# Seismic tomography

Seismic tomography is an imaging technique that uses seismic waves generated by earthquakes or explosions to create two and three dimensional images of Earth’s interior.[1] The term tomography is derived from the Greek word tomos which means 'slice'. Each slice through the tomographic model typically uses different colors that represent the velocity perturbations above and below the average velocity or the absolute velocities. Seismic tomography images have shown that earth structure is more complicated and heterogeneous than what was previously thought.

Figure 1. Example of global tomographic results at different depths.[2]

## Overview

Before illustrating how Seismic tomography works, let's get started with the analogy of CT Scans. Doctors use CT scans to image the organs and bones inside of the body without surgery. CT scan machines shoot X-rays through a patient’s body to obtain images that show the patient’s internal structures from different directions. Computers then combine these images into a three-dimensional picture of the body .[1]

In a technique similar to CT scans, seismologists use seismic waves to create images of the Earth’s interior. The energy is released from the focus of an earthquake as seismic waves that spread outwards in all directions. These seismic waves travel through the Earth's interior until they reach the surface. Upon arrival at the Earth's surface, these waves shake the ground, and seismometers digitally record the earthquakes at hundreds of stations distributed on the Earth's surface all over the world. Each station has seismometers, which are the instruments that record the up-and-down and side-to-side motions of the ground in the form of squiggly lines known as Seismograms.[1]

By recording the seismograms of many earthquakes, seismologists are able to create high-resolution images of Earth’s interior using the method of seismic tomography. Using the travel distance of the wave from the focus of the earthquake to the seismometer at the recording station, seismologists can calculate the average speed of the seismic waves. The speed of the seismic waves depends on the type of rock materials, the temperature of the rocks (hot molten rocks or cold rocks) and the stability of the area ( tectonically active area or areas located within the plate). Generally speaking, seismic waves travel slower through less-stiff rock materials, hot molten rocks and tectonically active area while they move faster through rigid rock materials, cold rocks and stable areas that located withinplate. .[1]

Seismic tomography can show the structures inside the earth that have different physical properties than the surrounding mediums such as magma chamber. The clarity of the tomographic results is contingent upon using large number of stations and distributing them well on the ground. The good coverage of raypaths gives high resolution seismic tomographic results.

Figure 2. Because of using few number of recording stations, few recorded waves that pass through the structures inside the earth. But, by increasing the number of the recording stations, it is able to get much data and that will lead, in turn, to envision the shape and the size of the structures in the tomographic results.[1]
Figure 3. Raypaths coverage along North America continent .[3]

## Theory

Scientists can model the earth by using a forward problem with a starting model of the earth structure and its properties. They use, for example, the physical properties of the waves in the case of doing seismic modeling to predict the observations by using this equation d=F(m), where d are the data, F represents the forward problem function and m is the given model.[2] On the other hand, seismologists use the observations to predict the Earth’s structure. By using an inverse problem, they make a combination between the physical properties of the waves and a linear or non linear inversion technique. The basis of any tomographic method depends on the following linear equation that relates the observed data to the source and the medium parameters.[2]

d = Gm + e

G is matrix coefficient, d stands for input data, m stands for the model parameters that represents the velocity of the subsurface, and e represents the errors.

For a given area, where the observed data dobs and the initial model is mo, then the difference between dobs − g(mo) can allow seismologists to predict how well the current model can predict the observed data. In the next step, the inverse problem then attempts to minimize the difference between input and predicted data. This is why seismic tomography is typically referred to as an inverse problem.[4]

## Methodology

### Model parmeterization

The structure of the area of interest is represented seismologically by a set of model parameters using a block, 3D grid or boundary grid approach. The boundary grid approach is often preferred as it can deal with complex velocity discontinuities. This model is represented by a 3D grid layer bounded by two discontinuities within which meshes of grid nodes. .[4]

Figure 4. a) Block approach, B) Grid approach and C) Boundary grid approach .[4]

The velocity at each grid node is regarded as an unknown parameter. By using an interpolation function, the velocity perturbation at any point can be calculated.

