DOI: 10.5281/zenodo.13800064
title: Training data set for: Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries

description: Overview

This is a synthetic volcano deformation dataset accompanying the publication of Graph Neural Network based elastic deformation emulators for magmatic reservoirs of complex geometries, on the journal Volcanica. 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 & Walter (2015). Please reference our paper for details of computational methods.

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  random number) * 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. 

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". 

Naming of each zip file

The numbers after the underscore, N:M, indicate that this file contains N of the M total chamber realizations for this particular setup. 

sph_20AspRatios_1e4:151211.zip: deformation corresponding to spheroidal magma chambers parameterized by aspect ratios. 

sh_complex_1e4:152283.zip: deformation corresponding to chamber geometry produced by superposition of spherical harmonic modes. 

sh_mode_approx_1e4:138380.zip: 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)

sh_spheroid_approx1e4:202272.zip: deformation corresponding to chambers approximating spheroids, but parameterized by spherical harmonics.

sh_spheroid_perturb_1e4:180247.zip: same as above, but with additional random perturbations parameterized in spherical harmonics.

Variables in each file

Input contains the following fields:

dp2mu: pressure change to shear modulus ratio.

dx, dy, dz: the coordinates of chamber centroid [meters]

mu: dimensionless crustal shear modulus (always set to 1)

nu: crustal Poisson's ratio (always set to 0.25)

Ns: number of points on the surface where displacements are computed

Lh, Lv: 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)

for the spheroids -----------------------------------------------------------------------------------------------------------

the input files contain

asp: aspect ratio of chamber (length of the semi-major axis divided by that of the semi-minor axis)

ra, rb: semi-major, -minor, axis length [meters]

thetax, thetay, thetaz: counterclockwise rotation angles with regard to x, y, z axis [degrees]. thetax = [0, 90] degrees, thetay = 0 degrees, thetaz = 360 degrees.

for the general geometries--------------------------------------------------------------------------------------------------

the input files contain

ls, ms, fs: 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. 

normF: normalization factor applied to the shape parameterized by ls, ms, fs, such that the shape as a maximum radius of unity.

rmax: scale factor to scale the spherical harmonics parameterized shape to real dimensions [meters].

=============================================================================================

Output contains the following fields,

X, Y, Z: coordinates of points where displacement vectors are computed [meters]

Ux, Uy, Uz: displacements in x, y, z directions [meters]

P, T: coordinates [meters] of vertices for the triangular mesh used in BEM calculation, and the connectivity matrix 

C: coordinates [meters] of the center of each triangular element

that, dhat, nhat: 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).

Reference:

1. Nikkhoo, M., & Walter, T. R. (2015). Triangular dislocation: an analytical, artefact-free solution. Geophysical Journal International, 201(2), 1119-1141.