SeismicMesh 3.1.5

2D/3D serial and parallel triangular mesh generation for seismology

Create high-quality 2D/3D meshes from seismic velocity models.

SeismicMesh: Triangular Mesh generation in Python

SeismicMesh is a Python package for simplex mesh generation in two or three dimensions. As an implementation of DistMesh, it produces high-geometric quality meshes at the expense of speed. For increased efficiency, the core package is written in C++, works in parallel, and uses the Computational Geometry Algorithms Library. SeismicMesh can also produce mesh-density functions from seismological data to be used in the mesh generator.

SeismicMesh is distributed under the GPL3 license and more details can be found in our short paper.

Installation

Nov. 21, 2020 our software is not yet compatible with Python 3.9 because of the segyio package dependency which doesn't build yet with this version of Python. Until this is fixed, please use a Python version prior to 3.9 to run your scripts with this package.

For installation, SeismicMesh needs CGAL and pybind11:

sudo apt install libcgal-dev python3-pybind11

After that, SeismicMesh can be installed from the Python Package Index (pypi), so with:

pip install -U SeismicMesh

For more detailed information about installation and requirements see:

Install - How to install SeismicMesh.

Contributing

All contributions are welcome!

To contribute to the software:

1. Fork the repository.
2. Clone the forked repository, add your contributions and push the changes to your fork.
3. Create a Pull request

Before creating the pull request, make sure that the tests pass by running

tox

Some things that will increase the chance that your pull request is accepted:

• Write tests.
• Add Python docstrings that follow the Sphinx.
• Write good commit and pull request messages.

Problems?

If something isn't working as it should or you'd like to recommend a new addition/feature to the software, please let me know by starting an issue through the issues tab. I'll try to get to it as soon as possible.

Examples

The user can quickly build quality 2D/3D meshes from seismic velocity models in serial/parallel.

WARNING: To run the code snippet below you must download the 2D BP2004 seismic velocity model and then you must uncompress it (e.g., gunzip). This file can be downloaded from here

from mpi4py import MPI
import meshio

from SeismicMesh import get_sizing_function_from_segy, generate_mesh, Rectangle

comm = MPI.COMM_WORLD

"""
Build a mesh of the BP2004 benchmark velocity model in serial or parallel
Takes roughly 1 minute with 2 processors and less than 1 GB of RAM.
"""

# Name of SEG-Y file containg velocity model.
fname = "vel_z6.25m_x12.5m_exact.segy"

# Bounding box describing domain extents (corner coordinates)
bbox = (-12000.0, 0.0, 0.0, 67000.0)

# Desired minimum mesh size in domain
hmin = 75.0

rectangle = Rectangle(bbox)

# Construct mesh sizing object from velocity model
ef = get_sizing_function_from_segy(
    fname,
    bbox,
    hmin=hmin,
    wl=10,
    freq=2,
    dt=0.001,
    grade=0.15,
    domain_pad=1e3,
    pad_style="edge",
)

points, cells = generate_mesh(domain=rectangle, edge_length=ef)

if comm.rank == 0:
    # Write the mesh in a vtk format for visualization in ParaView
    # NOTE: SeismicMesh outputs assumes the domain is (z,x) so for visualization
    # in ParaView, we swap the axes so it appears as in the (x,z) plane.
    meshio.write_points_cells(
        "BP2004.vtk",
        points[:, [1, 0]] / 1000,
        [("triangle", cells)],
        file_format="vtk",
    )

WARNING: To run the code snippet below you must download (and uncompress) the 3D EAGE seismic velocity model from (WARNING: File is ~500 MB) here

WARNING: Computationaly demanding! Running this example takes around 3 minutes in serial and requires around 2 GB of RAM due to the 3D nature of the problem and the domain size.

