Variograms in 3-D¶
This file is meant to demonstrate the use of gstlearn for calculating variograms on 3-D Data.
In [1]:
import numpy as np
import sys
import os
import gstlearn as gl
import gstlearn.plot as gp
import gstlearn.document as gdoc
import gstlearn.plot3D as gop
import matplotlib.pyplot as plt
import plotly.graph_objects as go
gdoc.setNoScroll()
We define the space dimension
In [2]:
ndim = 3
gl.defineDefaultSpace(gl.ESpaceType.RN, ndim)
np.random.seed(3131)
Defining the 2D location of well headers
In [3]:
nwells = 10
nvert = 15
nsamples = nwells * nvert
colar = np.random.uniform(size = (nwells,2))
z = np.random.uniform(size=nvert)
z = np.cumsum(z) / 10
a = np.zeros(shape=(nsamples,4))
for i in range(nwells):
ind = np.arange(nvert)+nvert*i
a[ind,0:2] = colar[i,:]
a[ind,2] = z
for i in range(nsamples):
a[i,3] = np.random.uniform()
Loading this array of values in a Data Base
In [4]:
db = gl.Db.createFromSamples(nsamples, tab=a.flatten(), names=["X","Y","Z","value"],
locatorNames=["x1","x2","x3","z1"])
db
Out[4]:
Data Base Characteristics ========================= Data Base Summary ----------------- File is organized as a set of isolated points Space dimension = 3 Number of Columns = 5 Total number of samples = 150 Variables --------- Column = 0 - Name = rank - Locator = NA Column = 1 - Name = X - Locator = x1 Column = 2 - Name = Y - Locator = x2 Column = 3 - Name = Z - Locator = x3 Column = 4 - Name = value - Locator = z1
In [5]:
db.getExtremas()
Out[5]:
array([[0.2003584 , 0.97446612],
[0.10611527, 0.9628635 ],
[0.05598033, 1.03142542]])
Defining a omnidirectional variogram¶
In [6]:
varioparam = gl.VarioParam.createOmniDirection(npas=10, dpas=0.1)
vario = gl.Vario.computeFromDb(varioparam, db)
In [7]:
vario
Out[7]:
Variogram characteristics
=========================
Number of variable(s) = 1
Number of direction(s) = 1
Space dimension = 3
Variable(s) = [value]
Variance-Covariance Matrix 0.083
Direction #1
------------
Number of lags = 10
Direction coefficients = 1.000 0.000 0.000
Direction angles (degrees) = 0.000 0.000 0.000
Tolerance on direction = 90.000 (degrees)
Calculation lag = 0.100
Tolerance on distance = 50.000 (Percent of the lag value)
For variable 1
Rank Npairs Distance Value
0 73.000 0.029 0.074
1 383.000 0.096 0.088
2 309.000 0.200 0.072
3 956.000 0.307 0.079
4 844.000 0.410 0.080
5 1783.000 0.501 0.082
6 1361.000 0.599 0.084
7 1516.000 0.700 0.082
8 1401.000 0.795 0.088
9 871.000 0.894 0.087
In [8]:
ax = gp.variogram(vario)
ax.decoration(title="OmniDirectional variogram")
Directional variogram¶
Vertical and omnidirectional in horizontal plane¶
We create a vertical direction and one horizontal direction. Note that:
- we use a fine angular tolerance for calulation of the vertical direction
- we use a bench selection for the horizontal calculation to avoid mixing information from samples to far away vertically.
In [9]:
varioparam = gl.VarioParam()
# Omnidirection in horizontal plane
dirhor = gl.DirParam.create(npas=10, dpas=0.1, tolang=90, bench=1)
varioparam.addDir(dirhor)
# Vertical direction
dirvert = gl.DirParam.create(npas=10, dpas=0.1, tolang=0.001, codir=[0,0,1])
varioparam.addDir(dirvert)
# Calculate the variogram in several directions
vario = gl.Vario.computeFromDb(varioparam, db)
In [10]:
vario
Out[10]:
Variogram characteristics
=========================
Number of variable(s) = 1
Number of direction(s) = 2
Space dimension = 3
Variable(s) = [value]
Variance-Covariance Matrix 0.083
Direction #1
------------
Number of lags = 10
Direction coefficients = 1.000 0.000 0.000
Direction angles (degrees) = 0.000 0.000 0.000
Tolerance on direction = 90.000 (degrees)
Slice bench = 1.000
Calculation lag = 0.100
Tolerance on distance = 50.000 (Percent of the lag value)
For variable 1
Rank Npairs Distance Value
0 73.000 0.029 0.074
1 383.000 0.096 0.088
2 309.000 0.200 0.072
3 956.000 0.307 0.079
4 844.000 0.410 0.080
5 1783.000 0.501 0.082
6 1361.000 0.599 0.084
7 1516.000 0.700 0.082
8 1401.000 0.795 0.088
9 871.000 0.894 0.087
Direction #2
------------
Number of lags = 10
Direction coefficients = 0.000 0.000 1.000
Direction angles (degrees) = 0.000 0.000 90.000
Tolerance on direction = 0.001 (degrees)
Calculation lag = 0.100
Tolerance on distance = 50.000 (Percent of the lag value)
For variable 1
Rank Npairs Distance Value
0 20.000 0.022 0.094
1 210.000 0.098 0.088
2 140.000 0.195 0.071
3 180.000 0.298 0.083
4 150.000 0.411 0.080
5 100.000 0.512 0.090
6 80.000 0.603 0.077
7 60.000 0.695 0.084
8 70.000 0.801 0.096
9 30.000 0.905 0.097
In [11]:
ax = gp.variogram(vario, idir=-1, flagLegend=True)
ax.decoration(title="Directional variogram")
Vertical and several directions in horizontal plane¶
In [12]:
varioparam = gl.VarioParam()
# First direction in horizontal plane
dirhor1 = gl.DirParam.create(npas=10, dpas=0.1, tolang=45, bench=1, codir=[1,0,0])
varioparam.addDir(dirhor1)
# Second direction in horizontal plane
dirhor2 = gl.DirParam.create(npas=10, dpas=0.1, tolang=45, bench=1, codir=[0,1,0])
varioparam.addDir(dirhor2)
# Vertical direction
dirvert = gl.DirParam.create(npas=10, dpas=0.1, tolang=0.001, codir=[0,0,1])
varioparam.addDir(dirvert)
# Calculate the variogram in several directions
vario = gl.Vario.computeFromDb(varioparam, db)
In [13]:
ax = gp.variogram(vario, idir=-1, flagLegend=True)
ax.decoration(title="Directional variogram")
