Training data set for: Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries

<h2>Overview</h2> <p>This is a synthetic volcano deformation dataset accompanying the publication of&nbsp;<em><strong>Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries</strong></em>,<em><strong> </strong></em>on the journal <em>Volcanica</em>. Synthetic, quasi-static deformation is computed for magma chambers of various geometries, parameterized as spheroids or superpositions of spherical harmonics. Surface deformation is computed using the boundary element method (BEM) of Nikkhoo &amp; Walter (2015). Please reference our paper for details of computational methods.</p> <p>The dataset contains 50,000 realizations of magma chamber geometries/orientations/centroid depths and associated deformation fields. Surface deformation fields are sampled at discrete locations, with a uniform random distribution within [Lh x Lh], and a distribution that concentrates near the chamber (at radial distances, r = 10^(-3&nbsp;<em>&nbsp;random number) * </em>Lh/2). Note this dataset contains only a small fraction of the total dataset. In total, 824,393 realizations of magma chambers were used to train our emulators. For accessing the complete training data set, please contact the authors.&nbsp;</p> <p>Each .mat file contains the deformation field associated with a single chamber geometry. Use visData.m to visualize chamber geometry and associated surface displacement. Each file contains two MATLAB structures, "input" and "output".&nbsp;</p> <h2>Naming of each zip file</h2> <p>The numbers after the underscore, N:M, indicate that this file contains N of the M total chamber realizations for this particular setup.&nbsp;</p> <p><a href="../api/records/13800065/draft/files/sph_20AspRatios_1e4:151211.zip.zip/content" target="_blank" rel="noopener noreferrer">sph_20AspRatios_1e4:151211.zip</a>: deformation corresponding to spheroidal magma chambers parameterized by aspect ratios.&nbsp;</p> <p><a href="../api/records/13800065/draft/files/sh_complex_1e4:152283.zip/content" target="_blank" rel="noopener noreferrer">sh_complex_1e4:152283.zip</a>: deformation corresponding to chamber geometry produced by superposition of spherical harmonic modes.&nbsp;</p> <p><a href="../api/records/13800065/draft/files/sh_mode_approx_1e4:138380.zip/content" target="_blank" rel="noopener noreferrer">sh_mode_approx_1e4:138380.zip</a>: deformation corresponding to chamber geometries corresponding to individual spherical harmonic modes, combined with a spherical mode (the spherical mode prevents chamber surfaces from having zero radii locally)</p> <p><a href="../api/records/13800065/draft/files/sh_spheroid_approx1e4:202272.zip/content" target="_blank" rel="noopener noreferrer">sh_spheroid_approx1e4:202272.zip</a>: deformation corresponding to chambers approximating spheroids, but&nbsp;parameterized by spherical harmonics.</p> <p><a href="../api/records/13800065/draft/files/sh_spheroid_perturb_1e4:180247.zip/content" target="_blank" rel="noopener noreferrer">sh_spheroid_perturb_1e4:180247.zip</a>: same as above, but with additional random perturbations parameterized in spherical harmonics.</p> <h2>Variables in each file</h2> <p><strong>Input</strong> contains the following fields:</p> <p><strong>dp2mu</strong>: pressure change to shear modulus ratio.</p> <p><strong>dx</strong>, <strong>dy</strong>, <strong>dz</strong>: the coordinates of chamber centroid [meters]</p> <p><strong>mu:&nbsp;</strong>dimensionless crustal shear modulus (always set to 1)</p> <p><strong>nu</strong>: crustal Poisson's ratio (always set to 0.25)</p> <p><strong>Ns</strong>: number of points on the surface where displacements are computed</p> <p><strong>Lh</strong>, <strong>Lv</strong>: horizontal and vertical dimensions of the model domain [meters]. Lh is determined such that at the edge of the model domain, the displacement magnitude is below 10 percent of the maximum. Lv = Lh/2 + abs(dz)</p> <p>for the spheroids -----------------------------------------------------------------------------------------------------------</p> <p>the input files contain</p> <p><strong>asp</strong>: aspect ratio of chamber (length of the semi-major axis divided by that of the semi-minor axis)</p> <p><strong>ra</strong>, <strong>rb</strong>: semi-major, -minor, axis length [meters]</p> <p><strong>thetax</strong>, <strong>thetay</strong>, <strong>thetaz</strong>: counterclockwise rotation angles with regard to x, y, z axis [degrees]. thetax = [0, 90] degrees, thetay = 0 degrees, thetaz = 360 degrees.</p> <p>for the general geometries--------------------------------------------------------------------------------------------------</p> <p>the input files contain</p> <p><strong>ls</strong>, <strong>ms</strong>, <strong>fs</strong>: degree, order, coefficients of spherical harmonic modes. Spherical harmonics are sampled up to degree 5. fs is a complex vector of coefficients such that the resulting shape is real.&nbsp;</p> <p><strong>normF</strong>: normalization factor applied to the shape parameterized by ls, ms, fs, such that the shape as a maximum radius of unity.</p> <p><strong>rmax</strong>: scale factor to scale the spherical harmonics parameterized shape to real dimensions [meters].</p> <p>=============================================================================================</p> <p>Output contains the following fields,</p> <p><strong>X</strong>, <strong>Y</strong>, <strong>Z</strong>: coordinates of points where displacement vectors are computed [meters]</p> <p><strong>Ux</strong>, <strong>Uy</strong>, <strong>Uz</strong>: displacements in x, y, z directions [meters]</p> <p><strong>P</strong>, <strong>T</strong>: coordinates [meters] of vertices for the triangular mesh used in BEM calculation, and the connectivity matrix&nbsp;</p> <p><strong>C</strong>: coordinates [meters] of the center of each triangular element</p> <p><strong>that</strong>, <strong>dhat</strong>, <strong>nhat</strong>: unit vectors for orthogonal coordinate systems local to each triangular element. that ("t-hat") extends from vertex one to vertex two, nhat is outward normal, and dhat = cross (nhat, that).</p> <p>Reference:</p> <p>1. Nikkhoo, M., &amp; Walter, T. R. (2015). Triangular dislocation: an analytical, artefact-free solution.&nbsp;<em>Geophysical Journal International</em>,&nbsp;<em>201</em>(2), 1119-1141.</p>