Example 18 - Faulted 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 4022 m wide (W-E extent) and 2761 m high (N-S extent). The vertical model extent varies between 0 m and 1000 m. The model represents folded layers which are cut by a roughly N-S trending fault.

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_example18.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/example18/'
gg.download_gemgis_data.download_tutorial_data(filename="example18_faulted_folded_layers.zip", dirpath=file_path)

Downloading file 'example18_faulted_folded_layers.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample18_faulted_folded_layers.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example18'.

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_example18.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo18.shp')
topo.head()

	id	Z	geometry
0	None	700	LINESTRING (3.286 332.303, 62.614 304.560, 120...
1	None	700	LINESTRING (27.188 946.063, 60.480 983.196, 98...
2	None	500	LINESTRING (1024.228 2750.211, 1101.055 2721.1...
3	None	400	LINESTRING (317.849 2757.466, 375.042 2739.113...
4	None	300	LINESTRING (4.567 2715.638, 60.480 2702.407, 1...

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, 4022, 0, 2761], 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, 4022)
ax.set_ylim(0, 2761)

(0.0, 2761.0)

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 + 'raster18.tif', extent=[0, 4022, 0, 2761], 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 + 'raster18.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_example18.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces18.shp')
interfaces.head()

	id	formation	geometry
0	None	Fault	LINESTRING (2326.868 2757.893, 1812.982 1.522)
1	None	D	LINESTRING (4.567 1721.586, 117.246 1763.414, ...
2	None	C	LINESTRING (3.713 1860.728, 129.197 1896.580, ...
3	None	C	LINESTRING (4.140 279.378, 100.600 258.891, 20...
4	None	D	LINESTRING (4.140 101.823, 100.600 92.433, 196...

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=False)
interfaces_coords = interfaces_coords[interfaces_coords['formation'].isin(['Fault', 'D', 'C', 'B'])]
interfaces_coords.head()

	formation	geometry	X	Y	Z
0	Fault	POINT (2326.868 2757.893)	2326.87	2757.89	396.78
1	Fault	POINT (1812.982 1.522)	1812.98	1.52	645.29
263	D	POINT (3437.014 1929.018)	3437.01	1929.02	488.43
256	D	POINT (3007.638 2177.425)	3007.64	2177.42	371.88
257	D	POINT (3057.575 2147.121)	3057.57	2147.12	390.98

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')
plt.grid()
ax.set_xlabel('X [m]')
ax.set_ylabel('Y [m]')
ax.set_xlim(0, 4022)
ax.set_ylim(0, 2761)

(0.0, 2761.0)

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_example18.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes18.shp')
strikes.head()

	id	formation	Z	geometry
0	1	C2	300	LINESTRING (2391.317 2132.396, 2809.062 2132.076)
1	2	C2	400	LINESTRING (2334.977 1895.513, 3168.227 1897.754)
2	3	C2	500	LINESTRING (3747.308 1638.464, 2608.992 1647.107)
3	1	D2	400	LINESTRING (2393.237 2137.518, 3072.514 2137.838)
4	2	D2	500	LINESTRING (2273.516 1895.513, 3486.738 1900.315)

Calculate Orientations for each formation

orientations_d1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D1'].sort_values(by='Z', ascending=True).reset_index())
orientations_d1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	21.76	180.11	650.00	POINT (2901.894 492.786)	1.00	D1	2901.89	492.79

orientations_d2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D2'].sort_values(by='Z', ascending=True).reset_index())
orientations_d2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	22.69	359.82	450.00	POINT (2806.501 2017.796)	1.00	D2	2806.50	2017.80

orientations_d3 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D3'].sort_values(by='Z', ascending=True).reset_index())
orientations_d3

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0.00	0.00	400.00	POINT (645.350 1647.827)	1.00	D3	645.35	1647.83
1	21.14	0.41	450.00	POINT (507.462 1396.780)	1.00	D3	507.46	1396.78
2	21.96	359.46	550.00	POINT (333.881 1138.690)	1.00	D3	333.88	1138.69

orientations_d4 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D4'].sort_values(by='Z', ascending=True).reset_index())
orientations_d4

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	21.86	180.50	450.00	POINT (2683.258 2522.931)	1.00	D4	2683.26	2522.93

orientations_c1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C1'].sort_values(by='Z', ascending=True).reset_index())
orientations_c1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	22.06	180.54	350.00	POINT (865.026 1893.753)	1.00	C1	865.03	1893.75

orientations_c2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C2'].sort_values(by='Z', ascending=True).reset_index())
orientations_c2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	23.03	359.89	350.00	POINT (2675.896 2014.435)	1.00	C2	2675.90	2014.43
1	21.87	0.23	450.00	POINT (2964.876 1769.710)	1.00	C2	2964.88	1769.71

orientations_c3 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C3'].sort_values(by='Z', ascending=True).reset_index())
orientations_c3

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0.00	0.32	300.00	POINT (812.528 1648.067)	1.00	C3	812.53	1648.07
1	11.14	359.66	350.00	POINT (699.208 1512.340)	1.00	C3	699.21	1512.34
2	23.45	359.84	450.00	POINT (459.445 1139.411)	1.00	C3	459.45	1139.41
3	20.58	180.00	550.00	POINT (278.262 889.083)	1.00	C3	278.26	889.08

orientations_c4 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C4'].sort_values(by='Z', ascending=True).reset_index())
orientations_c4

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	21.54	180.38	350.00	POINT (2575.061 2523.892)	1.00	C4	2575.06	2523.89

orientations_c5 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C5'].sort_values(by='Z', ascending=True).reset_index())
orientations_c5

