Example 14 - Three Point Problem

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 2973 m wide (W-E extent) and 3698 m high (N-S extent). The vertical model extent varies between 0 m and 1000 m. This example represents a classic “three-point-problem” of planar dipping layers (blue and purple) above an unspecified basement. The interface points were not recorded at the surface but rather in boreholes at depth.

The map has been georeferenced with QGIS. The outcrops of the layers were digitized in QGIS. 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_example14.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/example14/'
gg.download_gemgis_data.download_tutorial_data(filename="example14_three_point_problem.zip", dirpath=file_path)

Downloading file 'example14_three_point_problem.zip' from 'https://rwth-aachen.sciebo.de/s/AfXRsZywYDbUF34/download?path=%2Fexample14_three_point_problem.zip' to 'C:\Users\ale93371\Documents\gemgis\docs\getting_started\example\data\example14'.

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_example14.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

topo = gpd.read_file(file_path + 'topo14.shp')
topo.head()

	id	Z	geometry
0	None	800	LINESTRING (373.021 427.168, 400.177 396.582, ...
1	None	800	LINESTRING (1394.650 431.742, 1406.656 411.732...
2	None	700	LINESTRING (3.131 921.975, 58.014 877.954, 104...
3	None	700	LINESTRING (263.826 1502.823, 293.269 1491.960...
4	None	600	LINESTRING (2110.419 2231.741, 2145.293 2212.3...

Interpolating the contour lines

topo_raster = gg.vector.interpolate_raster(gdf=topo, value='Z', method='rbf', res=15)

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, 2973, 0, 3698], 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, 2973)
ax.set_ylim(0, 3698)

(0.0, 3698.0)

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 + 'raster14.tif', extent=[0, 2973, 0, 3698], 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 + 'raster14.tif')

Interface Points of stratigraphic boundaries

The interface points for this three point example will be digitized as points with the respective height value as given by the contour lines and the respective formation.

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/interfaces_example14.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

interfaces = gpd.read_file(file_path + 'interfaces14.shp')
interfaces.head()

	id	formation	geometry
0	None	Sandstone	LINESTRING (491.899 1350.893, 476.463 1416.067...
1	None	Shale	LINESTRING (986.420 273.809, 976.701 356.706, ...
2	None	Sandstone	LINESTRING (2137.825 264.091, 2168.697 322.404...
3	None	Sandstone	LINESTRING (2295.614 934.124, 2339.635 938.126...
4	None	Shale	LINESTRING (1190.517 3118.020, 1213.957 3027.6...

Extracting Z coordinate from Digital Elevation Model

interfaces_coords = gg.vector.extract_xyz(gdf=interfaces, dem=topo_raster)
interfaces_coords.head()

	formation	geometry	X	Y	Z
0	Sandstone	POINT (491.899 1350.893)	491.90	1350.89	663.18
1	Sandstone	POINT (476.463 1416.067)	476.46	1416.07	656.31
2	Sandstone	POINT (470.174 1476.096)	470.17	1476.10	643.79
3	Sandstone	POINT (470.746 1548.702)	470.75	1548.70	625.64
4	Sandstone	POINT (475.891 1617.306)	475.89	1617.31	607.52

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, 2973)
ax.set_ylim(0, 3698)

(0.0, 3698.0)

Orientations from Strike Lines

For this three point example, an orientation is calculated using gg.vector.calculate_orientation_for_three_point_problem().

import matplotlib.pyplot as plt
import matplotlib.image as mpimg
img = mpimg.imread('../images/orientations_example14.png')
plt.figure(figsize=(10, 10))
imgplot = plt.imshow(img)
plt.axis('off')
plt.tight_layout()

orientations = gpd.read_file(file_path + 'orientations14.shp')
orientations

	id	formation	Z	geometry
0	None	Sandstone	600	POINT (477.321 1628.597)
1	None	Sandstone	700	POINT (2201.427 477.764)
2	None	Sandstone	600	POINT (2390.088 942.556)

orientations = gg.vector.calculate_orientation_for_three_point_problem(gdf=orientations)
orientations

	Z	formation	azimuth	dip	polarity	X	Y	geometry
0	633.33	Sandstone	-160.27	168.72	1	1689.61	1016.31	POINT (1689.612 1016.306)

Changing the Data Type of Fields

orientations['Z'] = orientations['Z'].astype(float)
orientations['azimuth'] = orientations['azimuth'].astype(float)
orientations['dip'] = orientations['dip'].astype(float)
orientations['dip'] = 180 - orientations['dip']
orientations['azimuth'] = 180 - orientations['azimuth']
orientations['polarity'] = orientations['polarity'].astype(float)
orientations['X'] = orientations['X'].astype(float)
orientations['Y'] = orientations['Y'].astype(float)
orientations.info()

<class 'geopandas.geodataframe.GeoDataFrame'>
RangeIndex: 1 entries, 0 to 0
Data columns (total 8 columns):
 #   Column     Non-Null Count  Dtype
---  ------     --------------  -----
 0   Z          1 non-null      float64
 1   formation  1 non-null      object
 2   azimuth    1 non-null      float64
 3   dip        1 non-null      float64
 4   polarity   1 non-null      float64
 5   X          1 non-null      float64
 6   Y          1 non-null      float64
 7   geometry   1 non-null      geometry
dtypes: float64(6), geometry(1), object(1)
memory usage: 192.0+ bytes

orientations

	Z	formation	azimuth	dip	polarity	X	Y	geometry
0	633.33	Sandstone	340.27	11.28	1.00	1689.61	1016.31	POINT (1689.612 1016.306)

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, 2973)
ax.set_ylim(0, 3698)

(0.0, 3698.0)

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('Model14')
geo_model

Model14  2022-04-05 11:06

Initiate Data

gp.init_data(geo_model, [0, 2973, 0, 3698, 0, 1000], [100, 100, 100],
             surface_points_df=interfaces_coords[interfaces_coords['Z'] != 0],
             orientations_df=orientations,
             default_values=True)

Active grids: ['regular']

Model14  2022-04-05 11:06

Model Surfaces

geo_model.surfaces

	surface	series	order_surfaces	color	id
0	Sandstone	Default series	1	#015482	1
1	Shale	Default series	2	#9f0052	2

Mapping the Stack to Surfaces

gp.map_stack_to_surfaces(geo_model,
                         {
                          'Strata1': ('Sandstone', 'Shale'),
                         },
                         remove_unused_series=True)
geo_model.add_surfaces('Conglomerate')

	surface	series	order_surfaces	color	id
0	Sandstone	Strata1	1	#015482	1
1	Shale	Strata1	2	#9f0052	2
2	Conglomerate	Strata1	3	#ffbe00	3

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	Sandstone	Strata1	1	#015482	1	25	1
1	Shale	Strata1	2	#9f0052	2	22	0
2	Conglomerate	Strata1	3	#ffbe00	3	0	0

Loading Digital Elevation Model

geo_model.set_topography(
    source='gdal', filepath=file_path + 'raster14.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([[  14.865     ,   18.49      ,    5.        ],
       [  14.865     ,   18.49      ,   15.        ],
       [  14.865     ,   18.49      ,   25.        ],
       ...,
       [2965.49242424, 3660.5708502 ,  428.21966553],
       [2965.49242424, 3675.54251012,  427.20385742],
       [2965.49242424, 3690.51417004,  426.23760986]])

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 0x1b5c3679b20>

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             4849.12
$C_o$           559855.55
drift equations       [3]

<gempy.core.interpolator.InterpolatorModel at 0x1b5bcc82a60>

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 0x1b5c9ea4820>

Plotting 3D Model

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