from mpi4py import MPI
import zipfile
import meshio

from SeismicMesh import (
    get_sizing_function_from_segy,
    generate_mesh,
    sliver_removal,
    Cube,
)

comm = MPI.COMM_WORLD

# Bounding box describing domain extents (corner coordinates)
bbox = (-4200.0, 0.0, 0.0, 13520.0, 0.0, 13520.0)

# Desired minimum mesh size in domain.
hmin = 150.0

# This file is in a big Endian binary format, so we must tell the program the shape of the velocity model.
path = "Salt_Model_3D/3-D_Salt_Model/VEL_GRIDS/"
if comm.rank == 0:
    # Extract binary file Saltf@@ from SALTF.ZIP
    zipfile.ZipFile(path + "SALTF.ZIP", "r").extract("Saltf@@", path=path)

fname = path + "Saltf@@"

# Dimensions of model (number of grid points in z, x, and y)
nx, ny, nz = 676, 676, 210

cube = Cube(bbox)

# A graded sizing function is created from the velocity model along with a signed distance function by passing
# the velocity grid that we created above.
# More details can be found here: https://seismicmesh.readthedocs.io/en/master/api.html

ef = get_sizing_function_from_segy(
    fname,
    bbox,
    hmin=hmin,
    dt=0.001,
    freq=2,
    wl=5,
    grade=0.15,
    hmax=5e3,
    domain_pad=250,
    pad_style="linear_ramp",
    nz=nz,
    nx=nx,
    ny=ny,
    byte_order="big",
    axes_order=(2, 0, 1),  # order for EAGE (x, y, z) to default order (z,x,y)
    axes_order_sort="F",  # binary is packed in a FORTRAN-style
)

points, cells = generate_mesh(domain=cube, edge_length=ef, max_iter=75)

# For 3D mesh generation, we provide an implementation to bound the minimum dihedral angle::
points, cells = sliver_removal(
    points=points, bbox=bbox, domain=cube, edge_length=ef
)

# Meshes can be written quickly to disk using meshio and visualized with ParaView::
if comm.rank == 0:

    # NOTE: SeismicMesh outputs assumes the domain is (z,x,y) so for visualization
    # in ParaView, we swap the axes so it appears as in the (x,y,z) plane.
    meshio.write_points_cells(
        "EAGE_Salt.vtk",
        points[:, [1, 2, 0]] / 1000.0,
        [("tetra", cells)],
    )

The user can still specify their own signed distance functions and sizing functions to generate_mesh (in serial or parallel) just like the original DistMesh algorithm but now with quality bounds in 3D. Try the codes below!

# Mesh a cylinder
from mpi4py import MPI
import meshio

import SeismicMesh

comm = MPI.COMM_WORLD

hmin = 0.10

cylinder = SeismicMesh.Cylinder(h=1.0, r=0.5)

points, cells = SeismicMesh.generate_mesh(
    domain=cylinder,
    edge_length=hmin,
)

points, cells = SeismicMesh.sliver_removal(
    points=points,
    domain=cylinder,
    edge_length=hmin,
)

if comm.rank == 0:
    meshio.write_points_cells(
        "Cylinder.vtk",
        points,
        [("tetra", cells)],
        file_format="vtk",
    )

# mesh a disk
import meshio
import SeismicMesh

disk = SeismicMesh.Disk([0.0, 0.0], 1.0)
points, cells = SeismicMesh.generate_mesh(domain=disk, edge_length=0.1)
meshio.write_points_cells(
    "disk.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

# mesh a square/rectangle
import meshio
import SeismicMesh

bbox = (0.0, 1.0, 0.0, 1.0)
square = SeismicMesh.Rectangle(bbox)
points, cells = SeismicMesh.generate_mesh(domain=square, edge_length=0.05)
meshio.write_points_cells(
    "square.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

# mesh a cuboid/cube
import meshio
import SeismicMesh

bbox = (0.0, 1.0, 0.0, 1.0, 0.0, 1.0)
cube = SeismicMesh.Cube(bbox)
points, cells = SeismicMesh.generate_mesh(domain=cube, edge_length=0.05)
points, cells = SeismicMesh.sliver_removal(points=points, domain=cube, edge_length=0.05)
meshio.write_points_cells(
    "cube.vtk",
    points,
    [("tetra", cells)],
    file_format="vtk",
)

