Example 5 - 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 3942 m wide (W-E extent) and 2710 m high (N-S extent). The vertical extent varies between -200 m and 1000 m. The model represents two folded layers (purple and blue) above a basement (yellow). 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_example05.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/example05/'
gg.download_gemgis_data.download_tutorial_data(filename="example05_folded_layers.zip", dirpath=file_path)

Downloading file 'example05_folded_layers.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample05_folded_layers.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example05'.

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_example05.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo5.shp')
topo.head()

	id	Z	geometry
0	None	700	LINESTRING (1.537 2299.193, 29.191 2272.378, 7...
1	None	600	LINESTRING (81.145 2708.127, 130.586 2641.927,...
2	None	600	LINESTRING (6.565 403.682, 56.006 360.945, 103...
3	None	600	LINESTRING (3278.040 2.289, 3308.208 32.456, 3...
4	None	600	LINESTRING (2258.218 1964.001, 2375.536 1953.1...

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, 3942, 0, 2710], 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, 3942)
ax.set_ylim(0, 2710)

(0.0, 2710.0)

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 + 'raster5.tif', extent=[0, 3942, 0, 2710], 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 + 'raster5.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_example05.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces5.shp')
interfaces.head()

	id	formation	geometry
0	None	A	LINESTRING (591.475 2.289, 609.073 69.327, 643...
1	None	A	LINESTRING (3448.150 3.127, 3500.105 128.824, ...
2	None	B	LINESTRING (265.501 1.451, 290.641 89.439, 317...
3	None	B	LINESTRING (2284.196 1.451, 2264.084 109.550, ...
4	None	B	LINESTRING (3480.832 2222.937, 3450.664 2140.8...

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

	formation	geometry	X	Y	Z
94	B	POINT (412.148 639.154)	412.15	639.15	538.20
129	B	POINT (2204.588 299.772)	2204.59	299.77	578.98
120	B	POINT (345.109 2463.437)	345.11	2463.44	588.11
121	B	POINT (412.986 2520.420)	412.99	2520.42	547.54
122	B	POINT (456.561 2560.643)	456.56	2560.64	518.60
...	...	...	...	...	...
61	A	POINT (1643.141 1228.254)	1643.14	1228.25	436.22
62	A	POINT (1606.270 1157.864)	1606.27	1157.86	419.63
63	A	POINT (1569.399 1074.066)	1569.40	1074.07	402.09
64	A	POINT (1537.555 1003.675)	1537.56	1003.68	390.91
0	A	POINT (591.475 2.289)	591.48	2.29	641.21

188 rows × 5 columns

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, 3942)
ax.set_ylim(0, 2710)

(0.0, 2710.0)

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_example05.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes5.shp')
strikes

	id	formation	Z	geometry
0	2	B1	700	LINESTRING (149.860 2191.094, 154.888 1214.846)
1	1	B1	600	LINESTRING (319.551 2436.622, 321.855 916.106)
2	3	A1	700	LINESTRING (481.281 2067.910, 488.404 1433.140)
3	2	A1	600	LINESTRING (636.098 2326.846, 655.529 174.023)
4	1	A1	500	LINESTRING (807.413 2426.933, 822.287 456.422)
5	2	A2	500	LINESTRING (1725.629 2204.030, 1737.885 473.391)
6	1	A2	400	LINESTRING (1556.253 2469.041, 1567.356 648.529)
7	1	B2	400	LINESTRING (1890.816 1193.007, 1900.453 810.050)
8	2	B2	500	LINESTRING (2062.183 564.521, 2056.317 1437.278)
9	3	B2	600	LINESTRING (2216.791 1955.150, 2236.483 196.648)
10	2	B3	500	LINESTRING (2056.527 1437.278, 2055.479 2190.203)
11	3	B3	600	LINESTRING (2216.581 1954.312, 2220.352 1718.839)
12	1	B3	400	LINESTRING (1877.199 2407.659, 1890.816 1192.692)
13	1	B4	200	LINESTRING (3799.212 1567.165, 3810.106 1043.427)
14	2	B4	300	LINESTRING (3636.644 1737.275, 3642.509 847.340)
15	3	B4	400	LINESTRING (3469.048 1945.932, 3469.886 688.961)
16	3	A	600	LINESTRING (3487.483 96.509, 3487.902 1969.395)
17	2	A	500	LINESTRING (3647.118 355.445, 3637.063 1740.627)
18	1	A	400	LINESTRING (3808.639 548.600, 3790.413 1580.992)

