Example 17 - Three Point Problem and Folded Layers

This example will show how to convert the geological map below using GemGIS to a GemPy model. This example is based on digitized data. The area is 3892 m wide (W-E extent) and 2683 m high (N-S extent). The model represents a coal seam that was encountered at the surface and in boreholes. A second coal seam is located 300 m vertically above the first one. The vertical model extent varies between 0 m and 1000 m.

The map has been georeferenced with QGIS. The stratigraphic boundaries were digitized in QGIS. Strikes lines were digitized in QGIS as well and will be used to calculate orientations for the GemPy model. The contour lines were also digitized and will be interpolated with GemGIS to create a topography for the model.

Map Source: An Introduction to Geological Structures and Maps by G.M. Bennison

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/cover_example17.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

Licensing

Computational Geosciences and Reservoir Engineering, RWTH Aachen University, Authors: Alexander Juestel. For more information contact: alexander.juestel(at)rwth-aachen.de

This work is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/)

Import GemGIS

If you have installed GemGIS via pip or conda, you can import GemGIS like any other package. If you have downloaded the repository, append the path to the directory where the GemGIS repository is stored and then import GemGIS.

import warnings
warnings.filterwarnings("ignore")
import gemgis as gg

Importing Libraries and loading Data

All remaining packages can be loaded in order to prepare the data and to construct the model. The example data is downloaded from an external server using pooch. It will be stored in a data folder in the same directory where this notebook is stored.

import geopandas as gpd
import rasterio

file_path = 'data/example17/'
gg.download_gemgis_data.download_tutorial_data(filename="example17_three_point_problem.zip", dirpath=file_path)

Downloading file 'example17_three_point_problem.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample17_three_point_problem.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example17'.

Creating Digital Elevation Model from Contour Lines

The digital elevation model (DEM) will be created by interpolating contour lines digitized from the georeferenced map using the SciPy Radial Basis Function interpolation wrapped in GemGIS. The respective function used for that is gg.vector.interpolate_raster().

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/dem_example17.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo17.shp')
topo.head()

	id	Z	geometry
0	None	600	LINESTRING (399.582 9.701, 373.041 104.254, 35...
1	None	900	LINESTRING (3680.737 2.651, 3702.716 47.854, 3...
2	None	800	LINESTRING (3390.857 3.480, 3398.322 17.995, 3...
3	None	700	LINESTRING (2564.763 4.725, 2631.530 33.339, 2...
4	None	800	LINESTRING (1224.018 1463.246, 1211.577 1384.4...

Interpolating the contour lines

topo_raster = gg.vector.interpolate_raster(gdf=topo, value='Z', method='rbf', res=10)

Plotting the raster

import matplotlib.pyplot as plt

from mpl_toolkits.axes_grid1 import make_axes_locatable

fix, ax = plt.subplots(1, figsize=(10, 10))
topo.plot(ax=ax, aspect='equal', column='Z', cmap='gist_earth')
im = plt.imshow(topo_raster, origin='lower', extent=[0, 3892, 0, 2683], cmap='gist_earth')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
cbar = plt.colorbar(im, cax=cax)
cbar.set_label('Altitude [m]')
ax.set_xlabel('X [m]')
ax.set_ylabel('Y [m]')
ax.set_xlim(0, 3892)
ax.set_ylim(0, 2683)

(0.0, 2683.0)

Saving the raster to disc

After the interpolation of the contour lines, the raster is saved to disc using gg.raster.save_as_tiff(). The function will not be executed as a raster is already provided with the example data.

gg.raster.save_as_tiff(raster=topo_raster, path=file_path + 'raster17.tif', extent=[0, 3892, 0, 2683], crs='EPSG:4326', overwrite_file=True)

Opening Raster

The previously computed and saved raster can now be opened using rasterio.

topo_raster = rasterio.open(file_path + 'raster17.tif')

Interface Points of stratigraphic boundaries

The interface points will be extracted from LineStrings digitized from the georeferenced map using QGIS. It is important to provide a formation name for each layer boundary. The vertical position of the interface point will be extracted from the digital elevation model using the GemGIS function gg.vector.extract_xyz(). The resulting GeoDataFrame now contains single points including the information about the respective formation.

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/interfaces_example17.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces17.shp')
interfaces.head()

	id	formation	geometry
0	None	Coal	LINESTRING (117.997 870.009, 159.675 952.743, ...
1	None	Nodules	LINESTRING (4.782 1414.932, 21.578 1466.563, 3...
2	None	Nodules	LINESTRING (974.572 2678.334, 1047.353 2644.74...
3	None	Coal	LINESTRING (1643.286 1185.393, 1675.011 1087.1...
4	None	Coal	LINESTRING (2798.761 137.845, 2842.927 113.585...

