Example 26 - Unconformable 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 1022 m wide (W-E extent) and 1172 m high (N-S extent). The model represents unconformable folded layers.

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: Unknown

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/cover_example26.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, 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 form 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/example26/'
gg.download_gemgis_data.download_tutorial_data(filename="example26_unconformable_folded_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_example26.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo26.shp')
topo['Z'] = topo['Z']*0.5
topo.head()

	id	Z	geometry
0	None	50.00	LINESTRING (1.874 31.940, 31.950 34.114, 67.10...
1	None	100.00	LINESTRING (2.961 153.696, 32.675 153.696, 65....
2	None	350.00	LINESTRING (924.099 1.864, 942.217 14.546, 974...
3	None	300.00	LINESTRING (844.378 1.139, 873.367 23.606, 899...
4	None	250.00	LINESTRING (793.284 1.864, 816.113 29.766, 834...

Interpolating the contour lines

topo_raster = gg.vector.interpolate_raster(gdf=topo, value='Z', method='rbf', res=5)

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 = ax.imshow(topo_raster, origin='lower', extent=[0,1022,0,1172], 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]')

Text(94.3788293897884, 0.5, 'Y [m]')

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 as raster is already provided with the example data.

gg.raster.save_as_tiff(raster=topo_raster, path=file_path + 'raster26.tif', extent=[0,1022,0,1172], 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 + 'raster26.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_example26.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces26.shp')
interfaces.head()

	id	formation	geometry
0	None	Limestone	LINESTRING (341.774 722.613, 381.997 720.438, ...
1	None	Limestone	LINESTRING (890.761 2.226, 914.315 24.330, 945...
2	None	Claystone	LINESTRING (765.744 0.777, 796.546 20.707, 833...
3	None	Claystone	LINESTRING (2.236 722.975, 34.487 765.010, 62....

Extracting XY coordinates 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.head()

	formation	geometry	X	Y	Z
0	Limestone	POINT (341.774 722.613)	341.77	722.61	338.52
54	Limestone	POINT (287.057 496.133)	287.06	496.13	312.83
62	Limestone	POINT (92.828 466.781)	92.83	466.78	329.27
61	Limestone	POINT (110.946 459.896)	110.95	459.90	328.27
60	Limestone	POINT (132.688 453.011)	132.69	453.01	325.96

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()
plt.xlabel('X [m]')
plt.ylabel('Y [m]')
plt.xlim(0,1022)
plt.ylim(0,1172)

(0.0, 1172.0)

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_example26.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes26.shp')
strikes['Z'] = strikes['Z']*0.5
strikes

	id	formation	Z	geometry
0	2	Limestone2	350.00	LINESTRING (208.061 655.212, 205.887 509.540)
1	1	Limestone2	350.00	LINESTRING (750.887 734.208, 750.887 632.021)
2	4	Claystone1	300.00	LINESTRING (953.088 757.400, 950.914 613.178)
3	3	Claystone1	250.00	LINESTRING (823.361 895.099, 821.911 464.607)
4	2	Limestone1	350.00	LINESTRING (962.510 24.693, 963.235 0.052)
5	1	Limestone1	350.00	LINESTRING (1009.618 51.508, 1009.618 2.226)
6	2	Claystone1	200.00	LINESTRING (712.476 909.594, 707.403 296.468)
7	1	Claystone1	150.00	LINESTRING (587.097 917.566, 576.226 147.898)
8	1	Claystone2	150.00	LINESTRING (387.070 1070.485, 385.621 221.096)
9	2	Claystone2	200.00	LINESTRING (202.988 919.016, 199.364 287.047)
10	3	Claystone2	250.00	LINESTRING (16.006 744.355, 12.382 374.740)
11	1	Claystone3	250.00	LINESTRING (822.636 462.433, 821.187 34.114)
12	2	Claystone3	300.00	LINESTRING (951.639 606.655, 955.987 85.570)

Calculate Orientations for each formation

orientations_claystone1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Claystone1'].sort_values(by='Z', ascending=True).reset_index())
orientations_claystone1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	21.73	270.68	175.00	POINT (645.801 567.882)	1.00	Claystone1	645.80	567.88
1	24.25	270.38	225.00	POINT (766.288 641.442)	1.00	Claystone1	766.29	641.44
2	21.26	270.26	275.00	POINT (887.319 682.571)	1.00	Claystone1	887.32	682.57

orientations_claystone2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Claystone2'].sort_values(by='Z', ascending=True).reset_index())
orientations_claystone2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	15.22	90.18	175.00	POINT (293.761 624.411)	1.00	Claystone2	293.76	624.41
1	15.05	90.39	225.00	POINT (107.685 581.289)	1.00	Claystone2	107.68	581.29

orientations_claystone3 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Claystone3'].sort_values(by='Z', ascending=True).reset_index())
orientations_claystone3

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	21.01	269.79	275.00	POINT (887.862 297.193)	1.00	Claystone3	887.86	297.19

orientations_limestone1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Limestone1'].sort_values(by='Z', ascending=True).reset_index())
orientations_limestone1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0.00	88.32	350.00	POINT (986.245 19.620)	1.00	Limestone1	986.24	19.62

orientations_limestone2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Limestone2'].sort_values(by='Z', ascending=True).reset_index())
orientations_limestone2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0.00	90.86	350.00	POINT (478.930 632.745)	1.00	Limestone2	478.93	632.75