where φ is latitude, λ is longitude, and h is the depth from the Earth’s surface; φi, λj, and hk represent the coordinates for the eight grid nodes surrounding the point (φ, λ, h). Vm(φi, λj ,hk) is the velocity at the grid net set for the mth layer.[4]

### Forward modeling

During the forward modeling step, the ray paths of the waves are traced by calculating the travel times and identifying the ray path in a 3D velocity model. One example is the 3D ray tracing alogarithm by Zhoa et al (1992).[4]

Figure 5. 3-D ray tracing algorithm .[4]

### Inversion

Because the data depends on the model parameters and the raypath geometry, tomography is non-linear method. To make inversion, the tomography should be firstly linearized by using this equation d = Gm + e. There are several approaches to solve this equation. The iterative matrix solution methods is the common inversion approach that has been used in most tomographic studies, such as Kaczmarz’ algorithm and the related algebraic reconstruction technique (ART), simultaneous iterative reconstruction technique (SIRT), and conjugate gradient least squares (CGLS). The LSQR is the most widely algorithm that has been used for the solution of significant least-squares problems in seismology.[2]

### Resolution test

It's an important understand the resolution capability of the model parameters. This is often tested by constructing a synthetic model. In this synthetic model, random errors similar in magnitude to those of the real data are added to the synthetic data and then inverted with the same algorithm used for the real data.[4] A common test model is the checkerboard test. The zones of large diamond shapes mean high resolution result while the zones of small diamond shapes mean low resolution result. During interpretation, seismologists can neglect the low resolution zones seen in the synthetic modeling from their interpretations.

Figure 6. Result of checkboard resolution test [5]

## Interpretation of Earthquake Tomographic results

Seismic tomographic results are typically displayed as slices at different depths of Vp, Vs and Vp/vs velocity structures. Before interpreting seismic tomographic results, seismologists take in consideration the other geological and geophysical features that were observed in the study area by other scientists. But, in general, the interpretation depends on the anomalies of Vp, Vs and the Vp/Vs velocity structures. For example, the low-Vp,low-Vs and high Vp/Vs anomalies in the uppermost mantle and lower crust can be interpreted as the occurrence of melting zones, while the low-Vp, low-Vs and low Vp/Vs anomalies in the upper crust can be interpreted as the presence of inclusions of H2O.[4]

## Applications of Seismic Tomography at some areas

### Subduction zone

Vertical cross sections of P-wave tomography beneath Northeastern Japan show the subducting Pacific plate that appears as high velocity anomalies (blue colors) while the low anomalies of p-wave are indicated by red colors and represent the zones that occur beneath the active volcanoes. .[6]

Figure 7. Vertical cross sections of P-wave tomography beneath Northeastern Japan .[6]

### Volcano

In this example, the seismic tomography results are imaging the magma chamber beneath Unzen volcano, which is an active volcano located in Japan. The low velocities anomalies of the p-waves are indicated by red colors which represents the molten hot rocks of the magma chamber .[6]

Figure 8. Vertical cross section of P-wave tomography shows magma chamber beneath Unzen volcano .[6]

### Hotspot

The Yellowstone Hotspot is the hotspot that is responsible for volcanic activity in the states of Oregon, Nevada, Idaho, and Wyoming. In this example, the low p-wave anomalies are represented by red colors and indicate the warm zone (Hotspot zone). .[7]

Figure 9. P wave Veolocity structures at different depths and 2D cross section tomography of p-wave shows hot spot that is indicated by red color.[7]

### North American Craton

Seismic tomographic results can also be performed on a continental scale to image the heterogeneity of the craton and its relation to the surrounding plates.

Figure 10. S wave velocity structure at 120 km depth and three cross sections along North American Craton .[3]

## Oil and gas exploration by Seismic Tomography

Seismic tomography has widely been used in earthquake seismology, but is also has applications for the exploration and development of oil and gas. The principles of tomography stay the same, but there are additional methods of seismic tomography that are used for oil and gas monitoring.