Extracting Z coordinate from Digital Elevation Model

interfaces_coords = gg.vector.extract_xyz(gdf=interfaces, dem=topo_raster)
interfaces_coords = interfaces_coords.sort_values(by='formation', ascending=True)
interfaces_coords.head()

	formation	geometry	X	Y	Z
0	Coal	POINT (117.997 870.009)	118.00	870.01	583.24
141	Coal	POINT (3095.794 190.409)	3095.79	190.41	703.05
140	Coal	POINT (3054.116 161.483)	3054.12	161.48	705.77
139	Coal	POINT (2999.064 127.892)	2999.06	127.89	708.86
138	Coal	POINT (2956.764 103.010)	2956.76	103.01	710.91

points = gpd.read_file(file_path + 'points17.shp')
points

	id	formation	Z	geometry
0	None	Coal	500	POINT (1191.049 1286.166)
1	None	Coal	400	POINT (1215.931 871.875)
2	None	Coal	400	POINT (541.619 659.753)

points_coords = gg.vector.extract_xy(gdf=points)
points_coords

	formation	Z	geometry	X	Y
0	Coal	500.00	POINT (1191.049 1286.166)	1191.05	1286.17
1	Coal	400.00	POINT (1215.931 871.875)	1215.93	871.87
2	Coal	400.00	POINT (541.619 659.753)	541.62	659.75

import pandas as pd

interfaces_coords = pd.concat([interfaces_coords, points_coords])
interfaces_coords = interfaces_coords[interfaces_coords['formation'].isin(['Coal', 'Nodules'])].reset_index()
interfaces_coords.head()

	index	formation	geometry	X	Y	Z
0	0	Coal	POINT (117.997 870.009)	118.00	870.01	583.24
1	141	Coal	POINT (3095.794 190.409)	3095.79	190.41	703.05
2	140	Coal	POINT (3054.116 161.483)	3054.12	161.48	705.77
3	139	Coal	POINT (2999.064 127.892)	2999.06	127.89	708.86
4	138	Coal	POINT (2956.764 103.010)	2956.76	103.01	710.91

Creating data for the coal seam 300 m heigher

interfaces_coal300 = interfaces_coords[interfaces_coords['formation']=='Coal']
interfaces_coal300['Z'] = interfaces_coal300['Z']+300
interfaces_coal300['formation'] = 'Coal300'
interfaces_coal300

	index	formation	geometry	X	Y	Z
0	0	Coal300	POINT (117.997 870.009)	118.00	870.01	883.24
1	141	Coal300	POINT (3095.794 190.409)	3095.79	190.41	1003.05
2	140	Coal300	POINT (3054.116 161.483)	3054.12	161.48	1005.77
3	139	Coal300	POINT (2999.064 127.892)	2999.06	127.89	1008.86
4	138	Coal300	POINT (2956.764 103.010)	2956.76	103.01	1010.91
...	...	...	...	...	...	...
64	1	Coal300	POINT (159.675 952.743)	159.68	952.74	892.40
65	7	Coal300	POINT (468.216 1355.837)	468.22	1355.84	906.89
169	0	Coal300	POINT (1191.049 1286.166)	1191.05	1286.17	800.00
170	1	Coal300	POINT (1215.931 871.875)	1215.93	871.87	700.00
171	2	Coal300	POINT (541.619 659.753)	541.62	659.75	700.00

69 rows × 6 columns

Merging the interface data

interfaces_coords = pd.concat([interfaces_coal300, interfaces_coords])
interfaces_coords = interfaces_coords[interfaces_coords['formation'].isin(['Coal300', 'Coal', 'Nodules'])].reset_index()
interfaces_coords.head()

	level_0	index	formation	geometry	X	Y	Z
0	0	0	Coal300	POINT (117.997 870.009)	118.00	870.01	883.24
1	1	141	Coal300	POINT (3095.794 190.409)	3095.79	190.41	1003.05
2	2	140	Coal300	POINT (3054.116 161.483)	3054.12	161.48	1005.77
3	3	139	Coal300	POINT (2999.064 127.892)	2999.06	127.89	1008.86
4	4	138	Coal300	POINT (2956.764 103.010)	2956.76	103.01	1010.91

