Plugin SeismicLab

Description
SeismicLab Plugin
This plugin implement various SeismicLab features. Plugin version: 1.0 Last modified: 2024-04-15 LabRPS version: All Author: Koffi Daniel
Author
Koffi Daniel
Download
None
Features
Horizontal Uniform Distribution, Vertical Uniform Distribution, Uniform Distribution, Grid Points, General Distribution, Import Simulation Points from File, Uniform Random Phases, Uniform Random Phases Import, Double Index Frequency Discretization, Single Index Frequency Discretization, Zerva Frequency Discretization, Cholesky Decomposition
Plugin Version
1.0
Date last modified
2024-04-15
LabRPS Version(s)
All
Default shortcut
None
See also
None

Contents 1 Horizontal Uniform Distribution 1.1 Properties 1.2 Scripting 2 Vertical Uniform Distribution 2.1 Properties 2.2 Scripting 3 Uniform Distribution 3.1 Properties 3.2 Scripting 4 Grid Points 4.1 Properties 4.2 Scripting 5 General Distribution 5.1 Properties 5.2 Scripting 6 Import Simulation Points from File 6.1 Properties 6.2 Scripting 7 Uniform Random Phases 7.1 Properties 7.2 Scripting 8 Uniform Random Phases Import 8.1 Properties 8.2 Scripting 9 Single Index Frequency Discretization 9.1 Scripting 10 Double Index Frequency Discretization 10.1 Scripting 11 Zerva Frequency Discretization 11.1 Scripting 12 Cholesky Decomposition 12.1 Feature Dependency 12.2 Scripting

You can find the source code of this plugin on the following Github repository: Get the code here!. This plugin is one of the official plugins provided by LabRPS. It provides very useful features (tools) for the simulation of seismic ground motion. Plugins are very easy to create in LabRPS, therefore, anyone can develop plugin for any random phenomenon in LabRPS. Go to this page to see how to create new plugin for LabRPS. You can get quick assistance from LabRPS community by sending your concern to the community forum.

Horizontal Uniform Distribution

This feature provides an efficient method to distribute seismic ground motion simulation points uniformly in space. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a horizontal line that is parallel to one of the coordinate system axis. This uniform distribution is critical in certain simulation methods. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

DataFirstPoint: This is a point in 3D space representing the first point the distribution will start from.
DataSpacing: This is the even space between any two adjacent points in the distribution.

Scripting

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy
import LabRPS

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
  
    # check if the simulation sucessfully created
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       return None
  
    featureType = "Horizontal Distribution"
    featureGroup = "Location Distribution"
  
    # create the feature
    newFeature= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not newFeature:
       LabRPS.Console.PrintError("Error on creating the feature.\n")
       return None

    # let's set the first point of the distribution (x =0, y = 0, z = 80m)
    newFeature.FirstPoint = vec(0,0,80000)

    # let's set the spacing (s = 10m)
    newFeature.Spacing = '10m'

    # compute the simulation points coordinates. SeismicLab will internally use the "newFeature" feature.
    simPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(simPoints)

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, simPoints, False)

compute()

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Vertical Uniform Distribution

This feature provides an efficient method to distribute seismic ground motion simulation points uniformly in space. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a vertical line. This uniform distribution is critical in certain simulation methods. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

DataLowestPoint: This is a point in 3D space representing the lowest point the distribution will start from. In many applications, this point should not be lower than 10 meters.
DataSpacing: This is the even space between any two adjacent points in the distribution.

