Seismic anisotropy, the directional dependency of seismic wave
+ velocities, is important for mapping the Earth’s structure and
+ understanding geodynamic processes. Seismic anisotropy primarily stems
+ from the development of mineral crystallographic preferred orientation
+ (i.e. texture) during the plastic deformation of rocks. In-depth
+ analysis of data from texture characterization techniques like
+ Electron Backscatter Diffraction (EBSD) enables the determination of
+ mineral and bulk-rock elastic properties. Although the influences of
+ pressure, temperature, and melt on elastic properties and seismic
+ anisotropy is well understood, they are often disregarded. To help
+ address this gap, we developed SAnTex: Seismic Anisotropy from
+ Texture, an open-source Python library that calculates the full
+ elastic tensor of rocks from modal mineral composition,
+ crystallographic orientation, and a crystal stiffness tensor catalogue
+ that accounts for the dependency of elasticity with pressure,
+ temperature and melt. The elastic wave velocities
+ (
Understanding seismic wave velocities and anisotropy is crucial for
+ deciphering the composition, structure, and rheological behaviour of
+ the Earth’s crust and mantle. Seismic anisotropy primarily emerges
+ from the propagation of waves through rocks that have developed
+ crystallographic preferred orientations (CPO) as a result of plastic
+ deformation
+ (
Seismic anisotropy calculations that rely on the integration of
+ textural data obtained by Electron Backscatter Diffraction (EBSD) with
+ experimentally determined elastic stiffness tensors have become
+ standard practice in rock-based geodynamic studies
+ (
Melt characteristics — such as fraction, shape, distribution, and
+ orientation have well-understood effects on seismic properties
+ (
To address these gaps, we have developed SAnTex (Seismic Anisotropy
+ from Texture), a free, open-source Python library. Built upon
+ open-source libraries such as ORIX
+ (
Hooke’s law characterizes the response of materials to tensile or
+ compressive forces. In its generalized formulation, the law asserts
+ that the stress tensor is linearly related to the strain tensor
+ through the material’s stiffness properties
+ (
where
The stiffness tensors are derived from laboratory experiments, and + represent the intrinsic elastic properties of individual minerals. The + calculated effective stiffness tensors, on the other hand, provide a + more realistic representation of rock behaviour in the Earth’s crust + and upper mantle. They account for the combined influence of pressure + and temperature.
+The pressure and temperature dependence of elastic constants is
+ primarily linear but can include non-linear effects that can be
+ approximated up to second-order terms using a Taylor series expansion
+ (
Within SAnTex,
Pressure and temperature have competing effects on the stiffness + tensor. Higher temperatures increase atomic vibrations, making it + easier for the material to deform, while higher pressures force atoms + closer together, making it more difficult for the material to + deform.
+In the current version of SAnTex, melt is considered as a
+ homogeneously distributed isotropic phase within an anisotropic host
+ rock
+ (
The fraction of melt,
EBSD maps after cleaning using (a) MTEX and (b) SAnTex. + Seismic Anisotropy maps using (c) MTEX at ambient pressure and + temperature and SAnTex at (d) ambient pressure and temperature, (e) + at 1.4 GPa and 1100° K, and (f) 1.4 GPa and 1100° K with 7% silicate + melt. Density, P and S wave velocities against (g) temperature and + (h) pressure. The gray shaded areas show the upper and lower + Hashin-Shtrikman bounds scaled by a factor of 1000 to demonstrate + the difference between lower and upper bounds.
SAnTex calculates seismic properties from EBSD crystal orientation + data using the following steps:
+-
+
Calculation of the effective tensor constants by incorporating + pressure and temperature derivatives. SAnTex includes an inbuilt + catalogue of minerals, for which it automatically calculates the + stiffness tensors and density for a range of pressure and + temperature conditions.
+Determination of the effective stiffness tensors by applying + Taylor series expansion.
+Computation of a mean stiffness tensor using the + Voigt-Reuss-Hill bounds. These bounds provide an estimate for the + effective elastic moduli of heterogeneous or anisotropic materials + by averaging the Voigt (upper bound, corresponding to uniform + strain) and Reuss (lower bound, corresponding to uniform stress) + approximations.
+Incorporation of the effect of melt on seismic properties + through a nonlinear peridotite melting curve between solidus and + liquidus (McKenzie & Bickle, 1988). Alternatively, a melt + fraction value can be imposed by the user.
+The capabilities of SAnTex are tested on previously published data
+ using MTEX for a peridotite xenolith from Marie Byrd Land volcanic
+ province in West Antarctica (Fig. 1)
+ (
SAnTex allows for (Fig. 2):
+-
+
Processing of EBSD data: Facilitates the processing and
+ cleaning of EBSD data. It leverages the ORIX software package for
+ the calculation of pole figures, pole density functions and
+ inverse pole figures
+ (
Tensor operations: Supports conversions between the Voigt + matrix representation and full stiffness tensor forms. + Additionally, tensor rotations are performed using orientations + (Euler angles following the ZXZ convention) to transform tensors + between different coordinate systems.
+Material analysis: Includes a comprehensive mineral catalogue + that facilitates the calculation of seismic properties based on a + given mineralogical composition. Users may either select phases + corresponding to EBSD-determined phase abundances or assume a + modal mineral composition.
+Calculation of seismic anisotropy: Computes seismic velocities + and anisotropy across a range of pressure (0–13 GPa) and + temperature (300–2000 K) conditions (Fig. 1d, e, f), and provides + interactive 2D and 3D plots for visualizing the results (Fig. + 3).
+Calculation of isotropic velocities: Computes isotropic seismic
+ wave velocities and Hashin-Shtrikman bounds
+ (
Workflow of SAnTex with fundamental methods and classes + outlined.
3D visualisation of (a) Forsterite Vs splitting, (b)
+ Olivine Vs splitting, (c) Olivine
This research was supported by the Australian Research Council + grants ARC-DP220100709 and ARC-LP190100146. U. Singh acknowledges + financial support from the School of Geosciences at The University of + Sydney.
+