Example 28 - 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 3954 m wide (W-E extent) and 2738 m high (N-S extent). The model represents folded layers that dip to the northeast or southwest, respectively.

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_example28.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/example28/'
gg.download_gemgis_data.download_tutorial_data(filename="example28_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().

img = mpimg.imread('../images/dem_example28.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo28.shp')
topo.head()

	id	Z	geometry
0	None	350	LINESTRING (1.385 62.877, 136.138 47.987, 292....
1	None	300	LINESTRING (1.571 124.111, 129.996 110.524, 22...
2	None	250	LINESTRING (0.082 198.374, 59.641 178.273, 118...
3	None	50	LINESTRING (863.690 271.706, 829.815 271.334, ...
4	None	100	LINESTRING (864.062 307.070, 828.326 304.092, ...

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=[0,865,0,867], 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(67.3456168134622, 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 + 'raster28.tif', extent=[0,865,0,867], crs='EPSG:4326', overwrite_file=True)

Raster successfully saved

Opening Raster

The previously computed and saved raster can now be opened using rasterio.

topo_raster = rasterio.open(file_path + 'raster28.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.

img = mpimg.imread('../images/interfaces_example28.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces28.shp')
interfaces.head()

	id	formation	Z	geometry
0	None	Layer1	0	LINESTRING (750.000 865.441, 764.514 845.629, ...
1	None	Layer1	50	LINESTRING (628.941 863.195, 637.925 850.294, ...
2	None	Layer1	100	LINESTRING (534.604 865.153, 549.463 845.687, ...
3	None	Layer1	150	LINESTRING (458.590 864.955, 473.370 845.597, ...
4	None	Layer1	100	LINESTRING (2.577 102.527, 17.435 83.097, 25.0...

Extracting XY coordinates from Digital Elevation Model

interfaces_coords = gg.vector.extract_xy(gdf=interfaces)
interfaces_coords = interfaces_coords.sort_values(by='formation', ascending=False)
interfaces_coords.head()

	formation	Z	geometry	X	Y
0	Layer1	0.00	POINT (750.000 865.441)	750.00	865.44
304	Layer1	350.00	POINT (345.483 629.092)	345.48	629.09
332	Layer1	350.00	POINT (669.435 197.325)	669.43	197.33
331	Layer1	350.00	POINT (653.053 219.421)	653.05	219.42
330	Layer1	350.00	POINT (648.227 227.168)	648.23	227.17

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]')

Text(67.45106220501688, 0.5, 'Y [m]')

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.

img = mpimg.imread('../images/orientations_example28.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes28.shp')
strikes

	id	Z	formation	geometry
0	1	100	Layer1a	LINESTRING (2.577 102.527, 78.137 1.951)
1	2	150	Layer1a	LINESTRING (3.720 276.250, 208.683 2.713)
2	3	200	Layer1a	LINESTRING (1.942 442.607, 335.546 1.697)
3	4	250	Layer1a	LINESTRING (1.307 583.693, 438.662 6.395)
4	5	300	Layer1a	LINESTRING (1.815 721.604, 544.572 2.967)
5	6	350	Layer1a	LINESTRING (1.466 864.659, 648.100 2.014)
6	8	350	Layer1b	LINESTRING (168.585 865.421, 817.632 2.522)
7	7	300	Layer1b	LINESTRING (267.892 865.294, 862.714 70.843)
8	6	250	Layer1b	LINESTRING (346.245 863.643, 862.841 176.372)
9	5	200	Layer1b	LINESTRING (407.708 863.135, 863.857 256.376)
10	4	150	Layer1b	LINESTRING (458.590 864.955, 863.317 326.157)
11	3	100	Layer1b	LINESTRING (534.604 865.153, 859.196 434.936)
12	2	50	Layer1b	LINESTRING (628.941 863.195, 862.767 552.331)
13	1	0	Layer1b	LINESTRING (750.000 865.441, 858.044 718.925)

Calculate Orientations for each formation

orientations_layer1a = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Layer1a'].sort_values(by='Z', ascending=True).reset_index())
orientations_layer1a

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	25.48	233.15	125.00	POINT (73.279 95.860)	1.00	Layer1a	73.28	95.86
1	26.81	232.96	175.00	POINT (137.473 180.816)	1.00	Layer1a	137.47	180.82
2	30.56	232.87	225.00	POINT (194.364 258.598)	1.00	Layer1a	194.36	258.60
3	31.23	232.90	275.00	POINT (246.589 328.665)	1.00	Layer1a	246.59	328.66
4	31.29	233.06	325.00	POINT (298.988 397.811)	1.00	Layer1a	298.99	397.81

orientations_layer1b = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Layer1b'].sort_values(by='Z', ascending=True).reset_index())
orientations_layer1b

