bruges

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Geophysical equations and rock physics calculations for seismic analysis.
Changelog: Source: GitHub https://github.com/SteadfastAsArt/geoscience-skills
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Current level: bruges/
📁 references/
- 📄 rock_physics.md 4.6 KB
- 📄 wavelets.md 4.7 KB
📁 scripts/
- 📄 avo_analysis.py 9.3 KB
📄 SKILL.md 6.6 KB
SKILL.md

---
name: bruges
description: |
  Geophysical equations and rock physics calculations for seismic analysis.
  Use when Claude needs to: (1) Calculate AVO responses (Zoeppritz, Shuey, Aki-Richards),
  (2) Perform Gassmann fluid substitution, (3) Generate seismic wavelets (Ricker, Ormsby),
  (4) Compute reflectivity and synthetic seismograms, (5) Calculate elastic moduli from
  velocities, (6) Apply Gardner/Castagna empirical relations, (7) Model rock physics effects.
version: 1.0.0
author: Geoscience Skills
license: MIT
tags: [Rock Physics, AVO, Gassmann, Wavelets, Seismic Modelling]
dependencies: [bruges>=0.5.0, numpy, scipy]
complements: [segyio, obspy, lasio, welly]
workflow_role: analysis
---

# bruges - Geophysics Equations

## Quick Reference

```python
import bruges
import numpy as np

# AVO - Zoeppritz reflectivity
from bruges.reflection import zoeppritz
theta = np.arange(0, 45, 1)
Rpp = zoeppritz(vp1, vs1, rho1, vp2, vs2, rho2, theta)

# Wavelet - Ricker
from bruges.filters import ricker
t, w = ricker(duration=0.128, dt=0.001, f=25)

# Fluid substitution
from bruges.rockphysics import gassmann
vp_new, vs_new, rho_new = gassmann(vp, vs, rho, k_min, rho_min,
                                    k_fl1, rho_fl1, k_fl2, rho_fl2, phi)
```

## Module Overview

| Module | Purpose |
|--------|---------|
| `bruges.reflection` | Zoeppritz, Shuey, Aki-Richards AVO equations |
| `bruges.rockphysics` | Gassmann, Gardner, Castagna, elastic moduli |
| `bruges.filters` | Ricker, Ormsby wavelets, convolution |

## AVO Analysis

```python
from bruges.reflection import zoeppritz, shuey, akirichards
theta = np.arange(0, 45, 1)  # degrees

Rpp = zoeppritz(vp1, vs1, rho1, vp2, vs2, rho2, theta)  # Exact
Rpp = shuey(vp1, vs1, rho1, vp2, vs2, rho2, theta)      # Fast (~30 deg)
Rpp, G = akirichards(vp1, vs1, rho1, vp2, vs2, rho2, theta, return_gradient=True)
```

## Fluid Substitution

```python
from bruges.rockphysics import gassmann

vp_new, vs_new, rho_new = gassmann(
    vp_sat, vs_sat, rho_sat,   # Original saturated rock
    k_min, rho_min,             # Mineral (quartz: 37 GPa, 2.65 g/cc)
    k_fl1, rho_fl1,             # Original fluid (brine: 2.5 GPa, 1.05 g/cc)
    k_fl2, rho_fl2,             # New fluid (oil: 0.9 GPa, 0.8 g/cc)
    phi                         # Porosity
)
```

## Wavelets

```python
from bruges.filters import ricker, ormsby

# Ricker (single frequency)
t, wavelet = ricker(duration=0.128, dt=0.001, f=25)

# Ormsby (bandpass: low cut, low pass, high pass, high cut)
t, wavelet = ormsby(duration=0.128, dt=0.001, f=[5, 10, 50, 60])
```

## Synthetic Seismogram

```python
from bruges.filters import ricker
from scipy.signal import convolve

rc = np.diff(impedance) / (impedance[:-1] + impedance[1:])  # Reflectivity
_, wavelet = ricker(0.128, 0.001, 30)
synthetic = convolve(rc, wavelet, mode='same')
```

