.. _seismic_tutorial: ============================== Seismic wave analysis tutorial ============================== :Last updated: |today| :Author: **Gianfranco Ulian** Preliminary operations ====================== Download the :download:`hydroxylapatite input file<../downloads/hydroxylapatite.dat>`, which contains the second-order elastic moduli tensor of hydroxylapatite in Voigt's notation (values in GPa) and the density of the mineral, expressed in :math:`kg\ m^{-3}`. [1]_ Put this file in a folder of your choice and enter in this folder via the command prompt (or console under Linux/Mac OSX). Analysis of the acoustic wave velocities by solving the Christoffel's equation ============================================================================== This analysis is conducted in an automated mode by Quantas, so it is sufficient to type: .. code-block:: console > quantas seismic hydroxylapatite.dat to perform it. Quantas reports the initial settings used in this analysis: .. code-block:: console ________ __ \_____ \ __ _______ _____/ |______ ______ / / \ \| | \__ \ / \ __\__ \ / ___/ / \_/. \ | // __ \| | \ | / __ \_\___ \ \_____\ \_/____/(____ /___| /__| (____ /____ > \__> \/ \/ \/ \/ v0.9.1 Authors: Gianfranco Ulian Copyright 2020, University of Bologna Calculator: wave velocities from Christoffel's equation Measurement units ------------------------------------- - pressure: GPa Number of angular points ------------------------------------- - ntheta: 180 - nphi: 720 Measurement units ------------------------------------- - pressure: GPa Plotting ------------------------------------- - requested: True - dpi: 80 - 3D plots: True - 2D plots: True - projection: Lambert equal area .. warning:: At the moment, only elastic constants expressed in GPa are supported. If you want to follow this tutorial with elastic constants for a system of your choice, and their value are not in GPa, please, convert them in this units before creating the input file and starting the analysis. Then, the input file is read and relevant properties are printed on screen (and in the output file ``hydroxylapatite_SEISMIC.txt``): .. code-block:: console Reading input file: hydroxylapatite.dat Analysis of the sound velocities in Hydroxylapatite Stiffness matrix (values in GPa) 187.2080 65.1930 84.7030 0.0000 0.0000 0.0000 65.1930 187.2080 84.7030 0.0000 0.0000 0.0000 84.7030 84.7030 222.6580 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 39.6870 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 39.6870 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 61.0070 Compliance tensor (values in TPa^-1) 6.758054 -1.437660 -2.023971 0.000000 0.000000 0.000000 -1.437660 6.758054 -2.023971 0.000000 0.000000 0.000000 -2.023971 -2.023971 6.031101 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 25.197168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 25.197168 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 16.391562 Then, the Quantas calculated the phase velocities, group velocities, power flow angle and the enhancement factor of the mineral along on different directions. .. code-block:: console Start calculation of velocities by solving Christoffel's equation [##################################################] 100% After this operation ended, both 3D (spherical) and 2D (polar) plots of the calculated properties are made. .. code-block:: console Calculated data exported to hydroxylapatite_SEISMIC.hdf5 - making 3D plots of phase velocity - making 2D plots of phase velocity * Slow Secondary: anisotropy = 16.6 % * Fast Secondary: anisotropy = 21.4 % * Primary: anisotropy = 10.4 % - making 3D plots of relative phase velocity - making 2D plots of relative phase velocity - making 3D plots of group velocity - making 2D plots of group velocity * Slow Secondary: anisotropy = 21.3 % * Fast Secondary: anisotropy = 21.4 % * Primary: anisotropy = 10.4 % - making 3D plots of relative group velocity - making 2D plots of relative group velocity - making 3D plots of powerflow angle - making 2D plots of powerflow angle - making 3D plots of enhancement factor - making 2D plots of enhancement factor - making 2D plots of different ratios: * S-wave anisotropy = 200*(v_s1-v_s2)/(v_s1+v_s2) * v_P/v_s1 * v_P/v_s2 - making 2D plots of polarization The produced polar plots should be like the following ones: .. image:: ../_static/hydroxylapatite_Vp_2D_eqar.png :align: center :alt: Upper hemisphere equal area projection of the slow secondary, fast secondary and primary phase velocities. Upper hemisphere equal area projection of the slow secondary, fast secondary and primary phase velocities. .. image:: ../_static/hydroxylapatite_Vg_2D_eqar.png :align: center :alt: Upper hemisphere equal area projection of the slow secondary, fast secondary and primary group velocities. Upper hemisphere equal area projection of the slow secondary, fast secondary and primary group velocities. .. image:: ../_static/hydroxylapatite_pf_angle_2D_eqar.png :align: center :alt: Upper hemisphere equal area projection of the slow secondary, fast secondary and primary power flow angle. Upper hemisphere equal area projection of the slow secondary, fast secondary and primary power flow angle. .. image:: ../_static/hydroxylapatite_enhancement_factor_2D_eqar.png :align: center :alt: Upper hemisphere equal area projection of the slow secondary, fast secondary and primary enhancement factor. Upper hemisphere equal area projection of the slow secondary, fast secondary and primary enhancement factor. .. image:: ../_static/hydroxylapatite_Vp_2D_eqar_polarization.png :align: center :alt: Upper hemisphere equal area projection of the slow secondary, fast secondary and primary polarization of the phase velocities. Upper hemisphere equal area projection of the slow secondary, fast secondary and primary polarization of the phase velocities. .. note:: The calculated data reported in the ``hydroxylapatite_SEISMIC.hdf5`` contains the values used to generate the 2D and 3D plots of the elastic properties of the crystalline material. They can be extracted to generate plots according to the user's preferences via: .. code-block:: console quantas export seismic hydroxylapatite_SEISMIC.hdf5 .. rubric:: References .. [1] Ulian, G., Valdre, G., 2018. Second-order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: comparison between DFT functionals and basis sets. Int. J. Quantum Chem. 118, e25500