# Seismic tomography

Seismic tomography is a technique for imaging Earth’s sub-surface characteristics in an effort to understand deep geologic structure. Gathering ample compressional wave (P-wave) and shear wave (S-wave) travel time measurements allows us to compile 3D images of earth’s velocity structure.[1]

## Theory

Tomography is solved as an inverse problem. First measurements are made of seismic waves passing through a material. The character of these measurements is then analyzed to make inferences on the material such waves have passed through (velocity, density, etc.).[2] The velocity of p and s waves depends on the rheology of the material that they travel through (density and elasticity). In short, variations in chemical compositions and thermal structure result in a change of velocity. Such waves can travel faster through relatively colder material.[3] It is observed that wave velocity increases with increasing depth from 2–8 km/s in the crust up to 13 km/s in the mantle. Current research is based on this premise.

## Process

Seismometers record ground movements in the form of seismic waves resulting from earthquakes or controlled explosions. These instruments are sensitive enough to record ground movement with a displacement 1000 times smaller than the width of a human hair (3x10−8 m). A compilation of arrival times, sometimes millions of data, allows seismologists to have a clearer picture of the location and size of sub-surface structures. The result is a 3D image of a slice through the earth that serves as a seismic velocity map. The image depicts where seismic waves were able to travel faster or slower based on the differing arrive times of the waves. This in turn warrants the interpretation of the thermal structure for the deep Earth.[4]

## Methods

As stated above, seismic tomography is typically solved as an inverse problem. In order to estimate P-wave velocity and further simplify seismic tomography, four main methods have been devised:

• Refraction traveltime tomography: Computationally simple but only reliable for making a shallow low resolution velocity structure. Within this method the observed data are the first arrival time, denoted as t: $t = Ls$. The model parameters (s) are the slowness of the waves and L is the ray path matrix.[5]
• Finite-frequency traveltime tomography: in an effort to obtain a higher resolution that the above method, the effects of wave diffraction are taken into account. Volumetric sensitivity kernels take the place of raypaths. Overall this allows the travel time and amplitude anomalies to be frequency-dependent, aiding the goal to increase resolution.[6]
• Reflection traveltime tomography
• Waveform tomography : Uses seismic data to its fullest potential. Seismograms are the observed data and are controlled by the acoustic wave equation which serves as an approximation to the elastic wave propagation

## Applications

Seismologists can use tomography to infer geologic structures such as the subduction of tectonic plates into the warmer mantle or the rise of a relatively hot plume body. Volcanologists use tomography to understand the scale of magma chambers beneath volcanoes. The study has also allowed for the correlation of tomographic observations with fluid dynamics models by providing a view of the internal thermal structure of the mantle.[4]

Yellowstone Tomography study: Project EarthScope is currently installing 20 new seismometers every month across the US in an effort to obtain higher resolution tomographic images. This will advance our understanding of how North America has and will evolve with special attention placed on the Yellowstone hotspot associated with the Yellowstone supervolcano.[4]

## Limitations

Seismic tomography provides only the current velocity anomalies and all prior velocity structures are unknown. It is also difficult to image slender structures due to the fact that long wavelengths are easier to recover.[7]