## Elastic Moduli

```python
from bruges.rockphysics import moduli

K = moduli.bulk(vp, vs, rho)      # Bulk modulus (GPa)
mu = moduli.shear(vs, rho)        # Shear modulus (GPa)
E = moduli.youngs(vp, vs, rho)    # Young's modulus (GPa)
nu = moduli.poissons(vp, vs)      # Poisson's ratio
```

## Empirical Relations

```python
from bruges.rockphysics import gardner, castagna

rho = gardner(vp)    # Density from Vp (g/cc)
vs = castagna(vp)    # Vs from Vp (mudrock line)
```

## AVO Classification

| Class | Intercept | Gradient | Description |
|-------|-----------|----------|-------------|
| I | + | - | High impedance sand |
| II | ~0 | - | Near-zero intercept |
| IIp | ~0 | + | Phase reversal |
| III | - | - | Low impedance sand |
| IV | - | + | Very low impedance |

## When to Use vs Alternatives

| Use Case | Tool | Why |
|----------|------|-----|
| AVO modelling and reflectivity | **bruges** | Complete Zoeppritz/Shuey/Aki-Richards suite |
| Gassmann fluid substitution | **bruges** | Clean API, validated equations |
| Seismic wavelets | **bruges** | Ricker, Ormsby, and more out of the box |
| Elastic moduli calculations | **bruges** | Bulk, shear, Young's, Poisson's from Vp/Vs |
| Advanced rock physics models | **rockphypy** | More models (Hashin-Shtrikman, DEM, etc.) |
| Simple impedance/reflectivity | **Custom numpy** | Fewer dependencies for basic calculations |
| Full seismic modelling (FD/FE) | **Devito / SimPEG** | Wave equation solvers |
| Well log processing | **welly / lasio** | LAS file I/O and log manipulation |

**Choose bruges when**: You need validated geophysical equations for AVO analysis,
fluid substitution, or synthetic seismogram generation. It provides clean, tested
implementations of standard rock physics equations.

**Choose rockphypy when**: You need a broader set of rock physics models beyond
what bruges offers, such as effective medium theories or contact models.

**Choose custom numpy when**: You only need a single equation (e.g., acoustic
impedance = Vp * rho) and want to avoid adding a dependency.

## Common Workflows

### AVO Analysis and Synthetic Seismogram Generation
- [ ] Define layer properties (Vp, Vs, density) from well logs or literature
- [ ] Compute acoustic impedance: `AI = Vp * rho`
- [ ] Compute reflectivity series using `zoeppritz()` or `shuey()` for each interface
- [ ] Classify AVO response (Class I-IV) from intercept and gradient
- [ ] Perform Gassmann fluid substitution to model fluid effects on Vp/Vs
- [ ] Recompute reflectivity with substituted properties
- [ ] Generate Ricker or Ormsby wavelet at target frequency
- [ ] Convolve reflectivity with wavelet to create synthetic seismogram
- [ ] Compare synthetic with observed seismic for well tie
- [ ] Compute elastic moduli (K, mu, E, nu) for crossplot analysis
- [ ] Create AVO crossplots (intercept vs gradient) to identify anomalies

## Common Issues

| Issue | Solution |
|-------|----------|
| Rpp blows up at high angles | Use Zoeppritz (exact) instead of Shuey above 30 degrees |
| Gassmann gives unrealistic Vp | Check mineral modulus and porosity values |
| Wavelet length too short | Increase `duration` parameter (try 0.128-0.256 s) |
| Negative shear modulus | Verify Vs < Vp and density is reasonable |
| Units mismatch | Ensure consistent units: m/s for velocity, g/cc for density |

## Tips

1. **Zoeppritz is exact** but slower - use Shuey for angles < 30 degrees
2. **Gassmann assumes** low frequency and connected pores
3. **Gardner/Castagna** are empirical - calibrate to your data
4. **Angles in degrees** for reflection functions

## References

- **[Rock Physics Equations](references/rock_physics.md)** - Velocity-porosity models and moduli
- **[Wavelets](references/wavelets.md)** - Wavelet types, parameters, and selection

## Scripts

- **[scripts/avo_analysis.py](scripts/avo_analysis.py)** - AVO modeling and classification
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