Ground-based optical clocks as a tool to monitor volcanaoes and the solid Earth tide

We discuss potential applications for optical clocks in a ground network (see the technical article; also the UZH press release in English or German;  our research was featured on phys.org, science daily, esciencenews, brunchnews, scienceweek, science.newzs.de; SWR radio, St. Gallen Tagblatt, Schweiz Magazine, myscience.ch, Austria's press reader, NZZ, der Kleine Bund, derstandard.at, ProPhysik.de, Welt.de, Sonntagszeitung, gizmag). My favorite title among the various news reports is "Einsteins tanz auf dem Vulkan" from Welt.de. Since 2000, the best clocks on Earth have been optical atomic clocks, which rely on atomic transitions in the spectrum of visible light. The latest optical clocks are so precise that if they ran for 10 billion years, they would lose less than a second. However, these superb clocks are mostly confined to the laboratory. Science and industry have yet to take full advantage of their unprecedented ability to measure time. 

 

Optical atomic clocks to monitor volcanoes

Near a GPS station on Mount Pelee

Mihai (my brother & co-author)

Optical clocks could provide constraints on the volume of new magma entering the chamber. A combination of clock and gravimeter data could determine whether a series of Earthquakes that lead to a gradual change in elevation over a period of a few days are associated with magma movements underground, and potentially with future eruptions.  The delay between the magma chamber filling up and the ground uplifting may also be determined.

Better monitoring of the solid Earth tide

Tides occur because the Earth moves in the gravitational field of the Sun and of the Moon. Our planet responds to this external field by deforming, which causes the ground (and the water level) to fall and rise periodically. On continents, ground uplift due to the tidal pull can be as high as 50 cm. A global clock network would have maximal sensitivity to the solid Earth tide. Data from such a network would help us investigate how the crust reacts to the tidal pull under high tension or before it cracks.

Clocks are sensitive to a different combination of tidal love numbers than gravimeters. A clock network on the continental scale that would continuously monitor the amplitude of the solid Earth tides could calibrate existing models. The crust may react differently to tidal deformations in different areas. Additionally, accurate tidal monitoring near fault lines may shed more light on the connection between tides and Earthquakes, and perhaps improve our understanding of triggered seismicity.

 Using general relativistic effects to monitor ground motion

Clocks do not click everywhere at the same rate. This slow down of time close to heavy objects is a general relativistic effect. Massive objects curve space-time slowing down time. An observer outside a black hole sees time stopping all together at the black hole horizon. Clocks near a neutron star would tick at about half their rate on Earth. Similarly, clocks closer to Earth tick slightly slower than clocks further away.  

Sources below ground affect the tick rates of local clocks. A magma chamber under a volcano that is filling with lava slows down the time of a local clock relative to a reference clock further away. The dominant effect that can be monitored with clocks is ground uplift or subsistence.   The best optical atomic clocks are sensitive to a vertical displacement of about 1 cm after about 7 hours of integration.  
  
How can clocks be connected? Like computers...

The most reliable and precise means to connect clocks is through fiber links like the ones used for Internet. They are capable of  disseminating frequencies over thousands of kilometers with a stability beyond that of the best available clock. Over distances of a few kilometers, optical atomic clocks can  communicate via optical links, which are primarily developed for wireless internet.

Comparison to prior work
In this paper, we consider dynamic sources (volcanoes) that cause both uplift/subsistence of the ground and mass redistribution underground. 

In the past, we argued that atomic clocks provide the most direct local measurements of the geoid,  which is the equipotential surface that extends the mean sea level to continents, and in clock language, it is the surface of constant clock tick rate.  Portable clocks provide variable spatial resolution and could add detail to satellite maps. Optical ground clock networks could also be used to calibrate these maps, which suffer from attenuation of the gravitational field at the location of the satellite and from aliasing errors due to effects that change the geoid faster than the sampling rate of the mission. Further, the tick rate of a portable clock would slow down when passing over an oil deposit (or over water, which has similar density to oil, but water reservoirs have different shapes).

Optical vs microwave atomic clocks
 Optical clocks use atomic transitions in the spectrum of visible light whose resonant linewidth is about 100, 000 times narrower than the microwave transitions. It’s like having a ruler with lines every cm versus one with lines every km; only it is used to measure time instead of distance. Optical clocks are still laboratory device. However, portable prototypes have been developed, and with enough interest and investment from industry, optical clocks could become field devices in a few years.

Clocks vs. GPS
GPS data often has to be integrated for years before providing a reliable estimate for the ground uplift and for the volume of new magma. Better timing resolution could enable the correlation of ground uplift or subsistence to events e.g., an earthquake or a volcanic eruption. Since the primary source of noise in GPS measurements is due to signal dispersion through the atmosphere, both differential GPS and post-processed GPS data perform better if networks are dense because many artefacts cancel across networks over which the ionosphere and troposphere can be assumed to be constant. GPS is sometimes able to measure vertical displacements of 1 cm over short timescales (hours) if the displacement is very localized in the network and/or the frequency of motion is different from the frequency of various artefacts that impact GPS accuracy. Ground clocks do not suffer from the same errors.

The atomic second and the atomic meter

Atomic clocks have been widely used on Earth for past 50 years - long before everyone had a GPS, which does not contain a clock, but something called a GPS receiver that receives signals from clocks in space.  Microwave atomic clocks are still used to define both the meter and the second. Since 1967 the second is "the duration of 9 192 631 770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the Caesium 133 atom".  The meter is defined in terms of the atomic second as "the length of the path traveled by light in vacuum during the time interval of 1/299792458 of a second" by fixing the speed of light. So, atomic clocks on the ground keep track of time on Earth and define our units for both time and distance. Eventually, our time keepers will have to be updated to optical clocks, which are more precise. However, this entails the understanding and modeling of vertical displacements, of the solid Earth tide, and, overall, of the geoid on a global level to a precision better than that of the clocks used, which is non-trivial.

Note: The short video is schematic. In realistic volcanoes, magma chambers are never entirely empty to begin with. Also, the slow down of the clock is severely exaggerated. The videos were developed by Thomas Gauninger in collaboration with myself and Mihai Bondarescu.

Literature:
Ruxandra Bondarescu, Andreas Schärer, Andrew P. Lundgren, György Hetényi, Nicolas Houlié, Philippe Jetzer, and Mihai Bondarescu, “Atomic Clocks as a Tool to Monitor Vertical Surface Motion”, Express letter in the Geophysical Journal International, in Press, arXiv:1506.02457. 

See also the ICNFP 2014 conference proceeding.