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Geophysical modeling and inversion with Python for geothermal monitoring
Geophysical modeling and inversion with Python for geothermal monitoringAn introduction to pyGIMLi
Geophysical monitoring of subsurface processes
Binley et al. (2015)
Quantitative imaging and monitoring is challenging
The evolution of geophysical imaging for subsurface characterization
–> model coupling is challenging and requires versatile open-source software
pyGIMLi is a versatile open-source toolbox with:
- management tools for structured and unstructured meshes in 2D & 3D
- computationally efficient finite-element and finite-volume solvers
- various geophysical forward operators: ERT/IP, Seismics/GPR traveltime, Gravity, Magnetics, SP, EM
- frameworks for constrained, joint and process-based inversions with region-specific regularization
- open-source, platform compatible, documented & tested code
- suitability for teaching & reproducible research
- v1.0 published in Computers and Geosciences (Rücker et al., 2017) (among 5 Most Downloaded papers and 480 citations) and broadly used since
Basic inversion framework
The default inversion framework is based on the generalized Gauss-Newton method and is compatible with any given forward operator and thus applicable to various physical problems.
\[ \mathbf{W}_\text{d} (\mathbf{F}(\mathbf{m})-\mathbf{d}) \|^2_2 + \lambda \| \mathbf{W}_\text{m} (\mathbf{m}-\mathbf{m_0}) \|^2_2 \rightarrow\min \]
Note
The inversion is physics-independent and very flexible in terms of adding prior information, regularization and integrating different geophysical methods.
Website and documentation: https://pygimli.org
Rücker, C., Günther, T., Wagner, F.M., 2017. pyGIMLi: An open-source library for modelling and inversion in geophysics, Computers and Geosciences, 109, 106-123.
Software design
pyGIMLi is organized in three different abstraction levels:
In the application level, ready-to-use method managers and frameworks are provided. Method managers (pygimli.manager) hold all relevant functionality related to a geophysical method. A method manager can be initialized with a data set and used to analyze and visualize this data set, create a corresponding mesh, and carry out an inversion. Various method managers are available in pygimli.physics. Frameworks (pygimli.frameworks) are generalized abstractions of standard and advanced inversions tasks such as time-lapse or joint inversion for example. Since frameworks communicate through a unified interface, they are method independent.
In the modelling level, users can set up customized forward operators that map discretized parameter distributions to a data vector. Once defined, it is straightforward to set up a corresponding inversion workflow or combine the forward operator with existing ones.
The underlying equation level allows to directly access the finite element (pygimli.solver.solveFiniteElements()) and finite volume (pygimli.solver.solveFiniteVolume()) solvers to solve various partial differential equations on unstructured meshes, i.e. to approach various physical problems with possibly complex 2D and 3D geometries.
Existing tutorials
- Transform 2021: creating geometries & meshes, modeling PDEs, synthetic data, inversion (also with external forward operator).
- Transform 2022: fundamental
pyGIMLiobjects (Mesh,DataContainer, matrix types, etc.), geostatistical vs. smoothness regularization, treatment of subsurface regions, adding prior data. - SEG webinar 2024: invert real-life 3D data (Hübner et al., 2017) to tweak your inversion beyond the standard practice.
- GELMON 2025: ERT time-lapse data processing and inversion + image appraisal
Join the pyGIMLi user community!
“In open source, we feel strongly that to really do something well, you have to get a lot of people involved.”
– Linus Torvalds
- Join the
#pyGIMLichat on Mattermost! - Open a discussion or raise an issue on GitHub.
- Contribute to the website via the “Improve this page” button in the right sidebar.
- Add your pyGIMLi-powered publication to this database.
- Send your example to mail@pygimli.org.
- Contribute to the code as described in our contribution guidelines.
Creating a simple subsurface model
import pygimli as pg
import pygimli.meshtools as mt
# Create a simple 3 layer model
world = mt.createWorld(start=[-20, 0], end=[20, -16], layers=[-2, -8],
worldMarker=False)
pg.show(world, markers=True)
Creating a simple subsurface model
import pygimli as pg
import pygimli.meshtools as mt
# Create a simple 3 layer model
world = mt.createWorld(start=[-20, 0], end=[20, -16], layers=[-2, -8],
worldMarker=False)
# Create a heterogeneous block
block = mt.createRectangle(start=[-6, -3.5], end=[6, -6.0],
marker=4, boundaryMarker=10, area=0.1)
# Merge geometrical entities
geom = world + block
pg.show(geom, markers=True)
Meshing the geometry
mesh = mt.createMesh(geom, quality=33, area=0.2, smooth=[1, 10])
pg.show(mesh)
Solving a PDE on the mesh
\[c \frac{\partial u}{\partial t} = \nabla\cdot(a \nabla u) + b u + f(\mathbf{r},t)~~|~~\Omega_{\text{Mesh}}\]
T = pg.solver.solveFiniteElements(mesh,
a={1: 1.0, 2: 2.0, 3: 3.0, 4:0.1},
bc={'Dirichlet': {8: 1.0, 4: 0.0}},
verbose=True)
ax, _ = pg.show(mesh, data=T, label='Temperature $T$',
cMap="hot_r", nCols=8, contourLines=False)
pg.show(geom, ax=ax, fillRegion=False)Mesh: Mesh: Nodes: 2987 Cells: 5782 Boundaries: 8768
Assembling time: 0.0465015
Solving time: 0.005456584
