LayTracer

Fast two-point seismic ray tracing in layered media.

LayTracer is an open-source Python package for computing ray paths, travel times, and amplitude attributes in horizontally layered (1D) velocity models with constant layer velocities. It is based on the dimensionless ray parameter method of Fang & Chen (2019), achieving rapid convergence.

Documentation: https://danikiev.github.io/LayTracer

---

✨ Features

Category	Capability
Ray tracing	Second-order (quadratic) Newton solver using the dimensionless q-parameter for robust, singularity-free convergence
Travel time	Layer-by-layer travel time summation from the solved ray parameter
Attenuation	Intrinsic absorption operator t* from quality factors Q
Spreading	Relative geometrical spreading from the analytical ray-tube Jacobian ∂X/∂p
Reflection/Transmission	Full angle-dependent Zoeppritz P-SV coefficients (all 8 R/T modes) with optional energy-flux normalization (Červený, 2001)
Brewster angles	Automatic detection of Brewster-like zeros in R/T coefficient curves
Parallel execution	Multi-ray tracing with joblib / loky backend for large surveys
Visualisation	2-D ray path plots (matplotlib) and interactive 3-D viewer (Plotly)
Documentation	Comprehensive Sphinx docs with extensive theory, gallery examples, and API reference

---

📦 Installation

Prerequisites

• Python 3.8–3.12 and pip
• Conda package manager (recommended for full reproducible setup via miniforge)

Install with conda

# 1. Create environment with all dependencies
conda env create -f environment.yml

# 2. Activate it
conda activate laytracer

# 3. Install LayTracer in editable mode
pip install -e .

Install from PyPI (stable releases only)

python -m pip install --upgrade pip
pip install laytracer

Check installed version

python -c "import laytracer; print(laytracer.__version__)"

Alternative:

python -m pip show laytracer

Use this mode when you want a published stable release. For development or latest unreleased changes, install from the repository with pip install -e ..

Quick install (Windows)

install.bat

Quick install (Linux / macOS)

chmod +x install.sh
./install.sh

Install with pip only (no conda)

# Linux / macOS
python -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
pip install -e .

# Windows (PowerShell)
python -m venv .venv
.\.venv\Scripts\Activate.ps1
python -m pip install --upgrade pip
pip install -e .

pip-only installation is suitable for running LayTracer. For a full pre-configured environment (including docs tooling), prefer the conda workflow.

Dependencies

• Python ≥ 3.8, < 3.13
• NumPy (< 2), SciPy, Pandas
• Matplotlib, Plotly, cmcrameri
• psutil, joblib

---

🚀 Quick Start

Define a velocity model

import laytracer
import numpy as np
import pandas as pd

vel_df = pd.DataFrame({
    "Depth": [0.0, 1000.0, 2000.0, 3500.0],
    "Vp":    [3000.0, 4500.0, 5500.0, 6500.0],
    "Vs":    [1500.0, 2250.0, 2750.0, 3250.0],
    "Rho":   [2200.0, 2500.0, 2700.0, 2900.0],
    "Qp":    [200.0,  400.0,  600.0,  800.0],
    "Qs":    [100.0,  200.0,  300.0,  400.0],
})

Trace a single 2-D ray

stack = laytracer.build_layer_stack(vel_df, z_src=3000.0, z_rcv=0.0)

result = laytracer.solve(
    stack,
    epicentral_dist=5000.0,
    z_src=3000.0,
    z_rcv=0.0,
    vel_type="Vp",
)

print(f"Travel time:   {result.travel_time:.4f} s")
print(f"Ray parameter: {result.ray_parameter:.6e} s/m")

Trace multiple rays in 3-D (with amplitude)

src = np.array([0.0, 0.0, 3000.0])
rcvs = np.column_stack([
    np.arange(500, 15001, 500),
    np.zeros(29),
    np.zeros(29),
])

result = laytracer.trace_rays(
    sources=src,
    receivers=rcvs,
    velocity_df=vel_df,
    source_phase="P",
    requested={"travel_times", "rays", "ray_parameters", "tstar", "spreading", "trans_product"},
    transcoef_method="standard",  # standard Zoeppritz coefficients without normalization
)