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_claystone1, orientations_claystone2, orientations_claystone3, orientations_limestone1, orientations_limestone2]).reset_index()
orientations['formation'] = ['Claystone', 'Claystone', 'Claystone', 'Claystone', 'Claystone', 'Claystone', 'Limestone', 'Limestone']
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	21.73	270.68	175.00	POINT (645.801 567.882)	1.00	Claystone	645.80	567.88
1	1	24.25	270.38	225.00	POINT (766.288 641.442)	1.00	Claystone	766.29	641.44
2	2	21.26	270.26	275.00	POINT (887.319 682.571)	1.00	Claystone	887.32	682.57
3	0	15.22	90.18	175.00	POINT (293.761 624.411)	1.00	Claystone	293.76	624.41
4	1	15.05	90.39	225.00	POINT (107.685 581.289)	1.00	Claystone	107.68	581.29
5	0	21.01	269.79	275.00	POINT (887.862 297.193)	1.00	Claystone	887.86	297.19
6	0	0.00	88.32	350.00	POINT (986.245 19.620)	1.00	Limestone	986.24	19.62
7	0	0.00	90.86	350.00	POINT (478.930 632.745)	1.00	Limestone	478.93	632.75

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()
plt.xlabel('X [m]')
plt.ylabel('Y [m]')
plt.xlim(0,1022)
plt.ylim(0,1172)

(0.0, 1172.0)

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('Model26')
geo_model

Model26  2022-04-11 08:40

Initiate Data

gp.init_data(geo_model, [0,1022,0,1172,0,900], [100,100,100],
             surface_points_df = interfaces_coords[interfaces_coords['Z']!=0],
             orientations_df = orientations,
             default_values=True)

Active grids: ['regular']

Model26  2022-04-11 08:40

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Limestone	Default series	1	#015482	1
1	Claystone	Default series	2	#9f0052	2

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('Limestone'),
                          'Strata2': ('Claystone')
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Sandstone')

	surface	series	order_surfaces	color	id
0	Limestone	Strata1	1	#015482	1
1	Claystone	Strata2	1	#9f0052	2
2	Sandstone	Strata2	2	#ffbe00	3

Adding additional Orientations

geo_model.add_orientations(X=250, Y=1000, Z=300, surface='Limestone', orientation = [0,0,1])
geo_model.add_orientations(X=750, Y=1000, Z=300, surface='Limestone', orientation = [0,0,1])
geo_model.add_orientations(X=250, Y=200, Z=300, surface='Limestone', orientation = [0,0,1])
geo_model.add_orientations(X=750, Y=200, Z=300, surface='Limestone', orientation = [0,0,1])
geo_model.add_orientations(X=500, Y=50, Z=100, surface='Claystone', orientation = [0,0,1])
geo_model.add_orientations(X=500, Y=600, Z=350, surface='Claystone', orientation = [0,0,1])
geo_model.add_orientations(X=500, Y=1000, Z=150, surface='Claystone', orientation = [0,0,1])

	X	Y	Z	G_x	G_y	G_z	smooth	surface
6	986.24	19.62	350.00	0.00	0.00	1.00	0.01	Limestone
7	478.93	632.75	350.00	0.00	0.00	1.00	0.01	Limestone
8	250.00	1000.00	300.00	0.00	0.00	1.00	0.01	Limestone
9	750.00	1000.00	300.00	0.00	0.00	1.00	0.01	Limestone
10	250.00	200.00	300.00	0.00	0.00	1.00	0.01	Limestone
11	750.00	200.00	300.00	0.00	0.00	1.00	0.01	Limestone
0	645.80	567.88	175.00	-0.37	0.00	0.93	0.01	Claystone
1	766.29	641.44	225.00	-0.41	0.00	0.91	0.01	Claystone
2	887.32	682.57	275.00	-0.36	0.00	0.93	0.01	Claystone
3	293.76	624.41	175.00	0.26	-0.00	0.96	0.01	Claystone
4	107.68	581.29	225.00	0.26	-0.00	0.97	0.01	Claystone
5	887.86	297.19	275.00	-0.36	-0.00	0.93	0.01	Claystone
12	500.00	50.00	100.00	0.00	0.00	1.00	0.01	Claystone
13	500.00	600.00	350.00	0.00	0.00	1.00	0.01	Claystone
14	500.00	1000.00	150.00	0.00	0.00	1.00	0.01	Claystone

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	Limestone	Strata1	1	#015482	1	85	6
1	Claystone	Strata2	1	#9f0052	2	90	9
2	Sandstone	Strata2	2	#ffbe00	3	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster26.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([[   5.11      ,    5.86      ,    4.5       ],
       [   5.11      ,    5.86      ,   13.5       ],
       [   5.11      ,    5.86      ,   22.5       ],
       ...,
       [1019.49509804, 1159.4248927 ,   76.11084747],
       [1019.49509804, 1164.45493562,   73.8138504 ],
       [1019.49509804, 1169.48497854,   71.72492218]])

Defining Custom Section

custom_section = gpd.read_file(file_path + 'customsection26.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	[3.685512376796794, 1168.3245583161138]	[1018.3144876418132, 2.95070672600923]	[100, 80]	1545.18

gp.plot.plot_section_traces(geo_model)

<gempy.plot.visualization_2d.Plot2D at 0x1f10c056a90>

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 0x1f107c86250>

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            1796.68
$C_o$           76858.76
drift equations   [3, 3]

<gempy.core.interpolator.InterpolatorModel at 0x1f10600b7c0>

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 0x1f108e93040>

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 0x1f108ff1c70>

Plotting 3D Model

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