This file is meant to demonstrate the use of gstlearn for calculating variograms on 3-D Data.
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
ndim = 3
gl.defineDefaultSpace(gl.ESpaceType.RN, ndim)
np.random.seed(3131)
Defining the 2D location of well headers
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
db = gl.Db.createFromSamples(nsamples, tab=a.flatten(), names=["X","Y","Z","value"],
locatorNames=["x1","x2","x3","z1"])
db
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
db.getExtremas()
array([[0.2003584 , 0.97446612], [0.10611527, 0.9628635 ], [0.05598033, 1.03142542]])
varioparam = gl.VarioParam.createOmniDirection(npas=10, dpas=0.1)
vario = gl.Vario.computeFromDb(varioparam, db)
vario
Variogram characteristics ========================= Number of variable(s) = 1 Number of direction(s) = 1 Space dimension = 3 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
ax = gp.variogram(vario)
ax.decoration(title="OmniDirectional variogram")
We create a vertical direction and one horizontal direction. Note that:
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)
vario
Variogram characteristics ========================= Number of variable(s) = 1 Number of direction(s) = 2 Space dimension = 3 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
ax = gp.variogram(vario, idir=-1, flagLegend=True)
ax.decoration(title="Directional variogram")
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)
ax = gp.variogram(vario, idir=-1, flagLegend=True)
ax.decoration(title="Directional variogram")