The slipweak Class

The main class used for creating slip weakening interfaces is the slipweak class.

class fdfault.slipweak(ndim, index, direction, bm, bp)

Class representing a slip weakening frictional interface

This class describes slip weakening friction laws. This is a frictional interface with parameter values. Tractions on the interface are set using load perturbations and load files. Parameter values are set using parameter perturbations (the swparam class) and parameter files (the swparamfile class). Parameters that can be specified include:

• The slip weakening distance \({d_c}\), dc
• The static friction value \({\mu_s}\), mus
• The dynamic friction value \({\mu_d}\), mud
• The frictional cohesion \({c_0}\), c0
• The forced rupture time \({t_{rup}}\), trup
• The characteristic weakening time \({t_c}\), tc

Slip weakening Frictional interfaces have the following attributes:

Variables:

• ndim – Number of dimensions in problem (2 or 3)
• iftype – Type of interface (‘locked’ for all standard interfaces)
• index – index of interface (used for identification purposes only, order is irrelevant in simulation)
• bm – Indices of block in the “minus” direction (tuple of 3 integers)
• bp – Indices of block in the “plus” direction (tuple of 3 integers)
• direction – Normal direction in computational space (“x”, “y”, or “z”)
• nloads – Number of load perturbations (length of loads list)
• loads – List of load perturbations
• lf – Loadfile holding traction at each point
• nperts – Number of parameter perturbations (length of perts list)
• perts – List of parameter perturbations (perturbations must be swparam type)
• pf – Paramfile holding traction at each point

__init__(ndim, index, direction, bm, bp)

Initializes an instance of the slipweak class

Create a new slipweak given an index, direction, and block coordinates.

Parameters:

• ndim (int) – Number of spatial dimensions (must be 2 or 3)
• index (int) – Interface index, used for bookkeeping purposes, must be nonnegative
• direction (str) – String indicating normal direction of interface in computational space, must be 'x', 'y', or 'z', with 'z' only allowed for 3D problems)
• bm (tuple) – Coordinates of block in minus direction (tuple of length 3 of integers)
• bp (tuple) – Coordinates of block in plus direction (tuple of length 3 or integers, must differ from bm by 1 only along the given direction to ensure blocks are neighboring one another)

Returns:

New instance of slipweak class

Return type:

slipweak

add_load(newload)

Adds a load to list of load perturbations

Method adds the load provided to the list of load perturbations. If the newload parameter is not a load perturbation, this will result in an error.

Parameters:newload (fdfault.load) – New load to be added to the interface (must have type load) Returns:None

add_pert(newpert)

Add new friction parameter perturbation to an interface

Method adds a frictional parameter perturbation to an interface. newpert must must have type swparam).

Parameters:newpert (swparam) – New perturbation to be added Returns:None

delete_load(index=-1)

Deletes load at position index from the list of loads

Method deletes the load from the list of loads at position index. Default is most recently added load if an index is not provided. index must be a valid index into the list of loads.

Parameters:index (int) – Position within load list to remove (optional, default is -1) Returns:None

delete_loadfile()

Deletes the loadfile for the interface.

Returns:None

delete_paramfile()

Deletes friction parameter file for the interface

Removes the friction parameter file for the interface. The interface must be a frictional interface that can accept parameter files.

Returns:None

delete_pert(index=-1)

Deletes frictional parameter perturbation from interface

index is an integer that indicates the position within the list of perturbations. Default is most recently added (-1).

Parameters:index (int) – Index within perturbation list of the given interface to remove. Default is last item (-1, or most recently added) Returns:None

get_bm()

Returns block on negative side

Returns tuple of block indices on negative size

Returns:Block indices on negative side (tuple of integers) Return type:tuple

get_bp()

Returns block on positive side

Returns tuple of block indices on positive size

Returns:Block indices on positive side (tuple of integers) Return type:tuple

get_direction()

Returns interface orientation

Returns orientation (string indicating normal direction in computational space).

