Measuring Gravity From a Moving Aircraft Requires a ‘Gravi-God’!

From: Joël Dubé, Engineer/Geophysicist at Sander Geophysics, OIB P-3 Gravity Team

One of the instruments used in Operation IceBridge (OIB) is an airborne gravimeter operated through a collaboration between Lamont Doherty Earth Observatory of Columbia University and Sander Geophysics of Ottawa, Canada.  People from other instrument teams have been heard to call it a gravity meter, gravity, gravitometer, gravy meter, gravel meter, gravitron, or blue couch-like instrument. As operators of the gravimeter, we are referred to as graviteers, gravi-geeks or gravi-gods!  This tells a lot about how mysterious and unknown this technology appears.

Let’s start with why is gravity data being acquired as part of OIB, and how is airborne gravity data acquired?

The Earth’s gravity field varies over space according to differences in topography and the distribution of density under the Earth’s surface.  Essentially, the greatest density contrasts are between air (0.001 g/cc), water and ice (1.00 and 0.92 g/cc, respectively) and rocks (2.67 g/cc in average).  Therefore, gravity data can be used for modeling the interface between these three elements.  On OIB we have other instruments that can help with some of these measures. The laser scanning ATM system can locate the interface between air and whatever surface is underneath it with great accuracy, yet not below that surface.  The ice penetrating radar system (on OIB we use a system called MCoRDS) is successful at locating the interface of the ice and what lies underneath, however, if the ice lies over water there is no airborne radar system that can “see” through water.  Hence, gravity data is needed to help determine the surface bathymetry beneath floating ice, whether it is off shore in the ocean, or ‘on shore’ when the radar finds sub-glacial lakes under the ice sheet.  The gravity measurements enable the creation of water circulation models, helps predict areas at the bottom of the ice that might be early to melt, and  predicts ice transport.

An additional benefit of our collection of airborne gravity data is that it can contribute to increasing the accuracy and resolution of the Earth Gravitational Model (EGM). The EGM is determined only with low resolution measures in remote locations such as the poles, being built mainly from data acquired with satellites.  Our high resolution data can fill in details in the data.

Most people don’t know that it is possible to acquire accurate gravity data from a moving platform such as an aircraft.  Due to the vibrations and accelerations experienced by the aircraft, it is definitively a challenge!  There are four key elements that make this possible.

1- Very accurate acceleration sensors, called accelerometers are needed to measure acceleration forces.

2- The accelerometers must be kept as stable as possible, and oriented in a fixed direction.  This is a job for gyroscopes (a device for measuring and maintaining orientation) coupled with a system of motors that keeps the accelerometers fixed in an inertial reference frame, independently of the attitude of the aircraft.  This is why the system we use is called AIRGrav, which stands for Airborne Inertially Referenced Gravimeter.  Damping is also necessary to reduce transmission of aircraft vibrations to the sensors.  The internal temperature of the gravimeter also has to be kept very stable.

This is all good, however, the accelerations we are measuring this way are not only due to the earth’s gravity pull (a static force), but also (and mostly) due to the aircraft motion (a dynamic force).

3- To correct for item #2  a very accurate GPS data is needed so that you can model the aircraft motion with great precision.

However, despite all these best efforts, ‘noise’ in the readings remains, mostly from GPS inaccuracies and aircraft vibrations that can’t be detected by GPS, so:

4- A low pass filter must be applied to the data, since the noise amplitude is greatest at high frequency.

Even with all these elements accounted for, a number of corrections have to be applied to the data before they can serve the scientific community.  The corrections aim to remove vertical accelerations that have nothing to do with the density distribution at the earth’s sub-surface.

The ‘Latitude correction’ removes the gravity component that is only dependent on latitude.  That is the gravity value that would be observed if the earth was treated as a perfect, homogeneous, rotating ellipsoid.  This value is also called the normal gravity.  Since the earth is flatter at the poles, being at high latitude means you are closer to the earth’s mass center, hence the stronger gravity.  Also, because of the earth’s rotation and the shorter distance to the spinning axis, a point close to the pole moves slower and this will add to gravity as well (as there is less centrifugal force acting against earth’s pull).

Anything traveling in the same direction as the earth’s rotation (eastward), will experience a stronger centrifugal force thus a weaker gravity, and the reverse is true for the opposite direction.  Traveling over a curved surface also reduces gravity no matter which direction is flown, similar to feeling lighter on a roller coaster as you come over the top of a hill.  This is known as the ‘Eötvös effect’ and is taken care of by the Eötvös correction.  This correction is particularly important for measurements taken from an aircraft moving at 250-300 knots.

The ‘Free Air correction’ simply accounts for the elevation at which a measurement is taken.  The further you are from the earth’s center, the weaker the gravity.

To give you an idea of how small the gravity signal that we are interested in is with respect to other vertical accelerations that have to be removed, let’s look at the following profiles made from a real data set.  All numbers are in mGals (1 m/s² = 100,000 mGals), except for the terrain and flying height, which are in meters.

“Raw Gravity” in this diagram means that GPS accelerations (aircraft motions) have been removed from inertial accelerations.  Notice the relative scales of the profiles, starting at 200,000 mGals, down to 20,000 mGals when aircraft motions are accounted for, down to 200 mGals after removing most of the high frequency noise, and ending at 50 mGals for Free Air corrected gravity.  Free Air gravity is influenced by the air/water/ice/rock interfaces described earlier, and since OIB uses the gravity data to locate the rock interface (the unknown), Free Air gravity is the final product.  [As a side note, for other types of gravity surveys, we usually want to correct for the terrain effect (the air/water/rock interfaces are known in these cases), so that we are left with the gravity influenced only by the variations of density within the rocks (geologic information).  This is called Bouguer gravity and is also shown in the figure.]

Notice the inverse correspondence between flying height (last profile, in blue) and the profiles before the free air correction (going higher, further from the earth, decreases gravity), and the correspondence between terrain (last profile, in black) and the free air corrected data.

Now, let’s look at some data acquired during the current 2011 mission in western Greenland.

These three images are all of the same area called the Umanaq region along the coast of west Greenland. You can match the images by the black flight lines that run across them.  The first two images are from ETOPO1, a global relief model made from numerous data sets covering the entire Earth. The datasets above integrate land topography with ocean bathymetry as they are collected along the coastline. The data images can be “bedrock” (base of the ice sheet where the ice has been removed) or “ice surface” where you see the ice elevation overlaying the bedrock. The left panel is ‘ice surface’ over land but the ocean section shows as bathymetry, as if the water has been drained from the ocean showing the surface elevation of the bedrock under the ocean. In this section the lower elevation ranges from a low of blue to green to yellow, and where the ice surface is present, this higher elevation shows as red.

The middle panel shows both ice and water being removed, so you see only ‘bedrock’ elevation under the base of the ice sheet.

The right panel shows the actual Free Air gravity acquired in the last few weeks, which is like removing the ice and looking to see what is beneath.  Most channels, called fjords, are well mapped by the gravity data (showing as a low area in blue).  It is interesting to see that the gravity data infers the presence of a sub-glacial channel (shown in green and noted by the red arrow) where no channel is mapped (yet?) on the bedrock map.  The most likely reason for this is that this particular region has not been covered by previous ice radar surveys (there are huge portions of the Greenland ice sheet that remain unexplored).  Note that the MCoRDS ice radar data that was acquired as part of the current campaign will improve the resolution in this area, and when matched with this gravity data will enable a better comparison of both data sets in the future.

Congratulations you have just completed Gravity 101!