Variography¶

Introduction¶

Libraries¶

In [1]:

import plotly.io as pio
pio.renderers.default = 'sphinx_gallery'

import plotly.io as pio pio.renderers.default = 'sphinx_gallery'

GeoLime package can be imported as such:

In [2]:

import geolime as geo

import geolime as geo

Data¶

Data used in this tutorial are coming from the Walker Lake Dataset, introduced by Isaaks and Srivastava and used in many geostatistical examples.

In [3]:

data = geo.datasets.load("walker_lake/walker_lake_sample.csv")

data = geo.datasets.load("walker_lake/walker_lake_sample.csv")

In [4]:

data.head()

data.head()

Out[4]:

	x	y	z	v	u	t
0	11.0	8.0	0.0	0.0	NaN	2
1	8.0	30.0	0.0	0.0	NaN	2
2	9.0	48.0	0.0	224.4	NaN	2
3	8.0	69.0	0.0	434.4	NaN	2
4	9.0	90.0	0.0	412.1	NaN	2

GeoLime PointCloud are created from coordinates (XYZ) and an object name.

In [5]:

point_cloud = geo.PointCloud('WalkerLake', data[['x', 'y', 'z']])

point_cloud = geo.PointCloud('WalkerLake', data[['x', 'y', 'z']])

Properties are added in the same fashion. The v property is added to the PointClound in order to perform experimental variography.

In [6]:

point_cloud.set_property('V', data['v'])

point_cloud.set_property('V', data['v'])

Experimental variography¶

Definition of lags and lag tolerance¶

Creation of 10 lags of 20 meters with a lag tolerance of 50%.

In [7]:

lags, tol = geo.generate_lags(20, 50, 10)

lags, tol = geo.generate_lags(20, 50, 10)

In [8]:

lags

lags

Out[8]:

array([  0.,  20.,  40.,  60.,  80., 100., 120., 140., 160., 180.])

In [9]:

tol

tol

Out[9]:

10.0

VarioMap of the V property, using 20 different azimuth to compute the values and an angular tolerance of 20 degrees.

VarioMap¶

In [10]:

geo.vario_map(
    geo_object=point_cloud,
    attribute='V',
    region=None,
    lags=lags,
    tol=tol,
    n_az=20,
    atol=20
)

geo.vario_map( geo_object=point_cloud, attribute='V', region=None, lags=lags, tol=tol, n_az=20, atol=20 )

VarioContour¶

VarioContour compute the same results but displays it in a continuous form, allowing to better distinguish the trends.

In [11]:

geo.vario_contour(
    geo_object=point_cloud,
    attribute='V',
    region=None,
    lags=lags,
    tol=tol,
    n_az=20,
    atol=20
)

geo.vario_contour( geo_object=point_cloud, attribute='V', region=None, lags=lags, tol=tol, n_az=20, atol=20 )

1D Semi Variogram¶

Once major trends have been identified on the variomap, 1D semi-variogram is computed to determine an approximating theoretical model.

In [12]:

vario_exp_160_major = geo.variogram(
    object=point_cloud,
    attribute='V',
    region=None,
    geographic_azimuth=160,
    dip=0,
    pitch=0,
    lags=lags,
    tol=tol,
    atol=45
)

vario_exp_160_major = geo.variogram( object=point_cloud, attribute='V', region=None, geographic_azimuth=160, dip=0, pitch=0, lags=lags, tol=tol, atol=45 )

In [13]:

vario_exp_160_minor = geo.variogram(
    object=point_cloud,
    attribute='V',
    region=None,
    geographic_azimuth=70,
    dip=0,
    pitch=0,
    lags=lags,
    tol=tol,
    atol=45
)

vario_exp_160_minor = geo.variogram( object=point_cloud, attribute='V', region=None, geographic_azimuth=70, dip=0, pitch=0, lags=lags, tol=tol, atol=45 )

In [14]:

geo.plot_semivariogram(
    variograms=[vario_exp_160_major, vario_exp_160_minor], 
    display_npairs=True
)

geo.plot_semivariogram( variograms=[vario_exp_160_major, vario_exp_160_minor], display_npairs=True )

Fitting A Model¶

A theoretical model is created and can be plotted on top of the experimental variogram.

Theorethical model available in GeoLime are :

• Nugget
• Spherical
• Gaussian
• Exponential

Create a Model¶

In [15]:

model = (
    7000 * geo.Nugget(dimension=2) 
    + 88000 * geo.Spherical(
        dimension=2, 
        metric=geo.Metric(angles=160,scales=[70,30])
    )
)

model = ( 7000 * geo.Nugget(dimension=2) + 88000 * geo.Spherical( dimension=2, metric=geo.Metric(angles=160,scales=[70,30]) ) )

GeoLime Metric Object allows users to specify anisotropy in geostatistics algorithm. It enables users to directly input geologist angles (Azimuth, Dip & Pitch) as angles for the anisotropic scales.

Plotting Model on top of 1D Semi Variogram¶

In [16]:

geo.plot_semivariogram(
    variograms=[vario_exp_160_major, vario_exp_160_minor], 
    model=model,
    model_angles=[{"azi":160.,"dip":0.,"pitch":0.}, {"azi":70.,"dip":0.,"pitch":0.}]
)

geo.plot_semivariogram( variograms=[vario_exp_160_major, vario_exp_160_minor], model=model, model_angles=[{"azi":160.,"dip":0.,"pitch":0.}, {"azi":70.,"dip":0.,"pitch":0.}] )

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Last update: 2023-10-13