Returns:Interface orientation in computational space (‘x’, ‘y’, or ‘z’) Return type:str

get_index()

Returns index

Returns the numerical index corresponding to the interface in question. Note that this is just for bookkeeping purposes, the interfaces may be arranged in any order as long as no index is repeated. The code will automatically handle the indices, so this is typically not modified in any way.

Returns:Interface index Return type:int

get_load(index=None)

Returns load at position index

Returns a load from the list of load perturbations at position index. If no index is provided (or None is given), the method returns entire list. index must be a valid list index given the number of loads.

Parameters:index (int or None) – Index within load list (optional, default is None to return full list) Returns:load or list

get_loadfile()

Returns loadfile for interface

Loadfile sets any surface tractions set for the interface. Note that these tractions are added to any any set by the constant initial stress tensor, initial heterogeneous stress, or interface traction perturbations

Returns:Current loadfile for the interface (if the interface does not have a loadfile, returns None) Return type:loadfile or None

get_nloads()

Returns number of load perturbations on the interface

Method returns the number of load perturbations presently in the list of loads.

Returns:Number of load perturbations Return type:int

get_nperts()

Returns number of friction parameter perturbations on interface

Method returns the number of parameter perturbations for the list

Returns:Number of parameter perturbations Return type:int

get_paramfile()

Returns paramfile (holds arrays of heterogeneous friction parameters) for interface. Can return a subtype of paramfile corresponding to any of the specific friction law types.

Returns:Paramfile for this interface Return type:paramfile

get_pert(index=None)

Returns perturbation at position index

Method returns a perturbation from the interface. index is the index into the perturbation list for the particular index. If index is not provided or is None, the method returns the entire list.

Parameters:index (int or None) – Index into the perturbation list for the index in question (optional, if not provided or None, then returns entire list) Returns:pert or list

get_type()

Returns string of interface type

Returns the type of the given interface (“locked”, “frictionless”, “slipweak”, or “stz”)

Returns:Interface type Return type:str

set_index(index)

Sets interface index

Changes value of interface index. New index must be a nonnegative integer

Parameters:index (int) – New value of index (nonnegative integer) Returns:None

set_loadfile(newloadfile)

Sets loadfile for interface

newloadfile is the new loadfile (must have type loadfile). If the index is bad or the loadfile type is not correct, the code will raise an error. Errors can also result if the shape of the loadfile does not match with the interface.

Parameters:newloadfile (loadfile) – New loadfile to be used for the given interface Returns:None

set_paramfile(newparamfile)

Sets paramfile for the interface

Method sets the file holding frictional parameters for the interface.

newparamfile must be a parameter perturbation file of type swparam. Errors can also result if the shape of the paramfile does not match with the interface.

Parameters:newparamfile (swparamfile) – New frictional parameter file Returns:None

write_input(f, probname, directory, endian='=')

Writes interface details to input file

This routine is called for every interface when writing problem data to file. It writes the appropriate section for the interface in the input file. It also writes any necessary binary files holding interface loads, parameters, or state variables.

Parameters:

• f (file) – File handle for input file
• probname (str) – problem name (used for naming binary files)
• directory (str) – Directory for output
• endian (str) – Byte ordering for binary files ('<' little endian, '>' big endian, '=' native, default is native)

Returns:

None

class fdfault.swparam(perttype='constant', t0=0.0, x0=0.0, dx=0.0, y0=0.0, dy=0.0, dc=0.0, mus=0.0, mud=0.0, c0=0.0, trup=0.0, tc=0.0)

Class representing slip weakening parameter perturbations to frictional interfaces

The swparam class represents slip weakening parameter perturbations that can be expressed in a simple functional form. The swparam class holds information on the shape of the perturbation and the six parameter values for the interface.