# Access results
print(result.travel_times)   # travel times (s)
print(result.tstar)          # attenuation operator t*
print(result.spreading)      # geometrical spreading
print(result.trans_product)  # product of transmission coefficients

Visualise results

# 2-D ray paths over velocity cross-section
laytracer.plot.rays_2d(vel_df, rays=[r.ray_path for r in ...])

# 1-D velocity profile
laytracer.plot.velocity_profile(vel_df, param="Vp")

# Interactive 3-D viewer
fig = laytracer.plot.rays_3d(vel_df, rays=result.rays, sources=src, receivers=rcvs)
fig.show()

---

📐 API Overview

Model

Symbol	Description
LayerStack	Data class holding layer thicknesses, velocities (Vp, Vs), densities, and Q-factors
ModelArrays	Pre-extracted NumPy arrays from a velocity DataFrame for efficient repeated tracing
build_layer_stack(vel_model, z_src, z_rcv)	Extract the traversed layer stack between source and receiver depths (accepts DataFrame or ModelArrays)

Solver

Symbol	Description
solve(stack, epicentral_dist, ...)	Solve the two-point ray tracing problem for one source–receiver pair
RayResult	Result container: travel time, ray path, ray parameter, t*, spreading, transmission product
offset(q, h, lmd)	Total horizontal offset X(q)
offset_dq(q, h, lmd)	First derivative dX/dq
offset_dq2(q, h, lmd)	Second derivative d²X/dq²
q_from_p(p, vmax) / p_from_q(q, vmax)	Convert between slowness p and dimensionless q
initial_q(X_target, h, lmd)	Asymptotic initial estimate for Newton iteration
newton_step(q_i, X_target, h, lmd)	One quadratic Newton step

Amplitude

Symbol	Description
psv_rt_coefficients(p, vp1, vs1, rho1, vp2, vs2, rho2)	All 8 P-SV reflection/transmission coefficients (Zoeppritz)
normalize_rt_coefficient(coeff, p, v_in, rho_in, v_out, rho_out)	Energy-flux normalization of R/T coefficients (Červený, 2001)
find_brewster_angles(rt_coefficients, angles, ...)	Detect Brewster-like zeros in R/T curves

Multi-ray

Symbol	Description
trace_rays(sources, receivers, velocity_df, ...)	Trace all source–receiver pairs with optional parallelism
TraceResult	Container: travel times, ray paths, ray parameters, t*, spreading, transmission products

Visualisation (laytracer.plot)

Function	Description
velocity_profile(vel_df, ...)	1-D velocity–depth step profile (matplotlib)
rays_2d(vel_df, rays, ...)	2-D ray paths over layered velocity cross-section (matplotlib)
rays_3d(vel_df, rays, ...)	Interactive 3-D ray visualisation (Plotly)

---

📖 Documentation

Full documentation is built with Sphinx and includes:

• Getting Started — installation and environment setup
• Methodology — complete mathematical derivations (dimensionless parameter, Newton iteration, travel time, t*, geometrical spreading, Zoeppritz coefficients, critical & Brewster angles, 3-D extension)
• Examples Gallery — runnable scripts rendered with Sphinx-Gallery
• API Reference — auto-generated from docstrings with numpydoc

Build the docs

conda activate laytracer
# Windows
build-docs.bat
# Linux / macOS
chmod +x build-docs.sh
./build-docs.sh

Build docs with PDF output:

conda activate laytracer
# Windows
build-docs.bat -pdf
# Linux / macOS
chmod +x build-docs.sh
./build-docs.sh -pdf

You can do also using make commands:

conda activate laytracer
cd docs
# Build HTML
make html
# Build PDF
make latexpdf
# Run a local server to view HTML
cd build/html
python -m http.server

Automatic docs deployment to GitHub Pages

This repository includes a GitHub Actions workflow at .github/workflows/docs.yml that runs on every push to main and:

• builds Sphinx HTML docs,
• builds the PDF (laytracer.pdf),
• copies the PDF into the published site (_static/laytracer.pdf),
• deploys HTML docs to GitHub Pages,
• uploads the PDF as a workflow artifact.

