Example 16 - Unconformal 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 3968 m wide (W-E extent) and 2731 m high (N-S extent). The model represents folded and faulted layers (red, yellow, green) as well as layers separated by an unconfirmity (light red to light green) above an unspecified basement (light blue). The vertical model extent varies between 0 m and 1000 m.

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_example16.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/example16/'
gg.download_gemgis_data.download_tutorial_data(filename="example16_all_features.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_example16.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo16.shp')
topo.head()

	id	Z	geometry
0	None	200	LINESTRING (1.591 265.171, 32.840 230.967, 79....
1	None	200	LINESTRING (2.436 851.918, 33.473 889.712, 73....
2	None	100	LINESTRING (1.803 2469.855, 62.188 2493.502, 1...
3	None	200	LINESTRING (2.014 2215.436, 17.849 2238.028, 6...
4	None	900	LINESTRING (3559.448 2.095, 3595.764 16.875, 3...

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, 3968, 0, 2731], 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, 3968)
ax.set_ylim(0, 2731)

(0.0, 2731.0)

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 + 'raster16.tif', extent=[0, 3968, 0, 2731], 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 + 'raster16.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_example16.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces16.shp')
interfaces.head()

	id	formation	geometry
0	None	Fault	LINESTRING (1401.636 2725.330, 1370.388 2586.8...
1	None	H	LINESTRING (3403.207 2406.937, 3334.799 2401.8...
2	None	G	LINESTRING (3290.883 2728.708, 3235.987 2687.3...
3	None	D	LINESTRING (3461.481 1326.764, 3425.165 1298.0...
4	None	D	LINESTRING (2837.362 1560.703, 2908.304 1494.8...

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

	formation	geometry	X	Y	Z
351	H	POINT (3476.260 416.767)	3476.26	416.77	699.70
44	H	POINT (3711.466 1652.758)	3711.47	1652.76	664.07
359	H	POINT (3109.728 291.774)	3109.73	291.77	747.18
358	H	POINT (3185.737 288.818)	3185.74	288.82	745.14
357	H	POINT (3244.855 294.308)	3244.86	294.31	734.68

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, 3968)
ax.set_ylim(0, 2731)

(0.0, 2731.0)

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_example16.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes16.shp')
strikes.head()

	id	formation	Z	geometry
0	1	Fault2	300	LINESTRING (1369.455 2575.828, 1108.966 1461.029)
1	2	Fault2	400	LINESTRING (1331.187 2325.368, 1176.529 1650.260)
2	1	Fault1	400	LINESTRING (1021.872 873.278, 846.365 36.387)
3	2	Fault1	500	LINESTRING (973.575 482.148, 931.611 286.847)
4	2	B4	300	LINESTRING (92.345 2105.786, 115.570 1859.812)

Calculate Orientations for each formation

orientations_f1 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Fault1'].sort_values(by='Z', ascending=True).reset_index())
orientations_f1

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	72.24	281.86	450.00	POINT (943.356 419.665)	1.00	Fault1	943.36	419.67

orientations_f2 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Fault2'].sort_values(by='Z', ascending=True).reset_index())
orientations_f2

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	78.84	283.09	350.00	POINT (1246.534 2003.121)	1.00	Fault2	1246.53	2003.12

orientations_f3 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'Fault3'].sort_values(by='Z', ascending=True).reset_index())
orientations_f3

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	72.65	281.34	350.00	POINT (1084.157 1262.429)	1.00	Fault3	1084.16	1262.43

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	20.35	85.12	250.00	POINT (347.292 491.913)	1.00	B1	347.29	491.91

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	21.95	265.66	350.00	POINT (2029.784 1223.500)	1.00	B2	2029.78	1223.50

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	0.00	85.61	400.00	POINT (2282.355 1220.333)	1.00	B3	2282.36	1220.33

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	21.87	85.18	250.00	POINT (230.639 1970.923)	1.00	B4	230.64	1970.92

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	22.48	85.96	250.00	POINT (585.612 498.643)	1.00	C1	585.61	498.64

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	22.41	264.42	350.00	POINT (1784.602 1228.779)	1.00	C2	1784.60	1228.78
1	0.00	0.00	400.00	POINT (2032.159 1240.391)	1.00	C2	2032.16	1240.39

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	11.47	85.21	450.00	POINT (2406.530 1229.571)	1.00	C3	2406.53	1229.57
1	0.00	0.00	500.00	POINT (2284.863 1233.002)	1.00	C3	2284.86	1233.00