Perturbations have the following attributes:

Variables:

• perttype – String describing perturbation shape. See available types below.
• t0 – Perturbation onset time (linear ramp function that attains its maximum at t0; t0 = 0. means perturbation is on at all times)
• x0 – Perturbation location along first spatial dimension (see below for details)
• dx – Perturbation scale along first spatial dimension (see below for details)
• y0 – Perturbation location along second spatial dimension (see below for details)
• dy – Perturbation scale along second spatial dimension (see below for details)
• dc – Slip weakening distance perturbation
• mus – Static friction coefficient perturbation
• mud – Dynamic friction coefficient perturbation
• c0 – Frictional Cohesion perturbation
• trup – Rupture time perturbation
• tc – Characteristic weakening time perturbation

By default, all time, shape, and friction parameters are set to zero.

There are several available types of perturbations:

• 'constant' – A spatially uniform perturbation. All spatial information is ignored
• 'boxcar' – Perturbation is constant within a rectangle centered at (x0, y0) with a half width of (dx, dy) in each spatial dimension
• 'ellipse' – Perturbation is constant within an ellipse centered at (x0, y0) with half axis lengths of (x0, y0)
• 'gaussian' – Perturbation follows a Gaussian function centered at (x0, y0) with standard deviations (dx, dy) in each spatial dimension
• 'linear' – Perturbation is a linear function with intercept x0 and slope 1/dx in the first spatial dimension and intercept y0 and slope 1/dy in the second spatial dimension. If either dx or dy is zero, the linear function is constant in that particular spatial dimension (i.e. set dy = 0. if you want to have a function that is only linear in the first spatial dimension)

The shape variables are only interpreted literally for rectangular blocks. If the block is not rectangular, then the shape variables are interpreted as if the block on the negative side were rectangular with the dimensions that are provided when setting up the problem. For example, if you run a problem with a dipping fault that has a trapezoidally shaped block on the minus side of the fault, then x0 and dx would be measured in terms of depth rather than distance along the interface, since the “rectangular” version of the block would have depth along the fault dimension.

If you are in doubt regarding how a perturbation will be interpreted for a particular geometry, it is usually less ambiguous to use a file to set values, as they explicitly set the value at each grid point. However, for some simple forms, perturbations can be more convenient as they use less memory and do not require loading information in parallel from external files.

__init__(perttype='constant', t0=0.0, x0=0.0, dx=0.0, y0=0.0, dy=0.0, dc=0.0, mus=0.0, mud=0.0, c0=0.0, trup=0.0, tc=0.0)

Initialize a new instance of an slip weakening parameter perturbation

Method creates a new instance of a slip weakening parameter perturbation. It calls the superclass routine to initialize the spatial and temporal details of the perturbation, and creates the variables holding the parameter values specific to the slip weakening law. Default values are provided for all arguments (all zeros, with a perttype of 'constant').

Parameters:

• perttype (str) – Perturbation type (string, default is 'constant')
• t0 (float) – Linear ramp time scale (default 0.)
• x0 (float) – Perturbation location along first interface dimension (default 0.)
• dx (float) – Perturbation scale along first interface dimension (default 0.)
• y0 (float) – Perturbation location along second interface dimension (default 0.)
• dy (float) – Perturbation scale along second interface dimension (default 0.)
• dc (float) – Slip weakening distance perturbation (negative in compression, default 0.)
• mus (float) – Static friction coefficient perturbation (default 0.)
• mud (float) – Dynamic friction coefficient perturbation (default 0.)
• c0 (float) – Frictional cohesion perturbation (negative in compression, default 0.)
• trup (float) – Forced rupture time perturbation (default 0.)
• tc (float) – Characteristic weakening time perturbation (default 0.)