### Passive seismic tomography

Microearthquakes (earthquakes of low Richter magnitudes) may occur naturally or are induced by hydraulic fracturing. By recording these microearhtquakes for several months instead of using explosions or vibroseis, geophysicists can produce 3D images of Vp, Vs, and Poission's ratio, and use them to predict the zones of fluid and gas within the reservoir.[8]

Figure 11. Vertical cross sections along the exploration block and comparison of passive seismic tomography with geology at one of these cross sections .[8]

### Cross well seismic tomography

This type of tomography is used for hydrocarbon monitoring by using two drilled wells. The source is lowered in one well while the receivers are lowered in the other one. The source generates seismic waves while being moved in a specific interval while the receivers are fixed. Then, the receivers are re-positioned and the process is repeated. Repeating the process many times allows for improved coverage of the area of interest by ray paths and that will lead to better results. By using this type of tomography, geophysicists use the received seismic waves to produce a cross sectional velocity model between the two wells. In addition, they can detect zones of reservoir rock.[9]

Figure 13. Raypath coverage between two wells [10] and Figure 14.Velocity model between two wells (The B zone is the zone of the reservoir rock. While other zones are rock types that are located above and below the reservoir rock). [11]

## References

1. Incorporated Research Institutions for Seismology, from http://www.iris.edu/hq/inclass/fact-sheet/seismic_tomography.
2. Thurber, C., & Ritsema, J. (2007). Theory and Observations–Seismic Tomography and Inverse Methods-1.10., from http://mrw.elsevier.com/tgp2/Example1.pdf
3. Bedle, H., & van der Lee, S. (2009). S velocity variations beneath North America. Journal of Geophysical Research: Solid Earth, 114(B7)., from http://www.earth.northwestern.edu/research/suzan/publications/53_Bedle_VdLee_JGR_2009.pdf.
4. Zhao, D. (2015). Methodology of Seismic Tomography. In Multiscale Seismic Tomography (pp. 21-54). Springer Japan. https://link.springer.com/chapter/10.1007/978-4-431-55360-1_2.
5. Salah, M. K. (2014). Upper crustal structure beneath Southwest Iberia north of the convergent boundary between the Eurasian and African plates. Geoscience Frontiers, 5(6), 845-854. from http://www.sciencedirect.com/science/article/pii/S1674987113001369
6. Dapeng, Z. (2012). Tomography and dynamics of Western-Pacific subduction zones., https://www.terrapub.co.jp/onlinemonographs/meep/pdf/01/0101.pdf.
7. Smith, R. B., Jordan, M., Steinberger, B., Puskas, C. M., Farrell, J., Waite, G. P., ... & O'Connell, R. (2009). Geodynamics of the Yellowstone hotspot and mantle plume: Seismic and GPS imaging, kinematics, and mantle flow. Journal of Volcanology and Geothermal Research, 188(1), 26-56. www.uusatrg.utah.edu/PAPERS/smith_jvgr2009complete.pdf .
8. Martakis, N., Tselentis, A., & Paraskevopoulos, P. High Resolution Passive Seismic Tomography-a NEW Exploration Tool for Hydrocarbon Investigation, Recent Results from a Successful Case History in Albania., from http://www.searchanddiscovery.com/pdfz/documents/2011/40729martakis/ndx_martakis.pdf.html
9. Lo, T. W., & Inderwiesen, P. L. (1992, January). Reservoir Characterization With Crosswell Tomography: A Case Study in the Midway Sunset Field, California. In International Meeting on Petroleum Engineering. Society of Petroleum Engineers. https://www.onepetro.org/conference-paper/SPE-22336-MS
10. Mathisen, M. E., Vasiliou, A. A., Cunningham, P., Shaw, J., Justice, J. H., & Guinzy, N. J. (1995). Time-lapse crosswell seismic tomogram interpretation: Implications for heavy oil reservoir characterization, thermal recovery process monitoring, and tomographic imaging technology. Geophysics, 60(3), 631-650., from http://library.seg.org/doi/pdf/10.1190/1.1443803
11. Zhu, T., & Harris, J. M. (2015). Applications of boundary-preserving seismic tomography for delineating reservoir boundaries and zones of CO2 saturation. Geophysics., from http://geophysics.geoscienceworld.org/content/80/2/M33