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

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

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

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

Scripts

• scripts/avo_analysis.py - AVO modeling and classification