(BIVN) – From this week’s U.S. Geological Survey Hawaiian Volcano Observatory Volcano Watch article by Tyler Paladino, a Postdoctoral Fellow with the USGS:

Interferograms are images created by radar satellites that show how the ground has changed shape, or deformed, over time. Today, we’ll dive into one of the trickiest parts of interpreting interferograms: the perspective of satellites.

USGS: “Panels A and B show what an interferogram would look like for a simple expanding spherical magma chamber from an ascending and descending orbital perspective. The star shows the true center of the inflating magma source. The arrow and bar denote satellite flight direction and look direction respectively. Each fringe represents approximately 1.55 cm. Panels C and D show the same event in a cross-section view. The black lines and arrows show the displacement as viewed by the SAR satellite in its line-of-sight (LOS), while the grey lines and arrows show the ground displacement physically occurring. The key in panel C gives the scale of the arrows. Notice in the ascending case, the deformation pattern is shifted and skewed west while the descending case shows the opposite.”

Volcanologists use interferograms to detect unrest by observing how the surface of a volcano is deforming in response to migrating magma beneath the ground. We can see changing subsurface magma reservoirs, their connections, and new paths magma creates as it travels closer to the surface. While interferograms can be beautiful and informative, they are also difficult to interpret. 

A “Volcano Watch” article from June 2019 discussed how to read the repeating cycles of color, called fringes (which often make bullseye or butterfly wing patterns), to figure out how much ground movement is occurring. To summarize quickly: count the fringes, starting from the outside of the feature towards the inside. Keep track of the sequence the color is cycling: is it red-yellow-blue or blue-yellow-red? Use the figure key to work out which direction the ground is moving, either towards or away from the satellite. The change in distance between the ground and satellite is called “range change”. Multiply the number of fringes by the range change value of a single fringe (also given in the figure key) and you’ve calculated displacement and its direction. Or have you? In reality, it’s a bit more complicated. 

To create interferograms, two Synthetic Aperture Radar (SAR) images (separated in time by a few weeks) are combined from satellites orbiting around the Earth. If the ground has moved enough within the timespan of the two images, fringes will be visible in the interferogram. Where this gets tricky is how the satellite looks at the surface of the Earth. SAR satellites don’t look straight down, they look to the side, often about 30 degrees from vertical. What effect does this have on interferogram interpretation?

If an area on the ground moved exactly upwards by 5 inches, from a SAR satellite’s perspective less than 5 inches of range change will be recorded. But why is this? Let’s pretend someone is shining a flashlight at you. If they shine it directly at you, it’s quite blinding! But if they tilt the light just a bit off-center, the light will still be visible, but not nearly as blinding. If the light is tilted fully away from you, you may see nothing at all. The intensity of the light hasn’t changed, but your perspective has.

Going back to the example above, a similar phenomenon is happening but instead of light intensity, we’re measuring range change. If the motion of the ground is tilted away from the SAR satellite’s look direction, less of the actual motion will be measured than is physically occurring. If the ground were to move 5 inches directly toward the satellite, then it would indeed record 5 inches of range change. In this manner, the direction of the ground motion is important, as is the orientation of the satellite.

To illustrate how satellite orientation affects an interferogram, we’ve created a simple model that shows a spherical inflating magma body (like an inflating balloon underground) and its effect on the surface viewed from multiple satellite perspectives. In these models, the magma body is in the exact center (white star), but that’s not what we see. We instead see a bullseye that looks somewhat skewed and shifted either to the West or the East depending on the viewing geometry.

This is due to the phenomena we just discussed. Since SAR satellites look to the side, the range change that we see as fringes is only a part of the actual motion of the ground if that motion is not in line with the satellite’s line-of-sight. Since inflation results in the ground moving upwards and outwards, there will be some motion that is captured and other motion that is missed or minimized. For example, if motion is perpendicular (or close to perpendicular) to the line-of-sight, the satellite will see barely any motion at all, just like the decrease in intensity as a light is being shined away from you. This results in the entire measured deformation pattern to be shifted, as outwards perpendicular motion away from the satellite will be small while motion towards the satellite will be larger.

Interferograms posted by the USGS Hawaiian Volcano Observatory will provide an arrow denoting the satellite flight direction and a perpendicular bar that shows its look direction. Using this information and your newfound knowledge of SAR perspectives, you can more accurately interpret how a volcano is deforming. In a future “Volcano Watch” article, we’ll discuss how perspective changes more complex signals such as propagating dikes (spoiler alert: it gets even more complicated).