Example 3 - Planar Dipping 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 3000 m wide (W-E extent) and 3740 m high (N-S extent). The vertical model extent varies between 200 m and 1200 m. The model represents several planar stratigraphic units (blue to purple) dipping towards the east above an unspecified basement (light red). 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_example03.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/example03/'
gg.download_gemgis_data.download_tutorial_data(filename="example03_planar_dipping_layers.zip", dirpath=file_path)

Downloading file 'example03_planar_dipping_layers.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample03_planar_dipping_layers.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example03'.

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_example03.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo3.shp')
topo.head()

	id	Z	geometry
0	None	800	LINESTRING (6.948 674.298, 97.151 781.847, 168...
1	None	900	LINESTRING (10.418 291.517, 78.648 414.099, 12...
2	None	1100	LINESTRING (978.357 1207.417, 1009.581 1271.02...
3	None	1000	LINESTRING (834.959 1363.536, 882.373 1447.956...
4	None	1100	LINESTRING (1778.613 2.407, 1712.696 100.704, ...

Interpolating the contour lines

topo_raster = gg.vector.interpolate_raster(gdf=topo, value='Z', method='rbf', res=50)

Plotting the raster

import matplotlib.pyplot as plt

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, 3000, 0, 3740], cmap='gist_earth')
cbar = plt.colorbar(im)
cbar.set_label('Altitude [m]')
ax.set_xlabel('X [m]')
ax.set_ylabel('Y [m]')
ax.set_xlim(0, 3000)
ax.set_ylim(0, 3740)

(0.0, 3740.0)

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 + 'raster3.tif', extent=[0, 3000, 0, 3740], 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 + 'raster3.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_example03.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces3.shp')
interfaces.head()

	id	formation	geometry
0	None	B	LINESTRING (2.323 3499.479, 65.927 3338.734, 1...
1	None	C	LINESTRING (389.730 3730.767, 463.742 3570.022...
2	None	C	LINESTRING (2067.723 2331.475, 2214.591 2427.4...
3	None	D	LINESTRING (2522.204 3256.627, 2393.839 3180.3...
4	None	E	LINESTRING (2389.213 3623.218, 2259.692 3551.5...

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
169	F	POINT (932.100 3354.924)	932.10	3354.92	1214.19
170	F	POINT (914.753 3459.004)	914.75	3459.00	1213.03
181	F	POINT (1630.589 267.231)	1630.59	267.23	1085.09
180	F	POINT (1527.666 276.483)	1527.67	276.48	1101.00
179	F	POINT (1417.804 261.449)	1417.80	261.45	1118.56
...	...	...	...	...	...
17	B	POINT (238.236 761.031)	238.24	761.03	854.53
18	B	POINT (161.911 615.320)	161.91	615.32	870.34
19	B	POINT (83.273 463.826)	83.27	463.83	886.53
20	B	POINT (11.574 307.707)	11.57	307.71	895.69
0	B	POINT (2.323 3499.479)	2.32	3499.48	898.42

339 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, 3000)
ax.set_ylim(0, 3740)

(0.0, 3740.0)

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_example03.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes3.shp')
strikes

	id	formation	Z	geometry
0	2	C	700	LINESTRING (2236.563 2441.337, 2244.658 1935.973)
1	1	C	600	LINESTRING (2752.335 2715.413, 2750.022 1809.921)
2	2	D	800	LINESTRING (2242.924 3096.460, 2290.338 441.276)
3	3	D	900	LINESTRING (1739.873 2780.752, 1758.376 1605.810)
4	4	D	1000	LINESTRING (1236.822 2394.501, 1239.134 1677.509)
5	4	E	1100	LINESTRING (1245.495 953.000, 1236.243 3100.507)
6	3	E	1000	LINESTRING (1749.124 3284.381, 1790.756 364.372)
7	2	E	900	LINESTRING (2242.345 63.698, 2259.692 3551.519)
8	1	F	1000	LINESTRING (2012.214 86.827, 2005.275 3738.862)
9	2	F	1100	LINESTRING (1534.026 272.435, 1499.911 3496.010)
10	1	A	800	LINESTRING (486.292 2124.473, 495.544 1456.051)
11	2	A	900	LINESTRING (2.323 3499.479, 11.574 307.707)
12	5	C	1000	LINESTRING (736.009 2693.445, 761.729 511.476)
13	1	B	800	LINESTRING (489.213 2109.525, 496.562 1470.183)
14	2	B	900	LINESTRING (2.323 3499.479, 11.574 307.707)
15	1	D	700	LINESTRING (2752.631 1310.960, 2747.732 3388.209)
16	1	E	800	LINESTRING (2745.282 835.740, 2750.181 3753.197)
17	3	C	800	LINESTRING (1759.324 1605.522, 1739.727 2783.774)
18	4	C	900	LINESTRING (1238.786 1676.560, 1237.562 2396.739)

Calculate Orientations for each formation

orientations_b = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'B'].sort_values(by='id', ascending=True).reset_index())
orientations_b

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.70	89.81	850.00	POINT (249.918 1846.723)	1.00	B	249.92	1846.72

orientations_c = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'C'].sort_values(by='id', ascending=True).reset_index())
orientations_c

