Seismic tomography

Seismic tomography is a methodology for estimating the earth's properties. In the seismology community, seismic tomography is just a part of seismic imaging, and usually has a more specific purpose to estimate properties such as propagating velocities of compressional waves (P-wave) and shear waves (S-wave). It can also be used to recover the attenuation factor Q. Another branch of seismic imaging is seismic migration in which the properties to be estimated include the reflection coefficient or reflectivity.

The simplest case of seismic tomography is to estimate P-wave velocity. Several methods have been developed for this purpose, e.g., refraction traveltime tomography, finite-frequency traveltime tomography, reflection traveltime tomography, waveform tomography.

Seismic tomography is usually formulated as an inverse problem. In refraction traveltime tomography, the observed data are the first-arrival traveltimes $t$ and the model parameters are the velocity $v$. The forward problem can be formulated as:$t\; =\; Lv$where $L$ is the forward operator which, in this case, is the raypath matrix.Refraction traveltime tomography is computationally efficient but can only provide a low-resolution image of the subsurface.

To obtain a higher-resolution image, waveform tomography has been developed. In this case, the seismograms are the observed data. The forward model is usually governed by the acoustic wave equation. This is an approximation to the elastic wave propagation. Elastic waveform tomography is much more difficult than acoustic waveform tomography. The acoustic wave equation is numerically solved by some numerical schemes such as finite-difference and finite-element methods.

References

* Stewart, R. R., "Exploration Seismic Tomography: Fundamentals", Society of Exploration Geophysicists, 1991

ee also

* seismology
* seismograph