Returns:

New instance of slip weakening parameter perturbation

Return type:

swparam

get_c0()

Returns frictional cohesion perturbation

Returns:Frictional cohesion perturbation Return type:float

get_dc()

Returns slip weakening distance perturbation

Returns:Slip weakening distance perturbation Return type:float

get_dx()

Returns perturbation scale along first interface coordinate

Returns:Scale of perturbation along first interface coordinate Return type:float

get_dy()

Returns perturbation scale along second interface coordinate

Returns:Scale of perturbation along second interface coordinate Return type:float

get_mud()

Returns dynamic friction coefficient perturbation

Returns:Dynamic friction coefficient perturbation Return type:float

get_mus()

Returns static friction coefficient perturbation

Returns:Static friction coefficient perturbation Return type:float

get_t0()

Returns onset time

Returns:Perturbation onset time Return type:float

get_tc()

Returns characteristic weakening time perturbation

Returns:Characteristic weakening time perturbation Return type:float

get_trup()

Returns forced rupture time perturbation

Returns:Forced rupture time perturbation Return type:float

get_type()

Returns perturbation type

Returns:Perturbation type Return type:str

get_x0()

Returns perturbation location in first interface coordinate

Returns:Location of perturbation along first interface coordinate Return type:float

get_y0()

Returns perturbation location in second interface coordinate

Returns:Location of perturbation along second interface coordinate Return type:float

set_c0(c0)

Sets frictional cohesion perturbation

Parameters:c0 (float) – New value of frictional cohesion perturbation Returns:None

set_dc(dc)

Sets slip weakening distance perturbation

Parameters:dc (float) – New value of slip weakening distance perturbation Returns:None

set_dx(dx)

Sets first coordinate of perturbation scale

Changes value of perturbation scale for first coordinate direction. New value must be nonnegative.

Parameters:dx (float) – New value of perturbation scale along second coordinate Returns:None

set_dy(dy)

Sets second coordinate of perturbation scale

Changes value of perturbation scale for second coordinate direction. New value must be nonnegative.

Parameters:dy (float) – New value of perturbation scale along second coordinate Returns:None

set_mud(mud)

Sets dynamic friction coefficient perturbation

Parameters:mud (float) – New value of dynamic friction coefficient perturbation Returns:None

set_mus(mus)

Sets static friction coefficient perturbation

Parameters:mus (float) – New value of static friction coefficient perturbation Returns:None

set_t0(t0)

Sets onset time

Changes value of onset time. New value must be nonnegative.

Parameters:t0 (float) – New value of onset time Returns:None

set_tc(tc)

Sets characteristic weakening time perturbation

Parameters:tc (float) – New value of characteristic weakening time perturbation Returns:None

set_trup(trup)

Sets forced rupture time perturbation

Parameters:trup (float) – New value of forced rupture time perturbation Returns:None

set_type(perttype)

Sets perturbation type

Resets the perturbation type to perttype. Note that the new type must be among the valid perturbation types.

Parameters:perttype (str) – New value for perttype, must be a valid perturbation type Returns:None

set_x0(x0)

Sets first coordinate of perturbation location

Parameters:x0 (float) – New value of perturbation location along first coordinate Returns:None

set_y0(y0)

Sets second coordinate of perturbation location

Parameters:x0 (float) – New value of perturbation location along second coordinate Returns:None

write_input(f)

Writes perturbation to input file

Method writes perturbation to input file (input file provided as input)

Parameters:f (file) – Output file to which the perturbation will be written Returns:none

class fdfault.swparamfile(n1, n2, dc, mus, mud, c0, trup, tc)

The swparamfile class is a class for loading heterogeneous friction parameter values from file. It is only used for slip weakening interfaces.

All swparamfile instances contain the following internal parameters:

Variables:

• n1 – Number of grid points along first coordinate direction
• n2 – Number of grid points along the second coordinate direction
• dc – Array holding slip weakening distance perturbation (numpy array with shape (n1,n2))
• mus – Array holding static friction coefficient perturbation (numpy array with shape (n1,n2))
• mud – Array holding dynamic friction coefficient perturbation (numpy array with shape (n1,n2))
• c0 – Array holding frictional cohesion perturbation (numpy array with shape (n1,n2))
• trup – Array holding forced rupture time perturbation (numpy array with shape (n1,n2))
• tc – Array holding characteristic failure time perturbation (numpy array with shape (n1,n2))