Plotting the Interface Points

fig, ax = plt.subplots(1, figsize=(10, 10))

interfaces.plot(ax=ax, column='formation', legend=True, aspect='equal')
interfaces_coords.plot(ax=ax, column='formation', legend=True, aspect='equal')
points_coords.plot(ax=ax, column='formation', legend=False, aspect='equal')
plt.grid()
ax.set_xlabel('X [m]')
ax.set_ylabel('Y [m]')
ax.set_xlim(0, 3892)
ax.set_ylim(0, 2683)

(0.0, 2683.0)

Orientations from Strike Lines

Strike lines connect outcropping stratigraphic boundaries (interfaces) of the same altitude. In other words: the intersections between topographic contours and stratigraphic boundaries at the surface. The height difference and the horizontal difference between two digitized lines is used to calculate the dip and azimuth and hence an orientation that is necessary for GemPy. In order to calculate the orientations, each set of strikes lines/LineStrings for one formation must be given an id number next to the altitude of the strike line. The id field is already predefined in QGIS. The strike line with the lowest altitude gets the id number 1, the strike line with the highest altitude the the number according to the number of digitized strike lines. It is currently recommended to use one set of strike lines for each structural element of one formation as illustrated.

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/orientations_example17.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes17.shp')
strikes.head()

	id	formation	Z	geometry
0	2	Coal2	800	LINESTRING (3799.965 1421.775, 3474.006 1008.728)
1	1	Coal2	700	LINESTRING (3158.000 249.816, 4109.750 1469.052)
2	1	Coal1	500	LINESTRING (1793.202 564.267, 1911.393 443.898)
3	2	Coal1	600	LINESTRING (1667.546 1093.328, 2477.467 175.791)
4	1	Nodules	500	LINESTRING (2038.915 1418.665, 2585.083 789.763)

Calculate Orientations for each formation

orientations_coal1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Coal1'].sort_values(by='Z', ascending=True).reset_index())
orientations_coal1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	22.04	228.51	550.00	POINT (1962.402 569.321)	1.00	Coal1	1962.40	569.32

orientations_coal2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Coal2'].sort_values(by='Z', ascending=True).reset_index())
orientations_coal2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	24.93	128.01	750.00	POINT (3635.430 1037.343)	1.00	Coal2	3635.43	1037.34

orientations_nodules = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Nodules'].sort_values(by='Z', ascending=True).reset_index())
orientations_nodules

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	10.45	228.04	550.00	POINT (2395.977 1421.931)	1.00	Nodules	2395.98	1421.93

orientations_coal3 = gg.vector.calculate_orientation_for_three_point_problem(gdf=points)
orientations_coal3['Z'] = orientations_coal3['Z'].astype(float)
orientations_coal3['azimuth'] = orientations_coal3['azimuth'].astype(float)
orientations_coal3['dip'] = orientations_coal3['dip'].astype(float)
orientations_coal3['dip'] = 180 - orientations_coal3['dip']
orientations_coal3['azimuth'] = 180 - orientations_coal3['azimuth']
orientations_coal3['polarity'] = orientations_coal3['polarity'].astype(float)
orientations_coal3['X'] = orientations_coal3['X'].astype(float)
orientations_coal3['Y'] = orientations_coal3['Y'].astype(float)
orientations_coal3

	Z	formation	azimuth	dip	polarity	X	Y	geometry
0	433.33	Coal	197.46	13.95	1.00	982.87	939.26	POINT (982.867 939.265)

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_coal1, orientations_coal2, orientations_coal3, orientations_nodules]).reset_index()
orientations['formation'] = ['Coal', 'Coal', 'Coal', 'Nodules']
orientations = orientations[orientations['formation'].isin(['Coal', 'Nodules'])]
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	22.04	228.51	550.00	POINT (1962.402 569.321)	1.00	Coal	1962.40	569.32
1	0	24.93	128.01	750.00	POINT (3635.430 1037.343)	1.00	Coal	3635.43	1037.34
2	0	13.95	197.46	433.33	POINT (982.867 939.265)	1.00	Coal	982.87	939.26
3	0	10.45	228.04	550.00	POINT (2395.977 1421.931)	1.00	Nodules	2395.98	1421.93

Plotting the Orientations

fig, ax = plt.subplots(1, figsize=(10, 10))

interfaces.plot(ax=ax, column='formation', legend=True, aspect='equal')
interfaces_coords.plot(ax=ax, column='formation', legend=True, aspect='equal')
orientations.plot(ax=ax, color='red', aspect='equal')
plt.grid()
ax.set_xlabel('X [m]')
ax.set_ylabel('Y [m]')
ax.set_xlim(0, 3892)
ax.set_ylim(0, 2683)

