Forward Modelling

pycsamt.forward contains the in-process forward modelling layer of pyCSAMT v2. It provides resistivity model containers, 1-D/2-D/quasi-3-D electromagnetic solvers, synthetic dataset generators, noise models, and diagnostic plotting utilities.

Forward modelling answers a controlled physical question:

If this earth model were true, what response would the survey record?

That question sits underneath every serious inversion workflow. Inversion searches for a model that explains observed data; forward modelling computes the data predicted by a known model. A good inversion setup therefore depends on forward modelling for sensitivity tests, synthetic recovery experiments, training data, uncertainty design, and quality control.

What This Section Covers

The forward documentation is organized around the full lifecycle of a synthetic experiment:

Concepts

Forward operators, model dimensionality, response quantities, noise, and the relationship between synthetic responses and inversion.

Forward Modelling Concepts

Configuration

Reproducible ForwardConfig, ForwardConfig2D, and ForwardConfig3D files for synthetic runs and solver setup.

Forward Configuration

Solvers and grids

LayeredModel, Grid2D, Grid3D, 1-D MT/CSAMT/TEM solvers, 2-D MT profiles, and quasi-3-D tensor responses.

Solvers And Grids

Synthetic datasets

Dataset generation for regression tests, survey experiments, and AI-assisted inversion training.

Synthetic Datasets And Noise

Plotting

Response curves, model sections, pseudo-sections, 3-D maps, tensor panels, dataset checks, and publication-ready figure hooks.

Forward Plotting

Forward to inversion

The handoff contract between synthetic forward responses and inversion backends, including units, shapes, geometry, and error models.

From Forward Modelling To Inversion

Forward And Model Integrations

The pycsamt.forward and pycsamt.models packages are related, but they should not be treated as the same layer.

Package	Main responsibility	Typical use
pycsamt.forward	Compute controlled synthetic responses inside Python using pyCSAMT model containers, solvers, dataset generators, noise models, and plotting helpers.	Test survey design, generate training data, validate inversion assumptions, compare response behaviour, and build reproducible synthetic examples.
pycsamt.models	Integrate external modelling and inversion engines such as Occam2D, ModEM, and MARE2DEM.	Prepare native engine files, run external binaries, load engine outputs, and manage backend-specific inversion projects.

Use pycsamt.forward when you need a controlled synthetic response from a known model. Use pycsamt.models when you need to prepare, run, or load a native external-engine project. The two layers meet when a forward synthetic experiment is converted into an inversion benchmark.

Package Map

The public forward API is built around a small set of object families.

Object family	Main objects	Role
Configuration	ForwardConfig, ForwardConfig2D, ForwardConfig3D	Store reproducible frequency/time axes, model ranges, station layouts, solver options, noise settings, and output choices.
Model containers	LayeredModel, Grid2D, Grid3D	Represent 1-D layered earths, 2-D profile grids, and quasi-3-D resistivity volumes.
Solvers	MT1DForward, CSAMT1DForward, TEM1DForward, MT2DForward, MT3DForward	Compute predicted electromagnetic responses from model containers.
Response containers	ForwardResponse, ForwardResponse2D, ForwardResponse3D	Hold predicted apparent resistivity, phase, transient values, impedance components, station geometry, and array conversion helpers.
Noise models	GaussianNoise, MultiplicativeNoise, FieldRealisticNoise	Convert ideal synthetic responses into more realistic observations.
Dataset containers	ForwardDataset, SurveyDataset3D	Store synthetic feature and target arrays, metadata, splits, and compressed .npz archives.
Plotting helpers	plot_response_1d, plot_model_2d, plot_pseudosection_2d, plot_model_3d, plot_response_map_3d, and related functions	Inspect models, responses, tensor components, noisy examples, and generated datasets before they are trusted downstream.

Core Workflow

A typical forward modelling workflow has six stages.

import numpy as np

from pycsamt.forward import LayeredModel, MT1DForward, plot_response_and_model_1d

freqs = np.logspace(-2, 3, 40)
model = LayeredModel(
    resistivity=[100.0, 15.0, 800.0],
    thickness=[250.0, 700.0],
)

solver = MT1DForward(freqs)
response = solver.run(model)

fig = plot_response_and_model_1d(response, model)
fig.savefig("runs/forward/mt1d_response.png", dpi=200)

For production work, the same idea should be driven by a configuration file and archived with outputs:

1. define the physical question and target dimensionality;

2. create a ForwardConfig* template;

3. build a model or grid from the configuration;

4. run the selected solver;

5. apply a documented noise model when simulating observations;

6. plot and archive the model, response, configuration, and metadata.