swparamfile will also define six numpy array with shape (n1,n2) holding the various friction parameters (slip weakening distance, static friction coefficient, dynamic friction coefficient, frictional cohesion, forced rupture time, and characteristic failure time. Slip weakening parameter files do not include any information about the shape of the boundary, and it is up to the user to ensure that that the parameter values correspond to the coordinates of the interface. However, because parameter files explicitly assign a value to each grid point, there is less ambiguity regarding the final values when compared to perturbations. Depending on the orientation of the interface, the two coordinate directions will have different orientations in space. The first coordinate direction is the \({x}\) direction for \({y}\) and \({z}\) interfaces (for \({x}\) interfaces, the first index is in the \({y}\) direction), and the second coordinate is in the \({z}\) direction except for \({z}\) interfaces, where \({y}\) is the second index}.

When writing swparamfile instances to disk, the code uses numpy to write information to disk in binary format. Byte-ordering can be specified, and should correspond to the byte-ordering on the system where the simulation will be run (default is native).

__init__(n1, n2, dc, mus, mud, c0, trup, tc)

Initialize a new instance of a swparamfile object

Create a new instance of a swparamfile, which is a class describing slip weakening parameter perturbations in a file. Required information is the number of grid points for the interface and one array for each of the six parameter perturbations. All the array shapes must be (n1, n2) or the code will raise an error.

Parameters:

• n1 (int) – Number of grid points along first coordinate direction
• n2 (int) – Number of grid points along the second coordinate direction
• dc (ndarray) – Slip weakening distance perturbation array
• mus (ndarray) – Static friction coefficient perturbation array
• mud (ndarray) – Dynamic friction coefficient perturbation array
• c0 (ndarray) – Frictional cohesion perturbation array
• trup (ndarray) – Forced rupture time perturbation array
• tc (ndarray) – Characteristic weakening time perturbation array

Returns:

New swparamfile instance

Return type:

swparamfile

get_c0(index=None)

Returns frictional cohesion at given indices

Returns frictional cohesion perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into frictional cohesion array (optional, if not provided returns entire array) Returns:Frictional cohesion perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

get_dc(index=None)

Returns slip weakening distance at given indices

Returns slip weakening distance perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into slip weakening distance array (optional, if not provided returns entire array) Returns:Slip weakening distance perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

get_mud(index=None)

Returns dynamic friction coefficient at given indices

Returns dynamic friction coefficient perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into dynamic friction coefficient array (optional, if not provided returns entire array) Returns:Dynamic friction coefficient perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

get_mus(index=None)

Returns static friction coefficient at given indices

Returns static friction coefficient perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into static friction coefficient array (optional, if not provided returns entire array) Returns:Static friction coefficient perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

get_n1()

Returns number of grid points in 1st coordinate direction

Returns:Number of grid points in 1st coordinate direction (\({x}\), except for \({x}\) interfaces, where \({y}\) is the first coordinate direction) Return type:int

get_n2()

Returns number of grid points in 2nd coordinate direction

Returns:Number of grid points in 2nd coordinate direction (\({z}\), except for \({z}\) interfaces, where \({y}\) is the second coordinate direction) Return type:int

get_tc(index=None)

Returns characteristic failure time at given indices

Returns characteristic failure time perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into characteristic failure time array (optional, if not provided returns entire array) Returns:Characteristic failure time perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

get_trup(index=None)

Returns force rupture time at given indices

Returns forced rupture time perturbation at the indices given by index. If no indices are provided, the method returns the entire array.

Parameters:index (float, tuple, or None) – Index into forced rupture time array (optional, if not provided returns entire array) Returns:Static forced rupture time perturbation (either ndarray or float, depending on value of index) Return type:ndarray or float

write(filename, endian='=')

Write perturbation data to file

Parameters:

• filename (str) – Name of binary file to be written
• endian (str) – Byte-ordering for output. Options inclue '=' for native, '<' for little endian, and '>' for big endian. Optional, default is native

Returns:

None