
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Slip rate for reverse slip in meters per second.
+ Use negative values for normal slip.
+ Applies to faults in 3D only.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+fault-opening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Slip rate for fault opening in meters per second.
+ Negative values imply penetration.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+slip_time
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\family typewriter
+slip_time
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Slip initiation time (
+\begin_inset Formula $t_{t})$
+\end_inset
+
+ in seconds.
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Caption
+
+\begin_layout Standard
+Values in spatial database used as parameters in the constant slip rate
+ slip time function.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Paragraph
+Brune Slip Time Function
+\end_layout
+
+\begin_layout Standard
+We use an integral of Brune's far-field time function
\begin_inset LatexCommand cite
key "Brune:1970"
@@ -2128,7 +2861,9 @@
\begin_layout Standard
\begin_inset Formula \begin{gather*}
-D(t)=D_{final}(1-e^{-(t-t_{r})/t_{0}}(1+(t-t_{r})/t_{0}))\,,\\
+D(t)=\left\{ \begin{array}{cc}
+0 & t<t_{r}\\
+D_{final}(1-e^{-(t-t_{r})/t_{0}}(1+(t-t_{r})/t_{0})) & t\ge t_{r}\end{array}\right.\,,\\
t_{0}=D/D_{final}eV_{max}\,,\end{gather*}
\end_inset
@@ -2190,10 +2925,18 @@
\end_layout
\begin_layout LyX-Code
-[pylithapp.problem.interfaces.fault.eq_src.slip_function]
+[pylithapp.problem.interfaces.fault.eq_srcs.ruptures]
\end_layout
\begin_layout LyX-Code
+slip_function = pylith.faults.BruneSlipFn
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.interfaces.fault.eq_srcs.rupture.slip_function]
+\end_layout
+
+\begin_layout LyX-Code
slip.iohandler.filename = finalslip.spatialdb
\end_layout
@@ -2205,10 +2948,6 @@
slip_time.iohandler.filename = sliptime.spatialdb
\end_layout
-\begin_layout Subsubsection
-Slip Time Function Spatial Database Files
-\end_layout
-
\begin_layout Standard
The spatial database files for the slip time function specify the spatial
variation in the parameters for the slip time function.
@@ -2294,7 +3033,7 @@
\begin_inset Text
\begin_layout Standard
-Amount of left-lateral final slip.
+Amount of left-lateral final slip in meters.
Use negative values for right-lateral slip.
Applies to faults in 2D and 3D only.
\end_layout
@@ -2327,7 +3066,7 @@
\begin_inset Text
\begin_layout Standard
-Amount of reverse slip.
+Amount of reverse slip in meters.
Use negative values for normal slip.
Applies to faults in 3D only.
\end_layout
@@ -2360,7 +3099,7 @@
\begin_inset Text
\begin_layout Standard
-Amount of fault opening.
+Amount of fault opening in meters.
Negative values imply penetration.
\end_layout
@@ -2398,7 +3137,7 @@
\begin_inset Formula $V_{max})$
\end_inset
-.
+ in meters per second.
\end_layout
\end_inset
@@ -2435,7 +3174,7 @@
\begin_inset Formula $t_{t})$
\end_inset
-.
+ in meters.
\end_layout
\end_inset
@@ -2452,8 +3191,7 @@
\begin_inset Caption
\begin_layout Standard
-Values in spatial database used as parameters in the elastic material constituti
-ve models.
+Values in spatial database used as parameters in the Brune slip time function.
\end_layout
\end_inset
Modified: short/3D/PyLith/trunk/doc/userguide/userguide.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/userguide.lyx 2008-06-13 19:24:24 UTC (rev 12187)
+++ short/3D/PyLith/trunk/doc/userguide/userguide.lyx 2008-06-13 19:44:28 UTC (rev 12188)
@@ -103,7 +103,7 @@
\begin_layout Author
© California Institute of Technology
\newline
-Version 1.1
+Version 1.2
\end_layout
\begin_layout Date
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