Similarly to when a bell is hit, and the arising standing wave patterns produce a sound, standing waves arise on the Earth after large magnitude earthquakes (typically magnitude 7.5 or larger). The vibrations that these standing waves (so-called normal modes) produce can be measured using seismometers – instruments that measure the displacement of the Earth’s surface. The resulting frequency measurements that we obtain can be related to the material inside the Earth: similarly to the sound of a bell or music instrument being dependent on the material or string thickness. 

When a large magnitude earthquake occurs and excites its normal modes, we do not just get one standing wave, but a multitude of them. To stay with the analogy of music instruments, the different waves can be seen as the fundamental tone and overtones in different directions. 

We name these standing waves using two numbers: the radial ordern and angular orderl to identify different normal modes. Each of these is sensitive to different depths in the Earth. If the Earth were entirely symmetric, with structure only varying with depth, the sound we measured in different locations would be the same, as would be the case for a pure bell. 

However, the presence of plate tectonics and mantle convection gives rise to three-dimensional structures within the Earth (as visualized in seismic tomography – see https://www.thingiverse.com/thing:3254056). The Earth is therefore more like a cracked bell and does not resonate with pure tones. Depending on where we make our measurements, we measure different frequency variations for each normal mode, which we visualize as a so-called splitting function map.

Typically, normal modes which are sensitive to different depths show different patterns in their frequency variation maps. This fact is used to map out how structures in the Earth vary and to answer questions related to mantle and core dynamics.

Here, we provide 3D-printable models of three different normal modes that are sensitive to different regions inside the Earth:

Normal mode 0S26 (measured by Koelemeijer et al., GRL, 2013): this normal mode is sensitive to structures in the upper mantle (~ 50 – 500 km depth). High frequencies (topographic lows) are seen under Southeastern Asia and South America, which are typically locations of deep subduction (and likely cold, dense material). Very low frequencies  topographic highs) are seen under central Africa and Afar, where hot, slow material is thought to be present. 

Normal mode 2S16 (measured by Koelemeijer et al., GRL, 2013): this normal mode is sensitive to structures in the lower mantle (~ 2000 – 3000 km depth). Very low frequencies  topographic highs) are observed under the Pacific and Africa, which are two regions of low seismic velocities and likely hot material. High frequencies (topographic lows) are observed in a Ring around the Pacific, which is likely where cold material from the Earth surface is accumulating. 

Normal mode 13S6 (measured by Deuss et al., GJI, 2013): this normal mode is sensitive to structures in the inner core (~ 5150 - 6371 km depth). This normal mode looks squashed at the poles due to high frequencies (topographic lows) at the poles and low frequencies (topographic highs) near the equator. This is a characteristic pattern of normal modes sensitive to the inner core, which has been interpreted as being due to direction-dependent velocity variations (anisotropy).

Print instructions

All globes are provided in 2 halves which print without support and can be glued together with superglue after printing.

Note that mode 02s16 has space for optional neodymium magnets to be inserted during printing. These are aligned so that the 180 degree rotational symmetry can be demonstrated - for details on how to set up your print to include this please see https://www.thingiverse.com/thing:3561651 which contains all the necessary information including which magnets to use. However, if you do not want / need this functionality, the globe should print just fine with the voids.

Notes:

See thing https://www.thingiverse.com/thing:3561651 for details on how to embed magnets to the 02s16 globe.

Print perimeters nice and slowly to avoid ringing and ghosting, as the surface topography is detailed and contains a lot of changes of direction. A carefully calibrated first layer height will give a good seam.

No support material is necessary - the uppermost part of the interior may be a little droopy but this becomes the interior of the model and should be no problem

How I Designed This

These globes, including the others in the series, were created by applying a bump map / displacement map to a sphere in Blender using UV mapping (see https://github.com/jeffwinterbourne/3D_globes/ for methodology)

The bump map itself was created by generating black and white images using the Generic Mapping Tools and composited using Python. Globes were hollowed out and cut into two for printing using Autodesk Meshmixer.

Category: Physics & Astronomy