One-time GitHub setup:

1. Open Settings → Pages in your GitHub repository.
2. Set Source to GitHub Actions.
3. Push to main.

Published docs URL:

https://danikiev.github.io/LayTracer

---

🔬 Theory

LayTracer implements the method of Fang & Chen (2019) for two-point ray tracing in horizontally layered media:

1. Dimensionless ray parameter q = p · v_max / √(1 − p² · v²_max) maps the full range of take-off angles to [0, ∞) without singularities.

2. Offset equation X(q) is a smooth, monotonically increasing function — ideal for Newton iteration.

3. Quadratic Newton solver with asymptotic initial estimate converges in 2–3 iterations.

4. Amplitude attributes are computed inline:

   • Travel time from vertical slowness summation
   • Attenuation t* from per-layer Q-factors
   • Geometrical spreading from analytic ∂X/∂p
   • Full Zoeppritz P-SV R/T coefficients (Lay & Wallace (1995) formulation)

Key references

• Fang, X. & Chen, X. (2019). A fast and robust two-point ray tracing method in layered media. Geophysical Prospecting, 67(7), 1648–1661. doi:10.1111/1365-2478.12799
• Aki, K. & Richards, P.G. (2002). Quantitative Seismology. 2nd ed., University Science Books.
• Lay, T. & Wallace, T.C. (1995). Modern Global Seismology. Academic Press.
• Červený, V. (2001). Seismic Ray Theory. Cambridge University Press. doi:10.1017/CBO9780511529399

---

🧪 Testing

LayTracer includes a comprehensive test suite covering the solver, amplitude calculations, API, and physical symmetries.

conda activate laytracer
pytest

Test modules:

• test_solver.py — Newton convergence, Snell's law, travel time accuracy
• test_amplitude.py — Zoeppritz coefficients, energy-flux normalization, Brewster detection
• test_api.py — multi-ray tracing interface
• test_generalized.py — generalized layered-media validation cases
• test_homogeneous_equivalence.py — homogeneous-medium equivalence checks
• test_symmetry.py — reciprocity and physical consistency checks

---

📂 Project Structure

LayTracer/
├── laytracer/               # Main package
│   ├── __init__.py          # Public API exports
│   ├── model.py             # LayerStack, ModelArrays, build_layer_stack
│   ├── solver.py            # Core ray tracing solver (q-parameter + Newton)
│   ├── amplitude.py         # Transmission coefficients, Zoeppritz, Brewster
│   ├── api.py               # High-level multi-ray interface (trace_rays)
│   └── plot.py              # Visualisation (2-D, 3-D, velocity profiles)
├── examples/                # Sphinx-Gallery example scripts
│   ├── 01_basic_raytracing.py
│   ├── 02_paper_examples.py
│   ├── 03_reflection_transmission.py
│   ├── 04_amplitude_analysis.py
│   ├── 05_homogeneous_equivalence.py
│   └── README.txt
├── pytests/                 # Test suite
│   ├── test_solver.py
│   ├── test_amplitude.py
│   ├── test_api.py
│   ├── test_generalized.py
│   ├── test_homogeneous_equivalence.py
│   └── test_symmetry.py
├── docs/                    # Sphinx documentation
│   └── source/
│       ├── index.rst
│       ├── getting_started.rst
│       ├── methodology.rst   # Full mathematical derivations
│       └── references.bib
├── pyproject.toml           # Build configuration (setuptools + setuptools-scm)
├── environment.yml          # Conda environment specification
├── pytest.ini               # Pytest configuration
└── LICENSE                  # MIT License

---

📄 License

LayTracer is released under the MIT License.

---

👤 Author

Denis Anikiev — danikiev@gmail.com

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📝 Citation

If you use a specific version of LayTracer in your research, please cite:

@software{Anikiev2026LayTracerVersion,
  author       = {Anikiev, Denis},
  title        = {{LayTracer}: {F}ast two-point seismic ray tracing in layered media},
  year         = {2026},
  publisher    = {Zenodo},
  version      = {0.3.0},  
  url          = {https://github.com/danikiev/LayTracer},
  license      = {MIT},
  doi          = {10.5281/zenodo.19020694}
}

To cite the whole collection (directs to the latest version) please use:

@misc{Anikiev2026LayTracer,
  author       = {Anikiev, Denis},
  title        = {{LayTracer}: {F}ast two-point seismic ray tracing in layered media},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.18850919},
  howpublished = {\url{https://doi.org/10.5281/zenodo.18850919}}
}