seidart.routines.materials module

seidart.routines.materials.anisotropic_boolean(im: ndarray | list, matbool: ndarray | list, angvect: ndarray | list) → Tuple[ndarray, ndarray]

Determines if materials identified in an image are anisotropic and provides corresponding angular file names if applicable.

Parameters:

  • im (Union[np.ndarray, list]) – An array representing material IDs in an image.

  • matbool (Union[np.ndarray, list]) – Array indicating whether a material is anisotropic.

  • angvect (Union[np.ndarray, list]) – Array of angular file names for anisotropic materials.

Returns:

A tuple of two arrays; the first indicates anisotropy (boolean), the second contains angular file names.

Return type:

Tuple[np.ndarray, np.ndarray]

seidart.routines.materials.bond(R: ndarray) → ndarray

Calculates the 6x6 Bond transformation matrix from a 3x3 rotation matrix, useful for transforming stiffness or compliance matrices in crystallography and materials science.

Parameters:

R (np.ndarray) – The 3x3 rotation matrix.

Return M:

The 6x6 Bond transformation matrix.

Rtype M:

np.ndarray

seidart.routines.materials.fujita_complex_permittivity(temperature: float, frequency: float) → float

Calculates the complex permittivity of ice using Fujita’s method, based on the provided temperature and frequency.

Parameters:

  • temperature (float) – The temperature of ice in degrees Celsius.

  • frequency (float) – The frequency at which to calculate permittivity, in Hz.

Returns:

The complex permittivity value.

Return type:

float

seidart.routines.materials.get_perm(material, modelclass) → ndarray

Computes the permittivity and conductivity tensors for materials based on attributes contained within material and model class instances.

Parameters:

  • material (Material) – An instance of a class containing attributes for materials, including temperature, density, porosity, water content, and anisotropic properties.

  • modelclass (Model) – An instance of a class containing modeling parameters, such as the frequency of interest for electromagnetic modeling.

Returns:

A tensor array containing permittivity and conductivity values for each material.

Return type:

np.ndarray

seidart.routines.materials.get_seismic(material_name: list | ndarray = [None], temp: list | ndarray = [None], rho: list | ndarray = [None], porosity: list | ndarray = [0], lwc: list | ndarray = [0], anisotropic: list | ndarray = [False], angfile: list | ndarray = [None]) → ndarray

Calculates seismic stiffness coefficients based on material properties, accounting for anisotropic conditions where applicable.

Parameters:

  • material_name (Union[list, np.ndarray], optional) – Names of materials.

  • temp (Union[list, np.ndarray], optional) – Temperatures associated with each material.

  • rho (Union[list, np.ndarray], optional) – Densities of materials.

  • porosity (Union[list, np.ndarray], optional) – Porosities of materials.

  • lwc (Union[list, np.ndarray], optional) – Liquid water contents of materials.

  • anisotropic (Union[list, np.ndarray], optional) – Indicates if materials are anisotropic.

  • angfile (Union[list, np.ndarray], optional) – Angular files associated with anisotropic materials.

Returns:

A tensor containing seismic stiffness coefficients.

Return type:

np.ndarray

seidart.routines.materials.ice_permittivity(temperature: float, density: float, center_frequency: float = None, method: str = 'fujita') → ndarray

Computes the complex permittivity of ice given its temperature, density, and the frequency of interest. Supports different methods of calculation.

Parameters:

  • temperature (float) – Temperature of the ice in degrees Celsius.

  • density (float) – Density of the ice in kg/m^3.

  • center_frequency (float, optional) – Frequency at which to compute permittivity, in Hz.

  • method (str) – The method used for calculating permittivity. Supports “kovacs” and “fujita”.

Returns:

The complex permittivity tensor for ice.

Return type:

np.ndarray

seidart.routines.materials.ice_stiffness(temperature: float = None, pressure: float = 0.0) → ndarray

Computes the stiffness tensor for ice under specified temperature and pressure conditions based on empirical relationships.

Parameters:

  • temperature (float, optional) – The temperature at which to compute the stiffness tensor.

  • pressure (float) – The pressure at which to compute the stiffness tensor.

Returns:

The stiffness tensor for ice.

Return type:

np.ndarray

seidart.routines.materials.isotropic_permittivity_tensor(temperature: float, porosity: float, water_content: float, material_name: str) → Tuple[ndarray, ndarray]

Computes the isotropic permittivity tensor for a material based on temperature, porosity, water content, and the material’s inherent properties.

Parameters:

  • temperature (float) – The temperature of the material.

  • porosity (float) – The porosity of the material.

  • water_content (float) – The water content in the material.

  • material_name (str) – The name of the material.

Returns:

A tuple containing the permittivity and conductivity tensors.