Scripting

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy
import LabRPS

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
  
    # check if the simulation sucessfully created
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       return None
  
    featureType = "Vertical Distribution"
    featureGroup = "Location Distribution"
  
    # create the feature
    newFeature= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not newFeature:
       LabRPS.Console.PrintError("Error on creating the feature.\n")
       return None

    # let's set the first point of the distribution (x =0, y = 0, z = 30m)
    newFeature.LowestPoint  = vec(0,0,30000)

    # let's set the spacing (s = 10m)
    newFeature.Spacing = '10m'

    # compute the simulation points coordinates. SeismicLab will internally use the "newFeature" feature.
    simPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(simPoints)

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, simPoints, False)

compute()

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Uniform Distribution

This feature may be seen as a general form of the horizontal and the vertical distribution features. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a line parallel to one of the coordinate system axis. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

DataFirstPoint: This is a point in 3D space representing the first point the distribution will start from. This should be the lowest point in case the distribution is parallel to the vertical axis and should not be lower than 10 meters in many application.
DataSpacing: This is the even space between any two adjacent points in the distribution.
DataDirection: Its value can be X, Y or Z. This is the axis the points distribution is parallel to.

Scripting

This feature can be used to produce vertical distribution as we did before in the Vertical Distribution feature.

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy
import LabRPS

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
    
    # check if the simulation does really exist
    if not sim:
        LabRPS.Console.PrintError("The simulation does not exist.\n")
        # abord the computation 
  
    featureType = "Uniform Distribution"
    featureGroup = "Location Distribution"
  
    # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
    # case you don't understand the next line)
    unifSimPoints= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not unifSimPoints:
        LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
        # abord the computation

    # set the direction of the distribution to be vertical
    unifSimPoints.Direction= 'Z'

    # let's set the first point of the distribution (x =0, y = 0, z = 30m)
    unifSimPoints.FirstPoint = vec(0,0,30000) # This is the lowest point in this case (Direction = 'Z')

    # let's set the spacing (s = 10m)
    unifSimPoints.Spacing = '10m'

    # compute the simulation points coordinates. SeismicLab will internally use the "unifSimPoints" feature.
    simPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(simPoints)

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, simPoints, False)

compute()

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Grid Points

This feature allows users to generate a set of grid points within a 3D spatial domain, ensuring that the points are evenly distributed in a plane parallel to one of the coordinate system planes (XY Plane, YZ Plane, XZ Plane).

Properties

DataSpacing1: This is the points spacing along one of the axis forming the plane.
DataSpacing2: This is the points spacing along the second axis.
DataLength1: This is the length within points are distributed along one of the axis forming the plane.
DataLength2: This is the length within points are distributed along the second axis.
DataCenterPoint: This is the center of the grid around which the points are generated. It is a 3D point.
DataNumberOfPoints: This is the resulting total number of points in the grid. This is a read only property for internal use. User cannot change its value directly.

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import LabRPS
import numpy
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def compute():
    # get an existing SeismicLab simulation called "Simulation"
    sim = SeismicLab.getSimulation("Simulation")
    
    # check if the simulation does really exist
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       # abord the computation 
  
    featureType = "Grid Points"
    featureGroup = "Location Distribution"
  
    # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
    # case you don't understand the next line)
    unifSimPoints= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not unifSimPoints:
       LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
       # abord the computation

    # set the plan the points grid is parallel to
    unifSimPoints.LocationPlan= 'YZ Plane'

    # let's set the center point of the distribution (x =0, y = 0, z = 0)
    unifSimPoints.CenterPoint = vec(0,0,0) 

    # let's set the spacing1 (s1 = 10m)
    unifSimPoints.Spacing1 = '10m'

    # let's set the spacing2 (s2 = 10m)
    unifSimPoints.Spacing2 = '10m'

    # let's set the length1 (l1 = 200m)
    unifSimPoints.Length1= '200m'

    # let's set the length2 (l2 = 200m)
    unifSimPoints.Length2= '200m'

    # compute the simulation points coordinates. SeismicLab will internally use the "unifSimPoints" feature.
    simPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(simPoints)

    # Example 3D points
    x = arr[:,1]
    y = arr[:,2]
    z = arr[:,3]

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, simPoints, False)

    # Create a figure
    fig = plt.figure()

    # Add 3D axes
    ax = fig.add_subplot(111, projection='3d')

    # Plot points
    ax.scatter(x, y, z, color='blue')

    # Hide all axes and labels
    ax.set_axis_off()

    # Set the title
    ax.set_title('3D Plotting of Points')

    # Show the plot
    plt.show()

compute()

