simpeg

SimPEG - Geophysical Simulation & Inversion

Quick Reference

from discretize import TensorMesh
from simpeg.electromagnetics.static import resistivity as dc
from simpeg import maps, data_misfit, regularization, optimization
from simpeg import inverse_problem, inversion, directives
import numpy as np

# Create mesh
hx, hz = np.ones(100) * 10, np.ones(50) * 5
mesh = TensorMesh([hx, hz], origin='CN')

# Forward model
simulation = dc.Simulation2DNodal(mesh, survey=survey, sigmaMap=maps.ExpMap(mesh))
dpred = simulation.dpred(model)

# Inversion
dmis = data_misfit.L2DataMisfit(data=data, simulation=simulation)
reg = regularization.WeightedLeastSquares(mesh)
opt = optimization.InexactGaussNewton(maxIter=20)
inv_prob = inverse_problem.BaseInvProblem(dmis, reg, opt)
inv = inversion.BaseInversion(inv_prob, directiveList=[...])
mrec = inv.run(m0)

Key Classes

Class	Purpose
TensorMesh, TreeMesh	Discretization (regular grid, adaptive octree)
Survey	Data acquisition geometry
Simulation	Forward modeling engine
Data	Observed/predicted data container
InvProblem	Combines misfit, regularization, optimization

Essential Operations

Create Mesh

from discretize import TensorMesh

# 2D mesh (x, z) - centered in x, top at z=0
hx, hz = np.ones(100) * 20, np.ones(50) * 10
mesh = TensorMesh([hx, hz], origin='CN')

# 3D mesh
mesh = TensorMesh([np.ones(50)*25, np.ones(50)*25, np.ones(30)*10], origin='CCN')

DC Resistivity Survey

from simpeg.electromagnetics.static import resistivity as dc

elec_locs = np.c_[np.linspace(-95, 95, 20), np.zeros(20)]
source_list = []
for i in range(17):  # dipole-dipole
    rx = dc.receivers.Dipole(elec_locs[[i+2]], elec_locs[[i+3]])
    src = dc.sources.Dipole([rx], elec_locs[i], elec_locs[i+1])
    source_list.append(src)
survey = dc.Survey(source_list)

Forward Model

model = np.ones(mesh.nC) * 100  # 100 ohm-m
simulation = dc.Simulation2DNodal(mesh, survey=survey, sigmaMap=maps.ExpMap(mesh))
dpred = simulation.dpred(np.log(1/model))  # input: log(conductivity)

Inversion

from simpeg import data_misfit, regularization, optimization
from simpeg import inverse_problem, inversion, directives, data

obs_data = data.Data(survey, dobs=dobs, standard_deviation=0.05*np.abs(dobs))
dmis = data_misfit.L2DataMisfit(data=obs_data, simulation=simulation)
reg = regularization.WeightedLeastSquares(mesh, alpha_s=1e-4, alpha_x=1, alpha_z=1)
opt = optimization.InexactGaussNewton(maxIter=20)
inv_prob = inverse_problem.BaseInvProblem(dmis, reg, opt)
dir_list = [directives.BetaSchedule(coolingFactor=2), directives.TargetMisfit()]
inv = inversion.BaseInversion(inv_prob, directiveList=dir_list)
mrec = inv.run(m0)

Common Maps

Map	Description	Use Case
IdentityMap	No transformation	Susceptibility, density
ExpMap	exp(m)	Log-parameterized conductivity
ReciprocalMap	1/m	Resistivity to conductivity
Wires	Split model	Joint inversion

Physical Property Ranges

Property	Typical Range	Units
Resistivity	1 - 10000	ohm-m
Conductivity	0.0001 - 1	S/m
Susceptibility	0 - 0.1	SI
Density contrast	-1 to 1	g/cc

When to Use vs Alternatives

Scenario	Recommendation
Multi-method geophysical inversion (DC, magnetics, gravity, EM)	SimPEG - broadest method coverage
Near-surface ERT with standard arrays	pyGIMLi - simpler API, built-in array support
ERT-focused inversion with GUI export	pyGIMLi - better ERT-specific tooling
Custom forward modelling with flexible physics	SimPEG - modular design, easy to extend
Joint inversion of multiple geophysical datasets	SimPEG - built-in support via Wires maps
Commercial ERT processing	Res2DInv / Res3DInv - industry standard

Choose SimPEG when: You need a unified framework for multiple geophysical methods, custom forward operators, or research-grade flexibility. Its modular design (mesh + survey + simulation + inversion) suits complex and non-standard problems.

Avoid SimPEG when: You only need standard ERT inversion (pyGIMLi is faster to set up), or you need a turnkey commercial solution.

Common Workflows

Run DC resistivity inversion from survey data

• Define electrode locations and build dipole-dipole (or other) survey geometry
• Create TensorMesh or TreeMesh with appropriate cell sizes
• Set up dc.Simulation2DNodal with mesh, survey, and ExpMap
• Load observed data into data.Data with standard deviations
• Configure L2DataMisfit, WeightedLeastSquares regularization, and optimizer
• Set directives: BetaSchedule, TargetMisfit
• Build BaseInvProblem and BaseInversion
• Run inversion with inv.run(m0) using a homogeneous starting model
• Plot recovered model and compare observed vs predicted data
• Check data misfit convergence (target chi-squared ~ 1)

Tips

1. Use log parameters for positive quantities (resistivity, susceptibility)
2. Start with coarse mesh and refine after initial tests
3. Check data fit by plotting observed vs predicted
4. Tune regularization to balance data fit and model smoothness
5. Use TreeMesh for 3D problems to improve efficiency

References

• Survey Types - Survey configurations and receiver types
• Mesh Types - Mesh discretization and refinement

Scripts

• scripts/dc_inversion.py - Complete DC resistivity inversion example