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	22.59	265.72	350.00	POINT (1723.636 2004.441)	1.00	C4	1723.64	2004.44
1	22.15	265.73	450.00	POINT (1968.554 2021.331)	1.00	C4	1968.55	2021.33

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	21.62	85.70	250.00	POINT (475.557 1973.562)	1.00	C5	475.56	1973.56

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	24.97	86.28	350.00	POINT (837.128 468.952)	1.00	D1	837.13	468.95

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	0.00	85.37	400.00	POINT (3288.420 1212.416)	1.00	D2	3288.42	1212.42
1	11.25	0.00	450.00	POINT (3159.890 1219.542)	1.00	D2	3159.89	1219.54

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	22.81	266.11	450.00	POINT (1481.621 1955.879)	1.00	D3	1481.62	1955.88

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	0.00	265.65	400.00	POINT (1283.945 1251.212)	1.00	D4	1283.94	1251.21
1	11.48	0.00	450.00	POINT (1407.460 1235.905)	1.00	D4	1407.46	1235.90

orientations_d5 = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation'] == 'D5'].sort_values(by='Z', ascending=True).reset_index())
orientations_d5

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	23.00	84.84	350.00	POINT (735.783 1952.448)	1.00	D5	735.78	1952.45

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

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	5.85	89.87	650.00	POINT (3475.011 1339.361)	1.00	G	3475.01	1339.36

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_f1, orientations_f2, orientations_f3, orientations_b1, orientations_b2, orientations_b3, orientations_b4, orientations_c1, orientations_c2, orientations_c3, orientations_c4, orientations_c5, orientations_d1, orientations_d2, orientations_d3, orientations_d4, orientations_d5, orientations_g]).reset_index()
orientations['formation'] = ['Fault', 'Fault', 'Fault', 'B', 'B', 'B', 'B', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'C', 'D', 'D', 'D', 'D', 'D', 'D', 'D', 'G']
orientations = orientations[orientations['formation'].isin(['Fault', 'B', 'C', 'D', 'G'])]
orientations.head()

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	72.24	281.86	450.00	POINT (943.356 419.665)	1.00	Fault	943.36	419.67
1	0	78.84	283.09	350.00	POINT (1246.534 2003.121)	1.00	Fault	1246.53	2003.12
2	0	72.65	281.34	350.00	POINT (1084.157 1262.429)	1.00	Fault	1084.16	1262.43
3	0	20.35	85.12	250.00	POINT (347.292 491.913)	1.00	B	347.29	491.91
4	0	21.95	265.66	350.00	POINT (2029.784 1223.500)	1.00	B	2029.78	1223.50

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()
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/orientations_example16.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

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('Model16')
geo_model

Model16  2022-04-05 11:10

Initiate Data

gp.init_data(geo_model, [0, 3968, 0, 2731, 0, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model16  2022-04-05 11:10

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	H	Default series	1	#015482	1
1	G	Default series	2	#9f0052	2
2	Fault	Default series	3	#ffbe00	3
3	F	Default series	4	#728f02	4
4	D	Default series	5	#443988	5
5	C	Default series	6	#ff3f20	6
6	B	Default series	7	#5DA629	7

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Fault1': ('Fault'),
                          'Strata1': ('H', 'G', 'F'),
                          'Strata2': ('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
Strata2	3	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
2	Fault	Fault1	1	#527682	1	22	3
0	H	Strata1	1	#9f0052	2	63	0
1	G	Strata1	2	#ffbe00	3	54	1
3	F	Strata1	3	#728f02	4	66	0
4	D	Strata2	1	#443988	5	116	7
5	C	Strata2	2	#ff3f20	6	139	8
6	B	Strata2	3	#5DA629	7	75	4
7	A	Strata2	4	#4878d0	8	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster16.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([[  19.84      ,   13.655     ,    5.        ],
       [  19.84      ,   13.655     ,   15.        ],
       [  19.84      ,   13.655     ,   25.        ],
       ...,
       [3963.00251889, 2705.99084249,  744.06182861],
       [3963.00251889, 2715.99450549,  742.93560791],
       [3963.00251889, 2725.9981685 ,  741.82879639]])

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 0x20a4d850f40>

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              4919.69
$C_o$            576271.07
drift equations  [3, 3, 3]

<gempy.core.interpolator.InterpolatorModel at 0x20a4b61e9a0>

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 0x20a4c1c94f0>

Plotting 3D Model

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