(0.0, 2683.0)

GemPy Model Construction

The structural geological model will be constructed using the GemPy package.

import gempy as gp

WARNING (theano.configdefaults): g++ not available, if using conda: `conda install m2w64-toolchain`
WARNING (theano.configdefaults): g++ not detected ! Theano will be unable to execute optimized C-implementations (for both CPU and GPU) and will default to Python implementations. Performance will be severely degraded. To remove this warning, set Theano flags cxx to an empty string.
WARNING (theano.tensor.blas): Using NumPy C-API based implementation for BLAS functions.

Creating new Model

geo_model = gp.create_model('Model17')
geo_model

Model17  2022-04-05 11:11

Initiate Data

gp.init_data(geo_model, [0, 3892, 0, 2683, 0, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model17  2022-04-05 11:11

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Coal300	Default series	1	#015482	1
1	Coal	Default series	2	#9f0052	2
2	Nodules	Default series	3	#ffbe00	3

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('Coal300', 'Coal', 'Nodules'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Basement')

	surface	series	order_surfaces	color	id
0	Coal300	Strata1	1	#015482	1
1	Coal	Strata1	2	#9f0052	2
2	Nodules	Strata1	3	#ffbe00	3
3	Basement	Strata1	4	#728f02	4

Showing the Number of Data Points

gg.utils.show_number_of_data_points(geo_model=geo_model)

	surface	series	order_surfaces	color	id	No. of Interfaces	No. of Orientations
0	Coal300	Strata1	1	#015482	1	69	0
1	Coal	Strata1	2	#9f0052	2	69	3
2	Nodules	Strata1	3	#ffbe00	3	103	1
3	Basement	Strata1	4	#728f02	4	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster17.tif')

Cropped raster to geo_model.grid.extent.
depending on the size of the raster, this can take a while...
storing converted file...
Active grids: ['regular' 'topography']

Grid Object. Values:
array([[  19.46      ,   13.415     ,    5.        ],
       [  19.46      ,   13.415     ,   15.        ],
       [  19.46      ,   13.415     ,   25.        ],
       ...,
       [3886.99742931, 2657.97201493,  594.15032959],
       [3886.99742931, 2667.98320896,  593.5199585 ],
       [3886.99742931, 2677.99440299,  592.91101074]])

Defining Custom Section

custom_section = gpd.read_file(file_path + 'customsection17.shp')
custom_section_dict = gg.utils.to_section_dict(custom_section, section_column='name')
geo_model.set_section_grid(custom_section_dict)

Active grids: ['regular' 'topography' 'sections']

	start	stop	resolution	dist
Section1	[6.648494638704051, 1585.9987115807176]	[3888.2970423641327, 402.8423753990243]	[100, 80]	4057.96

gp.plot.plot_section_traces(geo_model)

<gempy.plot.visualization_2d.Plot2D at 0x18708b29ac0>

Plotting Input Data

gp.plot_2d(geo_model, direction='z', show_lith=False, show_boundaries=False)
plt.grid()

gp.plot_3d(geo_model, image=False, plotter_type='basic', notebook=True)

<gempy.plot.vista.GemPyToVista at 0x187073560a0>

Setting the Interpolator

gp.set_interpolator(geo_model,
                    compile_theano=True,
                    theano_optimizer='fast_compile',
                    verbose=[],
                    update_kriging=False
                    )

Compiling theano function...
Level of Optimization:  fast_compile
Device:  cpu
Precision:  float64
Number of faults:  0
Compilation Done!
Kriging values:
                    values
range             4831.79
$C_o$           555860.79
drift equations       [3]

<gempy.core.interpolator.InterpolatorModel at 0x18706891c70>

Computing Model

sol = gp.compute_model(geo_model, compute_mesh=True)

Plotting Cross Sections

gp.plot_2d(geo_model, section_names=['Section1'], show_topography=True, show_data=False)

<gempy.plot.visualization_2d.Plot2D at 0x1870b8fa760>

gp.plot_2d(geo_model, direction=['x', 'x', 'y', 'y'], cell_number=[25, 75, 25, 75], show_topography=True, show_data=False)

<gempy.plot.visualization_2d.Plot2D at 0x187089cd670>

Plotting 3D Model

gpv = gp.plot_3d(geo_model, image=False, show_topography=True,
                 plotter_type='basic', notebook=True, show_lith=True)