Example 4 - Unconformably 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 2963 m wide (W-E extent) and 3715 m high (N-S extent). The vertical model extent varies between 0 m and 1000 m. The model represents several planar stratigraphic units (yellow to light red) dipping towards the west above an unspecified basement (green). The blue and purple unit overlay the remaining strata unconformably and dip to the north. 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_example04.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 and 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/example04/'
gg.download_gemgis_data.download_tutorial_data(filename="example04_unconformably_dipping_layers.zip", dirpath=file_path)

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_example04.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo4.shp')
topo.head()

	id	Z	geometry
0	None	600	LINESTRING (-1.172 334.506, 98.350 346.728, 21...
1	None	500	LINESTRING (1088.333 6.258, 1182.617 58.638, 1...
2	None	200	LINESTRING (2947.824 83.082, 2785.446 201.810,...
3	None	300	LINESTRING (2694.654 8.004, 2549.736 86.574, 2...
4	None	400	LINESTRING (2202.282 2.766, 2032.919 95.304, 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

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, 2963, 0, 3715], 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, 2963)
ax.set_ylim(0, 3715)

(0.0, 3715.0)

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='raster4.tif', extent=[0, 2963, 0, 3715], 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 + 'raster4.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_example04.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces4.shp')
interfaces.head()

	id	formation	geometry
0	None	M	LINESTRING (2320.137 7.131, 2206.647 164.271, ...
1	None	N	LINESTRING (1688.084 5.385, 1677.608 50.781, 1...
2	None	O	LINESTRING (1286.504 1.893, 1314.440 45.543, 1...
3	None	P	LINESTRING (760.957 0.147, 804.607 49.035, 830...
4	None	Y	LINESTRING (8.431 1206.634, 149.857 1281.712, ...

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
193	Z	POINT (1581.578 2671.529)	1581.58	2671.53	663.80
196	Z	POINT (1611.260 2462.009)	1611.26	2462.01	680.92
187	Z	POINT (305.251 1952.176)	305.25	1952.18	742.32
188	Z	POINT (200.491 1885.828)	200.49	1885.83	748.24
189	Z	POINT (81.763 1819.480)	81.76	1819.48	752.76
...	...	...	...	...	...
19	M	POINT (2760.129 1096.636)	2760.13	1096.64	378.75
20	M	POINT (2889.333 1084.414)	2889.33	1084.41	414.59
21	M	POINT (2950.443 1075.684)	2950.44	1075.68	430.87
1	M	POINT (2206.647 164.271)	2206.65	164.27	343.14
0	M	POINT (2320.137 7.131)	2320.14	7.13	375.57

271 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, 2963)
ax.set_ylim(0, 3715)

(0.0, 3715.0)

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_example04.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes4.shp')
strikes

	id	formation	Z	geometry
0	3	Z	700	LINESTRING (532.231 2126.776, 2622.195 2125.030)
1	2	Z	600	LINESTRING (729.529 2846.129, 2660.607 2863.589)
2	1	M	300	LINESTRING (2307.915 1121.080, 2065.220 359.823)
3	2	M	400	LINESTRING (2836.953 1094.890, 2479.023 -125.566)
4	2	N	400	LINESTRING (2019.824 1695.514, 1534.436 356.331)
5	1	N	300	LINESTRING (1466.342 1660.594, 902.383 96.177)
6	2	P	500	LINESTRING (1197.458 1655.356, 738.259 386.013)
7	1	P	400	LINESTRING (516.517 1208.380, 186.523 361.569)
8	3	N	500	LINESTRING (2490.372 1610.833, 1942.127 4.512)
9	1	Z	500	LINESTRING (616.039 3606.513, 2409.183 3614.370)

Calculate Orientations for each formation

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	10.99	286.72	350.00	POINT (2422.278 612.557)	1.00	M	2422.28	612.56

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.17	289.87	350.00	POINT (1480.746 952.154)	1.00	N	1480.75	952.15
1	11.95	289.29	450.00	POINT (1996.690 916.797)	1.00	N	1996.69	916.80

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	11.57	290.32	450.00	POINT (659.689 902.829)	1.00	P	659.69	902.83

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	7.56	359.61	550.00	POINT (1603.840 3232.650)	1.00	Z	1603.84	3232.65
1	7.91	359.79	650.00	POINT (1636.141 2490.381)	1.00	Z	1636.14	2490.38

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_m, orientations_n, orientations_p, orientations_y]).reset_index()
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	10.99	286.72	350.00	POINT (2422.278 612.557)	1.00	M	2422.28	612.56
1	0	11.17	289.87	350.00	POINT (1480.746 952.154)	1.00	N	1480.75	952.15
2	1	11.95	289.29	450.00	POINT (1996.690 916.797)	1.00	N	1996.69	916.80
3	0	11.57	290.32	450.00	POINT (659.689 902.829)	1.00	P	659.69	902.83
4	0	7.56	359.61	550.00	POINT (1603.840 3232.650)	1.00	Z	1603.84	3232.65
5	1	7.91	359.79	650.00	POINT (1636.141 2490.381)	1.00	Z	1636.14	2490.38

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, 2963)
ax.set_ylim(0, 3715)

(0.0, 3715.0)

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('Model4')
geo_model

Model4  2022-04-04 18:59

Initiate Data

gp.init_data(geo_model, [0, 2963, 0, 3715, 0, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model4  2022-04-04 18:59

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Z	Default series	1	#015482	1
1	Y	Default series	2	#9f0052	2
2	P	Default series	3	#ffbe00	3
3	O	Default series	4	#728f02	4
4	N	Default series	5	#443988	5
5	M	Default series	6	#ff3f20	6

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('Z', 'Y'),
                          'Strata2': ('P', 'O', 'N', 'M'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Basement')

	surface	series	order_surfaces	color	id
0	Z	Strata1	1	#015482	1
1	Y	Strata1	2	#9f0052	2
2	P	Strata2	1	#ffbe00	3
3	O	Strata2	2	#728f02	4
4	N	Strata2	3	#443988	5
5	M	Strata2	4	#ff3f20	6
6	Basement	Strata2	5	#5DA629	7

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	Z	Strata1	1	#015482	1	62	2
1	Y	Strata1	2	#9f0052	2	55	0
2	P	Strata2	1	#ffbe00	3	33	1
3	O	Strata2	2	#728f02	4	50	0
4	N	Strata2	3	#443988	5	49	2
5	M	Strata2	4	#ff3f20	6	22	1
6	Basement	Strata2	5	#5DA629	7	0	0

Loading Digital Elevation Model

geo_model.set_topography(source='gdal', filepath=file_path + 'raster4.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([[  14.815     ,   18.575     ,    5.        ],
       [  14.815     ,   18.575     ,   15.        ],
       [  14.815     ,   18.575     ,   25.        ],
       ...,
       [2958.01178451, 3690.03360215,  446.43917847],
       [2958.01178451, 3700.02016129,  445.69622803],
       [2958.01178451, 3710.00672043,  444.99276733]])

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 0x1f8883ae880>

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             4855.99
$C_o$           561442.71
drift equations    [3, 3]

<gempy.core.interpolator.InterpolatorModel at 0x1f88515ab50>

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 0x1f889906940>

Plotting 3D Model

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