Example 23 - 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 700 m wide (W-E extent) and 788 m high (N-S extent). The model represents southwards dipping planar 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('../../getting_started/images/cover_example23.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/example23/'
gg.download_gemgis_data.download_tutorial_data(filename="example23_planar_dipping_layers.zip", dirpath=file_path)

Downloading file 'example23_planar_dipping_layers.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample23_planar_dipping_layers.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example23'.

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('../../getting_started/images/dem_example23.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo23.shp')
topo.head()

	id	Z	geometry
0	None	600	LINESTRING (15.116 787.112, 22.878 758.803, 29...
1	None	600	LINESTRING (450.485 786.656, 457.791 773.642, ...
2	None	500	LINESTRING (1.189 660.177, 11.235 642.598, 21....
3	None	400	LINESTRING (0.790 532.842, 12.776 506.360, 26....
4	None	300	LINESTRING (3.872 351.115, 20.310 331.025, 34....

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=[0,700,0,788], 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(98.40090121128625, 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 + 'raster23.tif', extent=[0,700,0,788], 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 + 'raster23.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('../../getting_started/images/interfaces_example23.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces23.shp')
interfaces.head()

	id	formation	geometry
0	None	Layer1	LINESTRING (70.166 0.062, 62.317 20.308, 56.38...
1	None	Layer1	LINESTRING (631.470 216.874, 609.097 222.125, ...

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	Layer1	POINT (70.166 0.062)	70.17	0.06	166.32
107	Layer1	POINT (472.573 494.031)	472.57	494.03	393.99
100	Layer1	POINT (524.854 324.632)	524.85	324.63	289.36
101	Layer1	POINT (519.147 343.581)	519.15	343.58	294.85
102	Layer1	POINT (515.265 366.411)	515.27	366.41	304.13

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(116.99284374939245, 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('../../getting_started/images/orientations_example23.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

strikes = gpd.read_file(file_path + 'strikes23.shp')
strikes

	id	Z	formation	geometry
0	3	600	Layer1a	LINESTRING (46.044 702.206, 190.042 725.406)
1	2	500	Layer1a	LINESTRING (49.510 572.074, 271.908 618.474)
2	1	400	Layer1a	LINESTRING (69.244 368.876, 355.641 452.075)
3	2	300	Layer1b	LINESTRING (62.310 272.344, 266.042 247.811)
4	1	200	Layer1b	LINESTRING (54.844 118.745, 312.974 79.279)
5	2	300	Layer1c	LINESTRING (391.907 261.677, 459.106 340.610)
6	1	200	Layer1c	LINESTRING (436.706 178.478, 524.172 187.011)
7	4	600	Layer1d	LINESTRING (463.373 765.139, 612.705 747.006)
8	3	500	Layer1d	LINESTRING (412.173 672.340, 670.304 668.073)
9	2	400	Layer1d	LINESTRING (471.906 495.275, 625.505 476.075)
10	1	300	Layer1d	LINESTRING (519.906 352.343, 662.838 332.077)

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	28.63	165.42	450.00	POINT (186.576 502.875)	1.00	Layer1a	186.58	502.87
1	39.48	168.98	550.00	POINT (139.376 654.540)	1.00	Layer1a	139.38	654.54

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	33.10	187.99	250.00	POINT (174.042 179.545)	1.00	Layer1b	174.04	179.54

orientations_layer1c = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Layer1c'].sort_values(by='Z', ascending=True).reset_index())
orientations_layer1c

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	46.62	148.69	250.00	POINT (452.973 241.944)	1.00	Layer1c	452.97	241.94

orientations_layer1d = gg.vector.calculate_orientations_from_strike_lines(gdf=strikes[strikes['formation']=='Layer1d'].sort_values(by='Z', ascending=True).reset_index())
orientations_layer1d

	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	36.35	187.56	350.00	POINT (570.038 413.942)	1.00	Layer1d	570.04	413.94
1	29.60	182.57	450.00	POINT (544.972 577.941)	1.00	Layer1d	544.97	577.94
2	52.06	182.45	550.00	POINT (539.639 713.139)	1.00	Layer1d	539.64	713.14

Merging Orientations

import pandas as pd
orientations = pd.concat([orientations_layer1a, orientations_layer1b, orientations_layer1c, orientations_layer1d]).reset_index()
orientations['formation'] = 'Layer1'
orientations

	index	dip	azimuth	Z	geometry	polarity	formation	X	Y
0	0	28.63	165.42	450.00	POINT (186.576 502.875)	1.00	Layer1	186.58	502.87
1	1	39.48	168.98	550.00	POINT (139.376 654.540)	1.00	Layer1	139.38	654.54
2	0	33.10	187.99	250.00	POINT (174.042 179.545)	1.00	Layer1	174.04	179.54
3	0	46.62	148.69	250.00	POINT (452.973 241.944)	1.00	Layer1	452.97	241.94
4	0	36.35	187.56	350.00	POINT (570.038 413.942)	1.00	Layer1	570.04	413.94
5	1	29.60	182.57	450.00	POINT (544.972 577.941)	1.00	Layer1	544.97	577.94
6	2	52.06	182.45	550.00	POINT (539.639 713.139)	1.00	Layer1	539.64	713.14

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(116.99284374939245, 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('Model23')
geo_model

Model23  2022-04-07 09:15

Initiate Data

gp.init_data(geo_model, [0,700,0,788,0,400], [100,100,100],
             surface_points_df = interfaces_coords[interfaces_coords['Z']!=0].sample(n=100),
             orientations_df = orientations,
             default_values=True)

Active grids: ['regular']

Model23  2022-04-07 09:15

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	100	7
1	Basement	Strata1	2	#9f0052	2	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster23.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([[  3.5       ,   3.94      ,   2.        ],
       [  3.5       ,   3.94      ,   6.        ],
       [  3.5       ,   3.94      ,  10.        ],
       ...,
       [697.5       , 775.53164557, 559.49066162],
       [697.5       , 780.51898734, 563.62854004],
       [697.5       , 785.50632911, 567.61871338]])

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 0x167bcc5b100>

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            1127.36
$C_o$           30260.57
drift equations      [3]

<gempy.core.interpolator.InterpolatorModel at 0x167b4d80430>

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 0x167bc470160>

Plotting 3D Model

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