February 2017 Newsletter: Signal to Noise

signal to noise schematic — Image from socialresearchmethods.net

The relationship between signal to noise is something we environmental scientists, engineers and geophysicists need to understand and work with on a regular basis. But it is an important issue in all aspects of engineering and in life. What is exactly do I mean when I talk about the signal to noise relationship? Generally, we can think of the signal as the desired target result of an experiment or test. In contrast, the noise can be viewed as the background interference, or really everything else that can get in the way of focusing on the signal. More practically, let’s take Valentine’s Day as an example. You decide to buy your wife a new shovel for this romantic holiday. When you ask her what she thinks of it, she responds, “it’s fine.” There is a good deal of “noise” incorporated into the result of this experiment. By finding a way to remove the noise and focus on only the true result, we may see that her true signal response is something more like, “what do you think, dear?” Marriage can be the ultimate experiment in interpreting signal to noise ratios.

In science and engineering, focusing on the most meaningful signal often means removing as much error as possible to increase the clarity or resolution of each data point (or signal point). For example, when we are interpreting a groundwater hydrostatic level (groundwater elevation) or iso-concentration map, we are trying to make an extrapolation across a surface, sometimes based on a very limited data set (in this case, measurements from monitoring wells). The signal here is the groundwater level measurement taken from each well, and the noise includes the various things that can mask the signal, such as lab analysis errors or technician errors during data collection, etc. Initially, all the data, including the noise, is used to create a map. Then, data reduction and analysis can help to deal with the noise. This is where experience makes a huge difference in a geoscientist’s ability to filter out the noise by altering or in some cases throwing out pieces of information due to suspected lack of validity.

When I was studying geophysical data processing, I had an instructor that defined noise as unwanted sound. Another practical example would be if your stereo emits a hissing sound as you try and listen to your favorite album. Here, the music is the signal and the noise is…well the noise. Similarly, during a geophysical seismic test we are trying to record a specific noise signal (let’s call this the music playing), and at the same time eliminate all other background sound vibrations (or that pesky unwanted hiss in the background). If done correctly, it is quite amazing what a concerted effort to reduce noise vs signal can accomplish.

The two figures above show a cross section profile of resistivity data from a gas field near Paris, France. The profile on the right is generated from the same data as that of the left. The difference in the profiles is due to the type of processing. If you were interested in the size and location of the gas reservoir, the profile on the right shows the desired result (or signal) quite clearly, whereas the one on the left is problematic because the noise is much more dominant. The same signal is used for each profile, but it is the elimination of noise (in this case timing errors) by data processing that makes all the difference. The creators of this processing technique went on to build a business that was sold in 2007 for $348 Million. Sometimes eliminating noise really pays off.

Please give us a call at Pyramid Environmental or Pyramid Geophysical Services if you are looking for professionals in the art of clarifying the signal.