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.19	89.89	650.00	POINT (2495.895 2225.661)	1.00	C	2495.89	2225.66
1	11.52	89.05	750.00	POINT (1995.068 2191.652)	1.00	C	1995.07	2191.65
2	11.12	89.28	850.00	POINT (1493.850 2115.649)	1.00	C	1493.85	2115.65
3	11.52	89.38	950.00	POINT (993.522 1819.555)	1.00	C	993.52	1819.56

orientations_d = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D'].sort_values(by='id', ascending=True).reset_index())
orientations_d

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.82	89.31	750.00	POINT (2508.406 2059.226)	1.00	D	2508.41	2059.23
1	11.12	89.00	850.00	POINT (2007.877 1981.074)	1.00	D	2007.88	1981.07
2	11.11	89.29	950.00	POINT (1493.551 2114.643)	1.00	D	1493.55	2114.64

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.53	90.21	850.00	POINT (2499.375 2051.039)	1.00	E	2499.38	2051.04
1	12.45	89.83	950.00	POINT (2010.479 1815.993)	1.00	E	2010.48	1815.99
2	10.98	89.38	1050.00	POINT (1505.405 1925.565)	1.00	E	1505.40	1925.57

orientations_f = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'F'].sort_values(by='id', ascending=True).reset_index())
orientations_f

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.82	89.67	1050.00	POINT (1762.857 1898.533)	1.00	F	1762.86	1898.53

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_b, orientations_c, orientations_d, orientations_e, orientations_f])
orientations = orientations[orientations['formation'].isin(['F', 'E', 'D', 'C', 'B'])].reset_index()
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	11.70	89.81	850.00	POINT (249.918 1846.723)	1.00	B	249.92	1846.72
1	0	11.19	89.89	650.00	POINT (2495.895 2225.661)	1.00	C	2495.89	2225.66
2	1	11.52	89.05	750.00	POINT (1995.068 2191.652)	1.00	C	1995.07	2191.65
3	2	11.12	89.28	850.00	POINT (1493.850 2115.649)	1.00	C	1493.85	2115.65
4	3	11.52	89.38	950.00	POINT (993.522 1819.555)	1.00	C	993.52	1819.56
5	0	11.82	89.31	750.00	POINT (2508.406 2059.226)	1.00	D	2508.41	2059.23
6	1	11.12	89.00	850.00	POINT (2007.877 1981.074)	1.00	D	2007.88	1981.07
7	2	11.11	89.29	950.00	POINT (1493.551 2114.643)	1.00	D	1493.55	2114.64
8	0	11.53	90.21	850.00	POINT (2499.375 2051.039)	1.00	E	2499.38	2051.04
9	1	12.45	89.83	950.00	POINT (2010.479 1815.993)	1.00	E	2010.48	1815.99
10	2	10.98	89.38	1050.00	POINT (1505.405 1925.565)	1.00	E	1505.40	1925.57
11	0	11.82	89.67	1050.00	POINT (1762.857 1898.533)	1.00	F	1762.86	1898.53

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, 3000)
ax.set_ylim(0, 3740)

(0.0, 3740.0)

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('Model3')
geo_model

Model3  2022-04-04 15:53

Initiate Data

gp.init_data(geo_model, [0, 3000, 0, 3740, 200, 1200], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model3  2022-04-04 15:53

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	F	Default series	1	#015482	1
1	E	Default series	2	#9f0052	2
2	D	Default series	3	#ffbe00	3
3	C	Default series	4	#728f02	4
4	B	Default series	5	#443988	5

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('F'),
                          'Strata2': ('E'),
                          'Strata3': ('D'),
                          'Strata4': ('C'),
                          'Strata5': ('B'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('A')

	surface	series	order_surfaces	color	id
0	F	Strata1	1	#015482	1
1	E	Strata2	1	#9f0052	2
2	D	Strata3	1	#ffbe00	3
3	C	Strata4	1	#728f02	4
4	B	Strata5	1	#443988	5
5	A	Strata5	2	#ff3f20	6

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	F	Strata1	1	#015482	1	45	1
1	E	Strata2	1	#9f0052	2	68	3
2	D	Strata3	1	#ffbe00	3	113	3
3	C	Strata4	1	#728f02	4	77	4
4	B	Strata5	1	#443988	5	21	1
5	A	Strata5	2	#ff3f20	6	0	0

Loading Digital Elevation Model

geo_model.set_topography(source='gdal', filepath=file_path + 'raster3.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([[  15.        ,   18.7       ,  205.        ],
       [  15.        ,   18.7       ,  215.        ],
       [  15.        ,   18.7       ,  225.        ],
       ...,
       [2992.5       , 3702.6       ,  833.75482178],
       [2992.5       , 3717.56      ,  838.74261475],
       [2992.5       , 3732.52      ,  843.78088379]])

Defining Custom Section

custom_section = gpd.read_file(file_path + 'customsection3.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	[15.217892876134727, 1063.5514258527073]	[2991.4655480049296, 1046.4043200206897]	[100, 80]	2976.30

gp.plot.plot_section_traces(geo_model)

<gempy.plot.visualization_2d.Plot2D at 0x1d547775a90>

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 0x1d5431d25e0>

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                    4897.71
$C_o$                  571133.33
drift equations  [3, 3, 3, 3, 3]

<gempy.core.interpolator.InterpolatorModel at 0x1d541724ac0>

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 0x1d545715c70>

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 0x1d54868da30>

Plotting 3D Model

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