Return type:

Tuple[np.ndarray, np.ndarray]

seidart.routines.materials.isotropic_stiffness_tensor(pressure: float, density: float, material_limits: ndarray) → ndarray

Computes the isotropic stiffness tensor for a given material based on pressure, density, and predefined material properties.

Parameters:

  • pressure (float) – The hydrostatic pressure to which the material is subjected.

  • density (float) – The density of the material.

  • material_limits (np.ndarray) – An array containing the material’s velocity limits and other relevant properties.

Returns:

The isotropic stiffness tensor for the material.

Return type:

np.ndarray

seidart.routines.materials.porewater_correction(temperature: float, density: float, porosity: float, liquid_water_content: float) → Tuple[float, float, float]

Applies corrections to the bulk density of a material based on its porosity and water content, considering temperature adjustments to the densities of air and water.

Parameters:

  • temperature (float) – The temperature of the material.

  • density (float) – The initial density of the material.

  • porosity (float) – The porosity percentage of the material.

  • liquid_water_content (float) – The percentage of the pore space filled with water.

Returns:

A tuple containing the corrected density, the density contribution from air, and the density contribution from water.

Return type:

Tuple[float, float, float]

seidart.routines.materials.pressure_array(im: list | ndarray, temp: list | ndarray, rho: list | ndarray, dz: list | ndarray, porosity: list | ndarray = [0], lwc: list | ndarray = [0]) → Tuple[ndarray, ndarray, ndarray]

Computes the hydrostatic pressure, temperature, and density at each grid point based on material ID, accounting for porosity and water content.

Parameters:

  • im (Union[list, np.ndarray]) – An m-by-n array of integer values representing material IDs.

  • temp (Union[list, np.ndarray]) – Temperatures at each grid point.

  • rho (Union[list, np.ndarray]) – Densities at each grid point.

  • dz (Union[list, np.ndarray]) – Vertical spacing between grid points.

  • porosity (Union[list, np.ndarray], optional) – Porosities at each grid point, default is a list of zeros.

  • lwc (Union[list, np.ndarray], optional) – Liquid water contents at each grid point, default is a list of zeros.

Returns:

A tuple containing arrays for temperature, density, and hydrostatic pressure at each grid point.

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

seidart.routines.materials.read_ang(filepath: str) → ndarray

Reads Euler angles from a space delimited .ang file, typically associated with EBSD (Electron Backscatter Diffraction) data. Synthetic data can be built with the fabricsynth module.

Parameters:

filepath (str) – The path to the .ang file.

Returns:

An array of Euler angles extracted from the file.

Return type:

np.ndarray

Note

The .ang file is expected to contain columns for Euler angles in radians, following Bunge’s notation (z-x-z rotation), among other data related to EBSD measurements.

seidart.routines.materials.rho_water_correction(temperature: float = 0.0) → float

Corrects the density of water based on temperature using the empirical formula derived from the Kell equation.

Parameters:

temperature (float) – The temperature at which to compute the water density correction.

Returns:

The corrected water density.

Return type:

float

seidart.routines.materials.rotator_zxz(eul: ndarray) → ndarray

Generates a rotation matrix from Euler angles using the z-x-z rotation convention.

Parameters:

eul (np.ndarray) – An array containing the three Euler angles.

Returns:

The 3x3 rotation matrix derived from the Euler angles.

Return type:

np.ndarray

seidart.routines.materials.snow_conductivity(lwc: float = None, permittivity: ndarray = None, frequency: float = None) → ndarray

Computes the electrical conductivity of snow given its liquid water content (LWC), permittivity, and frequency of interest.

Parameters:

  • lwc (float, optional) – Liquid water content of the snow, optionally used if permittivity is not provided.

  • permittivity (np.ndarray, optional) – The complex permittivity of snow, if available.

  • frequency (float, optional) – Frequency at which conductivity is to be calculated, in Hz.

Returns:

The conductivity tensor for snow.

Return type:

np.ndarray

seidart.routines.materials.snow_permittivity(density: float = 917.0, temperature: float = 0.0, lwc: float = 0.0, porosity: float = 50.0, center_frequency: float = 10000000.0, method: str = 'shivola-tiuri') → ndarray

Calculates the complex permittivity of snow based on its density, temperature, liquid water content (LWC), porosity, and the chosen calculation method.

Parameters:

  • density (float) – Density of the snow in kg/m^3.

  • temperature (float) – Temperature of the snow in degrees Celsius.

  • lwc (float) – Liquid water content of the snow in percentage.

  • porosity (float) – Porosity of the snow in percentage.

  • method (str) – The method to be used for calculating permittivity. Defaults to “shivola-tiuri”.

Returns:

The complex permittivity tensor for snow.

Return type:

np.ndarray