Choosing A Path

Different users enter the forward section with different goals.

Goal	Start here	Then read
Understand the physics and vocabulary	Forward Modelling Concepts	Solvers And Grids, Forward Plotting
Build a reproducible synthetic run	Forward Configuration	Solvers And Grids, From Forward Modelling To Inversion
Generate training data for AI inversion	Synthetic Datasets And Noise	Forward Configuration, Forward Plotting, AI And Model-Zoo Agents
Compare 1-D, 2-D, and quasi-3-D behaviour	Solvers And Grids	Forward Modelling Concepts, Forward Plotting
Prepare an inversion benchmark	From Forward Modelling To Inversion	Classical model integrations, Pipeline System
Diagnose a generated dataset or response	Forward Plotting	Synthetic Datasets And Noise, From Forward Modelling To Inversion

Relationship To Theory

Forward modelling is practical, but it is not detached from theory. When a plot or synthetic response looks surprising, the relevant background pages are:

• ../theory/csamt_amt_mt_overview for the distinction between CSAMT, AMT, MT, and TDEM survey assumptions;

• ../theory/impedance_tensor for impedance, apparent resistivity, phase, and tensor notation;

• ../theory/static_shift for shallow distortion effects that can make synthetic and field curves disagree;

• ../theory/inversion_concepts for how forward responses are used inside objective functions and regularized inversion.

Documentation Contents

• Forward Modelling Concepts
  • The Forward Problem
  • Physical Inputs
  • Dimensionality
  • 1-D Forward Models
  • MT, CSAMT, And TEM Assumptions
  • 2-D Forward Modelling
  • Quasi-3-D Forward Modelling
  • Frequency, Period, And Depth Sensitivity
  • Response Quantities
  • Synthetic Priors
  • Noise And Realism
  • Synthetic Recovery
  • Common Failure Modes
  • Good Practice Checklist
  • Next Steps
• Forward Configuration
  • Configuration Classes
  • Template Files
  • 1-D Configuration
  • Geological Priors
  • TEM Configuration
  • 2-D Configuration
  • 2-D Grid Tuning
  • 3-D Configuration
  • 3-D Configuration Notes
  • Validation
  • Summaries And Provenance
  • What To Record
  • Recommended Run Layout
  • Common Mistakes
  • Next Steps
• Solvers And Grids
  • Solver Map
  • 1-D Layered Models
  • 1-D MT And CSAMT Solvers
  • 1-D TDEM Solver
  • 2-D Profile Grid Concepts
  • 2-D Profile Grid Constructors
  • 2-D MT Solver
  • 3-D Volume Grid Concepts
  • 3-D Volume Grid Constructors
  • Quasi-3-D Solver
  • Grid Design Rules
  • Response Containers And Feature Arrays
  • Debugging Solver Experiments
  • Next Pages
• Synthetic Datasets And Noise
  • 1-D Dataset Generation
  • ForwardDataset Contract
  • Saving, Loading, And Splitting
  • Configuration-Driven Generation
  • TDEM Datasets
  • Geological Priors
  • Noise Models
  • Clean And Noisy Dataset Pairs
  • Pseudo-3-D Survey Datasets
  • 2-D And Quasi-3-D Solver Datasets
  • Dataset QA
  • Recommended Archive Layout
  • Common Mistakes
  • Next Pages
• Forward Plotting
  • Plot Selection Guide
  • Saving Figures
  • 1-D Response Plots
  • 1-D Model Plots
  • 1-D Composite View
  • 2-D Grid Model Plots
  • 2-D Pseudo-Sections
  • 2-D Lateral Response Profiles
  • 3-D Model Slice Plots
  • 3-D Response Maps
  • 3-D Response Sections
  • 3-D Tensor Component Panels
  • Plotting Noisy Responses
  • Plotting Dataset Samples
  • Plotting Checklist
  • Common Mistakes
  • Next Pages
• From Forward Modelling To Inversion
  • The Handoff Contract
  • Why Synthetic Recovery Comes First
  • 1-D MT Recovery
  • 1-D TDEM Recovery
  • Stitched 2-D Profile Recovery
  • True 2-D Forward Response Handoff
  • Backend Choice After Forward Tests
  • Error Model Handoff
  • What To Compare
  • Common Failure Modes
  • Recommended Workflow