Calculate Orientations for each formation

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	33.31	89.37	450.00	POINT (3720.808 1056.416)	1.00	A	3720.81	1056.42
1	33.83	89.86	550.00	POINT (3564.892 1040.494)	1.00	A	3564.89	1040.49

orientations_a1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'A1'].sort_values(by='Z', ascending=True).reset_index())
orientations_a1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	30.57	89.52	550.00	POINT (730.331 1346.056)	1.00	A1	730.33	1346.06
1	32.70	89.47	650.00	POINT (565.328 1500.480)	1.00	A1	565.33	1500.48

orientations_a2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'A2'].sort_values(by='Z', ascending=True).reset_index())
orientations_a2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	30.80	269.62	450.00	POINT (1646.781 1448.748)	1.00	A2	1646.78	1448.75

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	30.99	89.85	650.00	POINT (236.538 1689.667)	1.00	B1	236.54	1689.67

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	31.99	269.44	450.00	POINT (1977.443 1001.214)	1.00	B2	1977.44	1001.21
1	31.03	269.41	550.00	POINT (2142.944 1038.399)	1.00	B2	2142.94	1038.40

orientations_b3 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'B3'].sort_values(by='Z', ascending=True).reset_index())
orientations_b3

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	30.70	269.51	450.00	POINT (1970.005 1806.958)	1.00	B3	1970.01	1806.96
1	31.88	269.85	550.00	POINT (2137.235 1825.158)	1.00	B3	2137.23	1825.16

orientations_b4 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'B4'].sort_values(by='Z', ascending=True).reset_index())
orientations_b4

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	31.77	89.41	250.00	POINT (3722.118 1298.802)	1.00	B4	3722.12	1298.80
1	30.84	89.85	350.00	POINT (3554.522 1304.877)	1.00	B4	3554.52	1304.88

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_a, orientations_a1, orientations_a2, orientations_b1, orientations_b2, orientations_b3, orientations_b4]).reset_index()
orientations['formation'] = ['A', 'A', 'A', 'A', 'A', 'B', 'B', 'B', 'B', 'B', 'B', 'B']
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	33.31	89.37	450.00	POINT (3720.808 1056.416)	1.00	A	3720.81	1056.42
1	1	33.83	89.86	550.00	POINT (3564.892 1040.494)	1.00	A	3564.89	1040.49
2	0	30.57	89.52	550.00	POINT (730.331 1346.056)	1.00	A	730.33	1346.06
3	1	32.70	89.47	650.00	POINT (565.328 1500.480)	1.00	A	565.33	1500.48
4	0	30.80	269.62	450.00	POINT (1646.781 1448.748)	1.00	A	1646.78	1448.75
5	0	30.99	89.85	650.00	POINT (236.538 1689.667)	1.00	B	236.54	1689.67
6	0	31.99	269.44	450.00	POINT (1977.443 1001.214)	1.00	B	1977.44	1001.21
7	1	31.03	269.41	550.00	POINT (2142.944 1038.399)	1.00	B	2142.94	1038.40
8	0	30.70	269.51	450.00	POINT (1970.005 1806.958)	1.00	B	1970.01	1806.96
9	1	31.88	269.85	550.00	POINT (2137.235 1825.158)	1.00	B	2137.23	1825.16
10	0	31.77	89.41	250.00	POINT (3722.118 1298.802)	1.00	B	3722.12	1298.80
11	1	30.84	89.85	350.00	POINT (3554.522 1304.877)	1.00	B	3554.52	1304.88

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, 3942)
ax.set_ylim(0, 2710)

(0.0, 2710.0)

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('Model5')
geo_model

Model5  2022-04-04 20:51

Initiate Data

gp.init_data(geo_model, [0, 3942, 0, 2710, -200, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model5  2022-04-04 20:51

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	B	Default series	1	#015482	1
1	A	Default series	2	#9f0052	2

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('A', 'B'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Basement')

	surface	series	order_surfaces	color	id
0	B	Strata1	1	#015482	1
1	A	Strata1	2	#9f0052	2
2	Basement	Strata1	3	#ffbe00	3

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	B	Strata1	1	#015482	1	101	7
1	A	Strata1	2	#9f0052	2	87	5
2	Basement	Strata1	3	#ffbe00	3	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster5.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([[  19.71      ,   13.55      , -194.        ],
       [  19.71      ,   13.55      , -182.        ],
       [  19.71      ,   13.55      , -170.        ],
       ...,
       [3937.01012658, 2685.        ,  182.10906982],
       [3937.01012658, 2695.        ,  181.02072144],
       [3937.01012658, 2705.        ,  179.95965576]])

Defining Custom Section

custom_section = gpd.read_file(file_path + 'customsection5.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	[6.565213969151387, 963.4523850507635]	[3931.665030709532, 366.8103975359992]	[100, 80]	3970.19

gp.plot.plot_section_traces(geo_model)

<gempy.plot.visualization_2d.Plot2D at 0x2388552d640>

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 0x238870ec850>

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            4931.88
$C_o$           579130.1
drift equations      [3]

<gempy.core.interpolator.InterpolatorModel at 0x238855398e0>

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 0x2388ccabf40>

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 0x2388cff4ee0>

Plotting 3D Model

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