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	23.45	180.08	650.00	POINT (1102.869 125.938)	1.00	C5	1102.87	125.94

orientations_b1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'B1'].sort_values(by='Z', ascending=True).reset_index())
orientations_b1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	24.55	180.05	450.00	POINT (1590.398 2647.615)	1.00	B1	1590.40	2647.61

orientations_b2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'B2'].sort_values(by='Z', ascending=True).reset_index())
orientations_b2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.29	0.26	450.00	POINT (1321.745 502.309)	1.00	B2	1321.74	502.31

orientations_fault = gpd.read_file(file_path + 'orientations18_fault.shp')
orientations_fault = gg.vector.extract_xyz(gdf=orientations_fault, dem=topo_raster)
orientations_fault

	formation	dip	azimuth	polarity	geometry	X	Y	Z
0	Fault	90.00	280.00	1.00	POINT (1918.192 566.731)	1918.19	566.73	490.30
1	Fault	90.00	280.00	1.00	POINT (2190.927 2031.561)	2190.93	2031.56	255.41

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_fault, orientations_d1, orientations_d2, orientations_d3, orientations_d4, orientations_c1, orientations_c2, orientations_c3[:-1], orientations_c4, orientations_c5, orientations_b1, orientations_b2]).reset_index()
orientations['formation'] = ['Fault', 'Fault', 'D', 'D', 'D', 'D', 'D', 'D', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'B', 'B']
orientations = orientations[orientations['formation'].isin(['Fault', 'D', 'C', 'B'])]
orientations

	index	formation	dip	azimuth	polarity	geometry	X	Y	Z
0	0	Fault	90.00	280.00	1.00	POINT (1918.192 566.731)	1918.19	566.73	490.30
1	1	Fault	90.00	280.00	1.00	POINT (2190.927 2031.561)	2190.93	2031.56	255.41
2	0	D	21.76	180.11	1.00	POINT (2901.894 492.786)	2901.89	492.79	650.00
3	0	D	22.69	359.82	1.00	POINT (2806.501 2017.796)	2806.50	2017.80	450.00
4	0	D	0.00	0.00	1.00	POINT (645.350 1647.827)	645.35	1647.83	400.00
5	1	D	21.14	0.41	1.00	POINT (507.462 1396.780)	507.46	1396.78	450.00
6	2	D	21.96	359.46	1.00	POINT (333.881 1138.690)	333.88	1138.69	550.00
7	0	D	21.86	180.50	1.00	POINT (2683.258 2522.931)	2683.26	2522.93	450.00
8	0	C	22.06	180.54	1.00	POINT (865.026 1893.753)	865.03	1893.75	350.00
9	0	C	23.03	359.89	1.00	POINT (2675.896 2014.435)	2675.90	2014.43	350.00
10	1	C	21.87	0.23	1.00	POINT (2964.876 1769.710)	2964.88	1769.71	450.00
11	0	C	0.00	0.32	1.00	POINT (812.528 1648.067)	812.53	1648.07	300.00
12	1	C	11.14	359.66	1.00	POINT (699.208 1512.340)	699.21	1512.34	350.00
13	2	C	23.45	359.84	1.00	POINT (459.445 1139.411)	459.45	1139.41	450.00
14	0	C	21.54	180.38	1.00	POINT (2575.061 2523.892)	2575.06	2523.89	350.00
15	0	C	23.45	180.08	1.00	POINT (1102.869 125.938)	1102.87	125.94	650.00
16	0	B	24.55	180.05	1.00	POINT (1590.398 2647.615)	1590.40	2647.61	450.00
17	0	B	11.29	0.26	1.00	POINT (1321.745 502.309)	1321.74	502.31	450.00

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, 4022)
ax.set_ylim(0, 2761)

(0.0, 2761.0)

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('Model18')
geo_model

Model18  2022-04-05 11:12

Initiate Data

gp.init_data(geo_model, [0, 4022, 0, 2761, 0, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model18  2022-04-05 11:12

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Fault	Default series	1	#015482	1
1	D	Default series	2	#9f0052	2
2	C	Default series	3	#ffbe00	3
3	B	Default series	4	#728f02	4

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Fault1': ('Fault'),
                          'Strata1': ('D', 'C', 'B'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('A')
geo_model.set_is_fault(['Fault1'])

Fault colors changed. If you do not like this behavior, set change_color to False.

	order_series	BottomRelation	isActive	isFault	isFinite
Fault1	1	Fault	True	True	False
Strata1	2	Erosion	True	False	False

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	Fault	Fault1	1	#527682	1	2	2
1	D	Strata1	1	#9f0052	2	125	6
2	C	Strata1	2	#ffbe00	3	137	8
3	B	Strata1	3	#728f02	4	108	2
4	A	Strata1	4	#443988	5	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster18.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([[  20.11      ,   13.805     ,    5.        ],
       [  20.11      ,   13.805     ,   15.        ],
       [  20.11      ,   13.805     ,   25.        ],
       ...,
       [4016.99751244, 2735.99094203,  715.64483643],
       [4016.99751244, 2745.99456522,  716.50982666],
       [4016.99751244, 2755.99818841,  717.38183594]])

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 0x1e57957d130>

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:  1
Compilation Done!
Kriging values:
                    values
range             4979.92
$C_o$           590466.79
drift equations    [3, 3]

<gempy.core.interpolator.InterpolatorModel at 0x1e578a9eb20>

Computing Model

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

Plotting Cross Sections

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 0x1e57c2d2d90>

Plotting 3D Model

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