# mesh a torus
import meshio
import SeismicMesh

hmin = 0.10

torus = SeismicMesh.Torus(r1=1.0, r2=0.5)
points, cells = SeismicMesh.generate_mesh(
    domain=torus,
    edge_length=hmin,
)
points, cells = SeismicMesh.sliver_removal(
    points=points, domain=torus, edge_length=hmin
)
meshio.write_points_cells(
    "torus.vtk",
    points,
    [("tetra", cells)],
)

# mesh a prism
import meshio

import SeismicMesh

hmin = 0.05
prism = SeismicMesh.Prism(b=0.5, h=0.5)

points, cells = SeismicMesh.generate_mesh(
    domain=prism,
    edge_length=hmin,
)
points, cells = SeismicMesh.sliver_removal(
    points=points, domain=prism, edge_length=hmin
)
meshio.write_points_cells(
    "prism.vtk",
    points,
    [("tetra", cells)],
    file_format="vtk",
)

# Compute the union of several SDFs to create more complex geometries
import meshio
import SeismicMesh

h = 0.10
rect0 = SeismicMesh.Rectangle((0.0, 1.0, 0.0, 0.5))
rect1 = SeismicMesh.Rectangle((0.0, 0.5, 0.0, 1.0))
disk0 = SeismicMesh.Disk([0.5, 0.5], 0.5)
union = SeismicMesh.Union([rect0, rect1, disk0])
points, cells = SeismicMesh.generate_mesh(domain=union, edge_length=h)
meshio.write_points_cells(
    "Lshape_wDisk.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

# Compute the intersection of several SDFs to create more complex geometries
import meshio
import SeismicMesh

h = 0.05
rect0 = SeismicMesh.Rectangle((0.0, 1.0, 0.0, 1.0))
disk0 = SeismicMesh.Disk([0.25, 0.25], 0.5)
disk1 = SeismicMesh.Disk([0.75, 0.75], 0.5)
intersection = SeismicMesh.Intersection([rect0, disk0, disk1])
points, cells = SeismicMesh.generate_mesh(domain=intersection, edge_length=h)
meshio.write_points_cells(
    "Leaf.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

# Compute the difference of two SDFs to create more complex geometries.
import meshio
import SeismicMesh

h = 0.05
rect0 = SeismicMesh.Rectangle((0.0, 1.0, 0.0, 1.0))
disk0 = SeismicMesh.Disk([0.5, 0.5], 0.1)
disk1 = SeismicMesh.Disk([0.75, 0.75], 0.20)
difference = SeismicMesh.Difference([rect0, disk0, disk1])
points, cells = SeismicMesh.generate_mesh(domain=difference, edge_length=h)
meshio.write_points_cells(
    "Hole.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

# Compute the difference of several SDFs in 3D
import meshio
import SeismicMesh

h = 0.10
cube0 = SeismicMesh.Cube((0.0, 1.0, 0.0, 1.0, 0.0, 1.0))
ball1 = SeismicMesh.Ball([0.5, 0.0, 0.5], 0.30)
ball2 = SeismicMesh.Ball([0.5, 0.5, 0.0], 0.30)
ball3 = SeismicMesh.Ball([0.0, 0.5, 0.5], 0.30)
ball4 = SeismicMesh.Ball([0.5, 0.5, 0.5], 0.45)
difference = SeismicMesh.Difference([cube0, ball1, ball2, ball3, ball4])
points, cells = SeismicMesh.generate_mesh(domain=difference, edge_length=h, verbose=1)
points, cells = SeismicMesh.sliver_removal(
    points=points, domain=difference, edge_length=h, verbose=1
)
meshio.write_points_cells(
    "Cube_wHoles.vtk",
    points,
    [("tetra", cells)],
    file_format="vtk",
)