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	27.42	53.15	25.00	POINT (774.938 749.973)	1.00	Layer1b	774.94	749.97
1	34.21	52.99	75.00	POINT (721.377 678.904)	1.00	Layer1b	721.38	678.90
2	39.39	53.04	125.00	POINT (678.927 622.800)	1.00	Layer1b	678.93	622.80
3	50.31	53.07	175.00	POINT (648.368 577.656)	1.00	Layer1b	648.37	577.66
4	45.68	53.07	225.00	POINT (620.163 539.881)	1.00	Layer1b	620.16	539.88
5	39.01	53.13	275.00	POINT (584.923 494.038)	1.00	Layer1b	584.92	494.04
6	32.97	53.11	325.00	POINT (529.206 451.020)	1.00	Layer1b	529.21	451.02

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_layer1a, orientations_layer1b]).reset_index()
orientations['formation'] = 'Layer1'
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	25.48	233.15	125.00	POINT (73.279 95.860)	1.00	Layer1	73.28	95.86
1	1	26.81	232.96	175.00	POINT (137.473 180.816)	1.00	Layer1	137.47	180.82
2	2	30.56	232.87	225.00	POINT (194.364 258.598)	1.00	Layer1	194.36	258.60
3	3	31.23	232.90	275.00	POINT (246.589 328.665)	1.00	Layer1	246.59	328.66
4	4	31.29	233.06	325.00	POINT (298.988 397.811)	1.00	Layer1	298.99	397.81
5	0	27.42	53.15	25.00	POINT (774.938 749.973)	1.00	Layer1	774.94	749.97
6	1	34.21	52.99	75.00	POINT (721.377 678.904)	1.00	Layer1	721.38	678.90
7	2	39.39	53.04	125.00	POINT (678.927 622.800)	1.00	Layer1	678.93	622.80
8	3	50.31	53.07	175.00	POINT (648.368 577.656)	1.00	Layer1	648.37	577.66
9	4	45.68	53.07	225.00	POINT (620.163 539.881)	1.00	Layer1	620.16	539.88
10	5	39.01	53.13	275.00	POINT (584.923 494.038)	1.00	Layer1	584.92	494.04
11	6	32.97	53.11	325.00	POINT (529.206 451.020)	1.00	Layer1	529.21	451.02

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]')

Text(67.45106220501688, 0.5, 'Y [m]')

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('Model28')
geo_model

Model28  2022-04-13 08:25

Initiate Data

gp.init_data(geo_model, [0,865,0,867,0,500], [50,50,50],
             surface_points_df = interfaces_coords[interfaces_coords['Z']!=0].sample(n=75, random_state=1),
             orientations_df = orientations,
             default_values=True)

Active grids: ['regular']

Model28  2022-04-13 08:25

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Layer1	Default series	1	#015482	1

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('Layer1'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Basement')

	surface	series	order_surfaces	color	id
0	Layer1	Strata1	1	#015482	1
1	Basement	Strata1	2	#9f0052	2

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	Layer1	Strata1	1	#015482	1	75	12
1	Basement	Strata1	2	#9f0052	2	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster28.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([[  8.65      ,   8.67      ,   5.        ],
       [  8.65      ,   8.67      ,  15.        ],
       [  8.65      ,   8.67      ,  25.        ],
       ...,
       [862.5       , 854.54310345, 363.79455566],
       [862.5       , 859.52586207, 364.32107544],
       [862.5       , 864.50862069, 364.75622559]])

Defining Custom Section

custom_section = gpd.read_file(file_path + 'customsections28.shp')
custom_section_dict = gg.utils.to_section_dict(custom_section, section_column='section')
geo_model.set_section_grid(custom_section_dict)

Active grids: ['regular' 'topography' 'sections']

	start	stop	resolution	dist
Section1	[1.593210345965275, 388.4453900184363]	[852.4277356922321, 865.9286460336549]	[100, 80]	975.66

gp.plot.plot_section_traces(geo_model)

<gempy.plot.visualization_2d.Plot2D at 0x1ebe7a01f10>

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 0x1ebe70f09d0>

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            1322.84
$C_o$           41664.62
drift equations      [3]

<gempy.core.interpolator.InterpolatorModel at 0x1ebe0d78af0>

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 0x1ebe71ad130>

gp.plot_2d(geo_model, direction=['x', 'x', 'y', 'y'], cell_number=[25,40,25,40], show_topography=True, show_data=False)

<gempy.plot.visualization_2d.Plot2D at 0x1ebe72b9460>

Plotting 3D Model

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