Cole-SAS-Maxwell Attenuation Model

Overview

This reprository contains a reference implementation of the Cole-SAS-Maxwell anelastic attenuation model, developed to computed frequency-, temperature-, and pressure-dependent shear attenuation $Q_\mu^{-1}(\omega; T,P)$ in water ice (ice Ih).

The model integrated the dominant anelastic relaxation mechanisms relevant to planetary cryospheres, including:

• Proton reorientation (H-bond),
• Dislocation-based anelasticity,
• Viscoelastic background response (Maxwell). It is designed for applications spanning planetary seismology / wave propagation in icy shells and investigating attenuation-controlled processes at relevant conditions.

Context

Intrinsic attenution models decribe the frequency-dependent viscoelastic response of materials and are widely used across disciplines such as seismology, geodynamics, and planetary science. This implementation targets conditions relevant to icy satellites and planetary cryospheres, bridging seismic (Hz) to tidal (mHz) frequency regimes.

This model is consistent with laboratory- and field-derived attenuation measurements and reproduces published quality factors over a wide range of thermodynamic conditions.

Features

Compute the (seismic) shear quality factor $Q_\mu^{-1}(\omega; T,P)$ for ice Ih.

Validity$^*$:

• Frequency range: 0.001-300 Hz
• Temperature: 94-260 K
• Pressure range: 0.1 (near-surface)-100 MPa (ice-ocean)

$*$ Tested against data under all conditions except P = 100 MPa.

Suitable for:

• synthetic seismogram modeling,
• depth-dependent attenuation profiles,
• tidal dissipation studies in icy shells

Run

Installation

Create the conda environement:

conda env create -f environment.yml
conda activate qmu-env

Install the project in editable mode:

pip intall -e .

Usage

Run the model from the project root directory:

python run_qmu_vs_T.py

References

If you use this code, please cite:

• Delaroque et al. 2026 - original developement of the Cole-SAS-Maxwell model

Other usefule references:

• Cole et al. (1995) - background attenuation model
• Castillo et al. (2011) – proton orientation formulation included in the Cole-SAS-Maxwell model
• Tobie et al. (2025) - Maxwell term for a best fit of low frequencies
• Cammarano et al. (2006); Tobie et al. (2025) - comparative attenuation models

Limitations

The model is currently calibrated for pure water ice (ice Ih). Some parameters associated with high-pressure ice polymorphs (e.g., III, V, VI) cannot be directly extrapolated to thermodynamic conditions comparable to those of ice Ih.

Grain size, impurities, and partial melt effects are not explicitly included.

Pressure dependence is parametrerized using activation volumes.

Contact

Developed by Lorraine Delaroque
Institut de Physique du Globe de Paris, U. Paris Cité
E-mail: delaroque .at. ipgp.fr