# Immerse a subdomain so that it's boundary is conforming in the mesh.
import numpy as np

import meshio

import SeismicMesh

box0 = SeismicMesh.Rectangle((-1.25, 0.0, -0.250, 1.250))
disk0 = SeismicMesh.Disk([-0.5, 0.5], 0.25)

hmin = 0.10


fh = lambda p: 0.05 * np.abs(disk0.eval(p)) + hmin

points, cells = SeismicMesh.generate_mesh(
    domain=box0,
    edge_length=fh,
    h0=hmin,
    subdomains=[disk0],
    max_iter=100,
)
meshio.write_points_cells(
    "Square_wsubdomain.vtk",
    points,
    [("triangle", cells)],
    file_format="vtk",
)

How does performance and cell quality compare to Gmsh and CGAL mesh generators?

• For an additional comparison of SeismicMesh against several other popular mesh generators head over to meshgen-comparison.

Here we use SeismicMesh 3.1.4, pygalmesh 0.8.2, and pygmsh 7.0.0 (more details in the benchmarks folder).

Some key findings:

• Mesh generation in 2D and 3D using analytical sizing functions is quickest when using Gmsh but a closer competition for CGAL and SeismicMesh.
• However, using mesh sizing functions defined on gridded interpolants significantly slow down both Gmsh and CGAL. In these cases, SeismicMesh and Gmsh perform similarly both outperforming CGAL's 3D mesh generator in terms of mesh generation time.
• All methods produce 3D triangulations that have a minimum dihedral angle > 10 degrees enabling stable numerical simulation (not shown)
• Head over to the benchmarks folder for more detailed information on these experiments.

• In the figure for the panels that show cell quality, solid lines indicate the mean and dashed lines indicate the minimum cell quality in the mesh.

• Note: it's important to point out here that a significant speed-up can be achieved for moderate to large problems using the parallel capabilities provided in SeismicMesh.

Changelog

The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.

Unreleased

• None

[3.1.5] - 2020-11-24

• Support for constraining/immersing subdomains represented as signed distance functions.
• Faster cell manipulation operations for ~5-10% better speedups in parallel.
• Projection of points back onto level set.

[3.1.4] - 2020-11-15

• Laplacian smoothing at termination for 2D meshing...significantly improves minimum cell quality.
• Made hmin a field of the SizeFunction class, which implies the user no longer needs to pass h0 to generate_mesh or sliver_removal.

[3.1.3] - 2020-11-06

Fixed

• Cylinder radius and height are now correct.
• Torus, Prism, and Cylinder now have dim tag.

Improved

• More control over the grad option in the mesh sizing function.

[3.1.2] - 2020-11-04

Improved

• Faster calculation of boundary vertices.
• More robust sliver removal in 3D.

Fixed

• Corners are only constrained for constant resolution meshes

[3.1.0] - 2020-10-28

Added

• New geometric primitives--torus, wedge/prism, and cylinder.
• Updated images on README.

Fixed

• Only constrain corners near 0-level set.
• Bug fix to 3D binary velocity reading.

[3.0.6] - 2020-10-21

Fixed

• Silence messages about pfix when verbose=0

Added

• Added more examples on README
• New unions/intersections/differences with several SDF primivitives
• Automatic corner constraints in serial

[3.0.5] - 2020-10-18

Fixed

• Preserving fixed points in serial.
• Units in km-s detection warning bug.
• Docstring fixes to generate_mesh
• Improved mesh quality in 3D

Added

• Automatic corner point extraction for cubes and rectangles.
• More support for reading binary files packed in a binary format.
• Check to make sure bbox is composed of all floats.

[3.0.4] - 2020-10-12

Added

• Improve conformity of level-set in final mesh through additional set of Newton boundary projection iterations.

More information

All other information is available at: https://seismicmesh.readthedocs.io

Getting started - Learn the basics about the program and the application domain.

Tutorials - Tutorials that will guide you through the main features.