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General Distribution

When the simulation points distribution is more general and does not follow any of the previous uniform distribution, this feature can be used. This feature allows users to input simulation points one by one using their coordinates based on the vector dialog shown below:

File:SeismicLab Tutorial001 Pic005 SeismicLab Feat Locations 2.png

Properties

DataLocations: This is a list holding the simulation points

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import LabRPS
import numpy

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
    
    # check if the simulation does really exist
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       # abord the computation 
  
    featureType = "General Distribution"
    featureGroup = "Location Distribution"
  
    # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
    # case you don't understand the next line)
    genSimPoints= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not genSimPoints:
       LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
       # abord the computation

    # create the simulation points by their coordinates
    v1 = vec(0, 0, 35000)
    v2 = vec(0, 0, 40000)
    v3 = vec(0, 0, 140000)

    # add the points to the locations
    genSimPoints.Locations = [v1, v2, v3]

    # compute the simulation points coordinates. SeismicLab will internally use the "genSimPoints" feature
    simPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(simPoints)

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, simPoints, False)

compute()

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Import Simulation Points from File

When the simulation points are stored in a file, this feature can be used. The feature allows users to import simulation points coordinates from file. Note that, for now only tab separated text file is supported and the file is expected to have number of rows and number of columns which are number of simulation points and four, respectively.

File:SeismicLab Tutorial001 Pic006 SeismicLab Feat Locations 1.png

Properties

DataFilePath: This is the path to the file.

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import LabRPS
import numpy

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
    
    # check if the simulation does really exist
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       # abord the computation 
  
    featureType = "Import Simulation Points from File"
    featureGroup = "Location Distribution"
  
    # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
    # case you don't understand the next line)
    simPoints= SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not simPoints:
       LabRPS.Console.PrintError("Error on creating the simulation points feature.\n")
       # abord the computation

    # set the direction of the distribution to be vertical
    simPoints.FilePath = "D:/Points.txt"

    # compute the simulation points coordinates. SeismicLab will internally use the "simPoints" feature.
    importedSimPoints = sim.computeLocationCoordinateMatrixP3()

    # now you can convert the coordinate matrix to numpy array and use it for any other purposes
    arr = numpy.asarray(importedSimPoints )

    # you can also show the result in a table, pass False as last argument to the function to ask 
    # LabRPS to only show the data without plotting them
    GeneralToolsGui.GeneralToolsPyTool.showArray(sim.getSimulationData().numberOfSpatialPosition, 4, importedSimPoints, False)

compute()

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Uniform Random Phases

In the simulation of seismic ground motion, one common technique is to represent the seismic ground motion as a sum of multiple sinusoidal components in the frequency domain. Each of these components is associated with a random phase, which determines the position of the sine wave relative to time. By assigning uniform random phases to each frequency component, the resulting time series will have random characteristics, while still adhering to the desired spectral properties, such as a specific power spectral density (PSD) or turbulence spectrum. The feature generate [math]\displaystyle{ n }[/math] sequences [math]\displaystyle{ (\phi_{1l}, \phi_{2l}, \phi_{3l},..., \phi_{nl}; l = 1, 2, 3, ..., N) }[/math] of independent random phase angles uniformly distributed over the interval [math]\displaystyle{ [0, 2\pi] }[/math] by default.

Properties

DataMinimumValue: The minimum value that can be generated
DataMaximumValue: The maximum value that can be generated

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing SeismicLab simulation called "Simulation"
 sim = SeismicLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Uniform Random Phases"
 featureGroup = "Randomness Provider"
  
 # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
 # case you don't understand the next line)
 randomness = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not randomness:
     LabRPS.Console.PrintError("Error on creating the randomness feature.\n")
     # abord the computation

 randomness.MinimumValue = 0
 randomness.MaximumValue = 6.28

 # generate random phase angle
 randomnessMatrix = sim.generateRandomMatrixFP()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(randomnessMatrix)

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Uniform Random Phases Import

When the simulation numbers are stored in a file, this feature can be used. The feature allows users to import random numbers from file. Note that, for now only tab separated text file is supported and the file is expected to have number of rows and number of columns which are number of frequency increments and number of simulation points, respectively.

