Halos of stone.

It looks as if someone with a good eye for design or, at the very least, a mischievous urge to baffle unwary geologists spent the entire afternoon in a desolate part of Spitsbergen, an island north of Norway, rearranging the rocks. The pattern of large stones lying in protective rings around mounds of soil is too distinct and remarkably regular to suggest anything but a human creator. And yet, it is nature's hand, not a person's, that sorts and arranges these stones into a honeycomb-like network that is unveiled every summer as the snow retreats and the arctic ground thaws.

Geologists have known about these so-called sorted circles for over a century. They grace periglacial and alpine regions worldwide from Antarctica to North Wales and Greenland--wherever the silty or clay soil exposed to moisture is seasonally frozen and thawed. The circles range-in size from a fraction of a meter, where they are surrounded by pebbles, to several meters in diameter, where boulders sometimes mark their borders.

Sorted circles are just one example of a large class of natural surface designs called patterned ground. Other geometric shapes include polygons, nets (forms between circles and polygons), steps and stripes. These shapes can be either sorted (in which case the rocks are separated from, an border, finer soil) or nonsorted (borders are commonly made by vegetation or cracks in the soil). These other forms are just as ubiquitous as circles and can reach sizes up to 50 meters in diameter. Relics of ancient surface patterns measuring up to 150 meters have been found in former permafrost regions.

Geologists believe that the patterns must be caused by some of the forces associated with cyclic freezing of the soil, and that this process can occur fairly rapidly; at one locale, scientists disrupting the pattern in one season have returned the next to find the rocks replaced neatly in the borders. But beyond that there is little consensus on the actual mechanics of pattern genesis and maintenance (see sidebar). "The patterns are just begging to be addressed in terms of an interesting problem in geology, and it is amazing to me that no one has really [solved] it yet," exclaims Bernard Hallet, a geomorphologist with the Quaternary Research Center at the University of Washington in Seattle.

Hallet is among a number of contemporary scientists who are reviving interest in the study of these intriguing patterns by trying to unravel the detailed physical forces that create them. With co-workers Suzanne Prestrud, Carrington Gregory and Christopher Stubbs, also at the University of Washington, Hallet has installed an extensive array of instruments near Ny-[angstrom]lesund, Spitsbergen, to monitor temperature, water content, pressure and soil movement. Recent advances in electronic recording technology enable the researchers for the first time to log data throughout the entire year, and not just during the summer months.

"We felt that the reason very little was known and no one could really say which of the hypotheses was the most likely is that we have never been able to document very well the physical properties of the soil and especially those that change with time," Hallet says. But by the end of next summer, his group should have some answers.

In the meantime, Hallet's working hypothesis is that sorted circles are formed by the movement, or convection, of the soil up toward the center of the mound and then down under the stone borders. "One of the attractive aspects of this idea is that it would mean that this material would be moving down under the gravel, very much like a subduction zone," says Hallet. This movement would keep the troughs around the mounds clean and free of rocks, maintaining a sharp angle between the mounds and borders, just as is observed at Spitsbergen. The convention theory is also supported by the observation that the earth in the center of the mound often appears churned up.

The soil convection model stands up to the preliminary data obtained so far by Hallet's group. Over three months of summer, the researchers recorded 1 degree of tilt with a tilt meter buried deep within a mound. Hallet suspects that the soil convects a little bit each summer so that the patterns form after a number of freeze-thaw cycles.

The researchers have also noticed that at the beginning of the thaw season the height differential between the mound and the bordering rocks drops by about 6 centimeters. Hallet interprets this to mean that the soil region is the first to thaw, lose water and consolidate. "One of my hunches is that it consolidates first near the surface, and as the thaw front propagates down, the consolidation takes place at deeper and deeper horizons," he says. The upper consolidating layers would then be more dense than the underlying ones. And Hallet's group has in fact measured such a density inversion in the soil near the rock border.

What happens to a system once a density inversion has formed is a classic problem in fluid dynamics -- called a Rayleigh-Tyalor instability--that has been applied to phenomena ranging from the evolution of rising plumes of magma (SNd 11/24/84, p. 324) to the fingers of gases that shoot out of the grasp of black holes (SN: 4/7/84, p. 220). The problem, essentially, is how the heavier material on top gets to its more comfortable position below the less dense matter. The two layers can't just flip over one another like acrobats. Instead, small instabilities, or perturbations, develop along the boundary between the two regions, creating flow pathways. Mathematically, the distance between these instabilities, and hence the size of the resulting convection cell, can be shown to measure a little more than twice the thickness of the convecting layer, regardless of the specific properties of the material.

At Spitsbergen, Hallet's group found just this relationship: The diameter of a sorted circle was 210 centimeters while the active soil layer measured about 1 meter deep. What's more, Hallet calculated for sorted circles the so-called Rayleigh number that gives an indication of how easy or difficult it is for convection to occur. "We actually get a number that is vastly greater than what is critical for convection," he says.

But the real icing on the cake occurred when Hallet say a series of computer simulations by two German physicists of the convection pattern of a liquid with an unstable density profile. Although the boundary conditions and type of material are different, the fundamental physics is the same. The similarity between sorted circle patterns and these computer designs was striking, Hallet notes.

Convection explains the size and regularity of the sorted patterns, but it doesn't really address the question of how the larger stones are sorted from the fine soil. According to Hallet, large rocks, or clasts, commonly freeze up through the soil. "Farmers find boulders in their fields and people who build highways find that rocks go right up through the base of the road and through the pavement," he says.

Halleths group has examined this "up-freezing" process in the laboratory. After four cycles of thawing and freezing in the laboratory, they found that a stone buried in the soil moved 3 centimeters above its original position. The researchers believe that the top of the rock freezes first and is pulled up by the inflated frozen soil. When the soil thaws, the rock settles down, but not quite as far, so that after a number of seasons the combined action of the soil convection and the clast movement results in a sorted pattern.

In the coming months at Spitsbergen the researchers want to verify and map the density profile as it changes, chart the freezing and thawing fronts that are thought to move through the soil mounds and search for soil motion that might accompany freezing as well as thawing. They are also interested in seeing if some motions they observed, such as the border rings appearing to shrink slightly, are erased or enhanced during a complete freeze-thaw cycle.

"Our study of gravitationally sorted patterns is far from being finished," says Hallet. "But I think we're on the right track."