A brief introduction to seismic travel-time tomography

One of the most destructive and well-known earthquakes happened in 2004 off the west coast of northern Sumatra, on the 26th of December with severe consequences. This event ruptured a 1600 km long portion of the fault boundary and generated a tsunami that caused more than 283,000 deaths across 10 countries. Therefore, understanding the subsurface is vital and the accurate location of an earthquake is essential if we are to quantify the likelihood of future events, including their potential magnitudes and geographic distribution. This will enable earthquake resilience to be improved by using building standards appropriate to the peak level of expected ground motion; furthermore, insurance companies can include these risk factors in their models.

Unfortunately, we do not have MRI scanners for the Earth, however, similar principles can be applied to investigate the Earth’s interior. This is where seismic tomography comes into play: it is another form of tomography like MRI but instead of studying the human body, it studies the Earth’s subsurface. The subsurface can be illuminated by seismic rays, which occur mainly from earthquakes or explosions and model the ray paths of seismic waves travelling through the Earth. There are a number of seismic waves but for simplicity, we will focus only on the Primary (P) and Secondary waves (S). A representation of the two waves is shown in the figure below.

The two aforementioned waves travel through the Earth at certain velocities which are the target value to be obtained. The velocity of the waves in the subsurface is particularly useful to understand the geological structure. Velocity strongly depends on temperature which identifies the parts of the subsurface which have been deep in the Earth and tend to be hotter while others dipping or sinking from the surface tend to be colder. For example, in the figure below we can see the SE Asia (Indonesia) region with the colour indicating positive (low temperature) or negative (high temperature) velocity anomalies. The differences in temperature highlight the tectonic plate boundaries because they were shallow and dipped “recently”; thus, these structures have different temperatures from the ambient mantle.

But how do we get from the data obtained on the surface to the velocity of the subsurface? We formulate an inverse problem where we only know the effects and not the cause. The effect is the travel-time (time taken for a seismic wave to reach the Earth’s surface) and the cause is the velocity of the seismic wave ray path within the model. The modelled area is usually represented as a grid of points with varying velocity.

The goal of the inverse problem is to adjust the model parameters (velocity) in order to reconcile the travel-times observed with the travel-times predicted. The travel-times observed are the ones obtained from the seismometers on the Earth’s surface while the travel-times predicted are the ones obtained from the modelled passage of seismic waves within the model.

To sum up, seismic travel-time tomography aims to obtain the velocity model of the subsurface by exploiting the seismic wave travel-times measured on the Earth’s surface. This is achieved through an inverse problem that adjusts the model parameters to match the observed data. The continuous hard work from geophysicists and the exploitation of higher quality data and advanced tomographic methods improve the Earth models. This provides a better understanding of the geological processes contributing to the generation of tsunamigenic earthquakes. The likelihood of future earthquakes can be better quantified since they happen mostly on the active tectonic boundaries which are imaged through seismic velocity. Thus, well-informed decisions on the safety measures can be taken to prevent the loss of lives either in the form of improved building standards or to avoid nuclear reactors, for example, being built in these areas.