Properties

DataFilePath: This is the path to the file.

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing SeismicLab simulation called "Simulation"
 sim = SeismicLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Uniform Random Phases Import"
 featureGroup = "Randomness Provider"
  
 # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
 # case you don't understand the next line)
 randomness = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not randomness:
     LabRPS.Console.PrintError("Error on creating the randomness feature.\n")
     # abord the computation

 randomness.FilePath = "myfolderpath/myfile.txt"

 # generate random phase angle
  randomnessMatrix = sim.generateRandomMatrixFP()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(randomnessMatrix)

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Single Index Frequency Discretization

This feature allows to discretize continuous frequency according to the following formula:

[math]\displaystyle{ \omega_{l} = l\Delta\omega; \quad l = 1, 2, 3, ..., N }[/math].

where:

[math]\displaystyle{ \Delta\omega }[/math] is the frequency increment,
[math]\displaystyle{ N }[/math] is the number of frequency increments,

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing SeismicLab simulation called "Simulation"
 sim = SeismicLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Single Index Frequency Discretization"
 featureGroup = "Frequency Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
 # case you don't understand the next line)
 frequency = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not frequency:
     LabRPS.Console.PrintError("Error on creating the frequency feature.\n")
     # abord the computation

 # compute the freqency distribution
 frequencyMatrix = sim.computeFrequenciesMatrixFP()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(frequencyMatrix)

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Double Index Frequency Discretization

This feature allows to discretize continuous frequency according to the following formula:

[math]\displaystyle{ \omega_{ml} = (l-1)\Delta\omega + \frac{m}{n}\Delta\omega; \quad m = 1, 2, 3, ..., n; \quad l = 1, 2, 3, ..., N }[/math].

where:

[math]\displaystyle{ \Delta\omega }[/math] is the frequency increment,
[math]\displaystyle{ n }[/math] is the number of simulation points,
[math]\displaystyle{ N }[/math] is the number of frequency increments,

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing SeismicLab simulation called "Simulation"
 sim = SeismicLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Double Index Frequency Discretization"
 featureGroup = "Frequency Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
 # case you don't understand the next line)
 frequency = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not frequency:
     LabRPS.Console.PrintError("Error on creating the frequency feature.\n")
     # abord the computation

 # compute the freqency distribution
 frequencyMatrix = sim.computeFrequenciesMatrixFP()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(frequencyMatrix)

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Zerva Frequency Discretization

This feature allow to discretize continuous frequency according to the following formula:

[math]\displaystyle{ \omega_{l} = (1+\frac{l}{2})\Delta\omega;\quad l = 1, 2, 3, ..., N }[/math],

where:

[math]\displaystyle{ \Delta\omega }[/math] is the frequency increment,
[math]\displaystyle{ N }[/math] is the number of frequency increments,

Scripting

The following script shows how this feature can be created and used.

import SeismicLab
import SeismicLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing SeismicLab simulation called "Simulation"
 sim = SeismicLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Zerva Frequency Discretization"
 featureGroup = "Frequency Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the SeismicLab Workbench page in 
 # case you don't understand the next line)
 frequency = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not frequency:
     LabRPS.Console.PrintError("Error on creating the frequency feature.\n")
     # abord the computation

 # compute the freqency distribution
  frequencyMatrix = sim.computeFrequenciesMatrixFP()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(frequencyMatrix)

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Cholesky Decomposition

This feature performs the Cholesky decomposition of a positive Hermitian power spectrum matrix and returns the lower triangular matrix (L) of the decomposition. The Cholesky decomposition is a numerical method used to decompose a positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. Specifically, for a matrix A, the decomposition is given by:

[math]\displaystyle{ \mathbf{A} = \mathbf{L L}^{*}, }[/math]

