Seismic migration images the subsurface by propagating a wave into the Earth and listening for the reflections that return to the surface. Like any waves, the major properties of seismic waves are speed, frequency and wavelength. Seismic wave speed is largely determined by the type of rock it is traveling through, as well as how much pressure that rock is under. Wave speeds in rock typically vary from 3000 m/s to 6000 m/s, which is up to 20 times the speed of sound in air. The frequency of the wave is determined by a few factors, but mostly by the type of energy that is injected at the surface and how well that energy travels through the rock (the dispersive nature of the rock). At the end of the day, usable seismic frequencies recorded at the surface are usually between 20Hz and 60Hz.

The seismic wavelength is determined by the other two properties: wavelength = speed / frequency. And it is wavelength that determines the resolution possible to achieve in seismic imaging. The smallest subsurface Earth feature that is visible to the seismic wave is approximately 1/4 of the wavelength. Typical seismic wavelengths therefore vary from

to

Putting this into perspective, a large mountain face is on the order of 1000m high and is made up of features from 100s of meters in size down to centimeter-sized details. The imaging resolution determines which features are visible and which are lost. Of course, the complex layering and folding of the visible geology above ground are similar to the complex structures that seismic imaging is meant to reveal in the subsurface.

Mt. Kidd, in Kananaskis Country, Alberta, is a great example of folded geology. The rock is limestone, and the visible layers are between 25m and 100m thick. Overlaid are seismic wavelets corresponding to 10Hz, 20Hz and 40Hz frequencies in this rock. At 3000 m/s, a seismic wave will travel from top to bottom and then back to the summit in less than one second.

Now that we have related a seismic wavelet to visible geology, it's interesting to reverse the process, and simulate which geological features are actually visible at different seismic frequencies, assuming that we can resolve features 1/4 of a seismic wavelength in size.

Mt. Kidd, as seen by 10Hz seismic. Rendered with 75m pixels, sharpening applied. At this resolution, no more than the basic shape of the mountain can be seen.

Mt. Kidd as seen by 20Hz seismic. Rendered with 38m pixels, sharpening applied. At this resolution, the near-vertical layers in the center of the face and the large anticline just right of center are becoming visible. It is difficult to identify the individual 50m thick layers of rock.

Mt. Kidd, 40Hz, rendered with 18m pixels, sharpening applied.  At 40Hz, the vertical layers and anticline are easily identified, and individual rock layers are quite clearly seen.

Obviously, seismic frequency is a tremendously important parameter, and it needs to be maximized from the beginning (data acquisition) to the end (migration) of the seismic imaging process. The survey acquisition is designed to capture the highest frequencies possible, and those high frequencies must be carried through to the final process, Reverse Time Migration.

In part II of this blog, we'll see why frequency is the dominant factor in the cost of Reverse Time Migration (RTM), and it will become clear why it is so important to run RTM on the fastest hardware possible.

Written by guest blogger and Acceleware Software Developer Darren Foltinek.