Bruges

bruges - Geophysics Equations

Quick Reference

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

AVO Analysis

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

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

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

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

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

from bruges.rockphysics import gardner, castagna

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

AVO Classification

When to Use vs Alternatives

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

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 - Velocity-porosity models and moduli
• Wavelets - Wavelet types, parameters, and selection

Scripts

• scripts/avo_analysis.py - AVO modeling and classification