[math]\displaystyle{ L_{j,j} = \sqrt{ A_{j,j} - \sum_{k=1}^{j-1} L_{j,k}^*L_{j,k} }, }[/math]

[math]\displaystyle{ L_{i,j} = \frac{1}{L_{j,j}} \left( A_{i,j} - \sum_{k=1}^{j-1} L_{j,k}^* L_{i,k} \right) \quad \text{for } i\gt j. }[/math]

where [math]\displaystyle{ L }[/math] is a lower triangular matrix with real and positive diagonal entries, and [math]\displaystyle{ L^* }[/math] denotes the conjugate transpose of [math]\displaystyle{ L }[/math].

The feature is optimized for performance and can handle large matrices efficiently using [math]\displaystyle{ O(n^3) }[/math] computational complexity in the worst case. It checks if the input matrix is indeed positive-definite and Hermitian before performing the decomposition and raises an error if the matrix does not meet these conditions. The feature belong to the PSD Decomposition Method feature group.

Feature Dependency

The features required by this feature are summarized as follows:

Scripting

The feature can be used from the python console as follows:

import SeismicLab
import GeneralToolsGui
import SeismicLabObjects
from LabRPS import Vector as vec
import LabRPS
import numpy

def compute():
    installResuslt = SeismicLab.installPlugin("SeismicLabPlugin")

    doc = LabRPS.ActiveDocument
    if not doc:
       doc = LabRPS.newDocument()

    # create SeismicLab simulation called "Simulation"
    sim = SeismicLabObjects.makeSimulation(doc, "Simulation")
  
    # check if the simulation sucessfully created
    if not sim:
       LabRPS.Console.PrintError("The simulation does not exist.\n")
       return None
  
    featureType = "Cholesky Decomposition"
    featureGroup = "Spectrum Decomposition Method"
  
    # create the feature
    decomposedPSD = SeismicLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
    # check if the created feature is good
    if not decomposedPSD :
       LabRPS.Console.PrintError("Error on creating the spectrum decomposition method.\n")
       return None
    
    # get the active simulation points feature and compute the simulation points coordinates
    simPoints = sim.computeLocationCoordinateMatrixP3()

    if not simPoints :
       LabRPS.Console.PrintError("Make sure you have an active location disttribution in the simulation with at least 3 simulation points.\n")
       return None

    # use a vector to represent a simulation point based on its coordinates
    v1 = vec(simPoints[0][1], simPoints[0][2], simPoints[0][3])
    v2 = vec(simPoints[1][1], simPoints[1][2], simPoints[1][3])
    v3 = vec(simPoints[2][1], simPoints[2][2], simPoints[2][3])

    # This feature is used to decompose power spectrum matrices which may vary in time. Let's assume that
    # the active power spectrun density function in this example is stationary. Meanning it is not varying in time.
    #Then, we use time instant of 0 second.
    time = 0.0

    # compute the decomposed cross spectrum between points 1 and 3, at time instant of 0 second and for all frequency
    # increments. Note that when the following code is run, SeismicLab will try to identify the active frequency distribution, 
    # the active power spectrum feature, the active coherence function feature and others. If SeismicLab fails to find any 
    # of these dependency features, the computation will fails and specific error messages will be sent to the report view.
    psd13 = sim.computeDecomposedCrossSpectrumVectorF(v1, v3, time)

    # psd13 can be converted to numpy vector and be used for some other purposes.
    arr = numpy.asarray(psd13)

compute()

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Plugin SeismicLab

Horizontal Uniform Distribution

Properties

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Vertical Uniform Distribution

Properties

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Uniform Distribution

Properties

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Grid Points

Properties

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General Distribution

Properties

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Import Simulation Points from File

Properties

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Uniform Random Phases

Properties

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Uniform Random Phases Import

Properties

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Single Index Frequency Discretization

Scripting

Double Index Frequency Discretization

Scripting

Zerva Frequency Discretization

Scripting

Cholesky Decomposition

Feature Dependency

Scripting

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