Antonio Zamora Podcast
Antonio Zamora Podcast

Antonio Zamora Podcast CB008

Carolina Bay Conic Sections

The perfect elliptical geometry of the Carolina Bays is a clue about the mechanism by which the bays were formed. A trail of evidence points toward an extraterrestrial impact that caused a mass extinction during the ice age.

Carolina Bay Conic Sections
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The origin of the Carolina Bays has been the subject of acrimonious controversies between proponents of impact hypotheses and proponents of terrestrial mechanisms. The predominant elliptical geometry of the Carolina Bays with width-to-length ratios of 0.58 ± 0.05 is the most convincing evidence that the bays were not formed by ordinary terrestrial processes, but if the Carolina Bays are conic sections, where are the cones? This was one of the questions that I tried to answer in my analysis of the bays. Regular geometrical structures can form when fundamental forces interact with matter, and I felt that the ellipses were clues about the origin of the bays. Today, I will present some of the background and mathematical analysis that led me to propose the Glacier Ice Impact Hypothesis.

In 1960, Eugene Shoemaker established criteria for distinguishing extraterrestrial impact sites from craters created by solution, volcanism or other terrestrial processes. According to these criteria, the Carolina Bays could not have formed as a result of high-speed extraterrestrial impacts. The Carolina Bays don’t have meteorite fragments, shatter cones, fused silica or shock metamorphism, but the Carolina Bays do have raised rims, which is a characteristic of impacts.

In 2001, Zanner and Kuzila announced that Nebraska had geological structures similar to the Carolina Bays. The Nebraska Rainwater Basins were originally discovered using Digital Orthophoto Quadrangles, a technology that preceded LiDAR. The Nebraska Rainwater Basins are oriented from the northeast to the southwest, almost perpendicular to the orientation of the Carolina Bays. Zanner and Kuzila theorized that the basins formed as blowouts in abandoned Platte River fluvial sands.

In 2007, Firestone and 25 co-authors proposed that an extraterrestrial impact caused the extinction of the North American megafauna and triggered the Younger Dryas cooling event. This paper reported microspherules and nanodiamonds at the Younger Dryas boundary as evidence of an extraterrestrial explosion over North America that destabilized the Laurentide Ice sheet and caused extensive biomass burning. Samples were taken from 15 Carolina Bays because previous authors had proposed that the bays had originated from an extraterrestrial impact.

In 2009, the TV program NOVA popularized the Younger Dryas Impact Hypothesis. Overhunting by humans and climate change were discussed as possibilities for the disappearance of the mammoths and other large animals, but an extraterrestrial impact was considered a very likely cause of the extinction. In the program, Prof. Peter Schultz demonstrated that a layer of ice could shield the surface and prevent the formation of a crater.

In 2009, Firestone replied to criticism about the 2007 paper. Firestone maintained that the spherules at the Younger Dryas Boundary were suitable indicators of an extraterrestrial airburst, and that the conflicting dates for the Carolina Bays could have resulted from inadvertent sampling of older sediment that may have shifted over time. He also suggested that an impact on the Laurentide ice sheet could have shielded the ground and prevented the formation of a crater, as had been demonstrated by Prof. Schultz. Firestone stated that the radial alignment of the Carolina Bays and the Nebraska Rainwater Basins was an indication of an extraterrestrial explosion in the Great Lakes or Hudson Bay, as shown in this image. He attributed the formation of the elliptical depressions to the wind from a shockwave, which he said was consistent with the theory that the bays were eolian in origin as proposed by previous researchers.

By 2010, LiDAR images were readily available, and Michael Davias established a database of images that could be viewed with Google Earth. The LiDAR images made it possible to see that most of the Carolina Bays were elliptical, but that many had been modified by water erosion and ground movement.

Michael Davias integrated hundreds of LiDAR images of Carolina Bays and Nebraska Rainwater Basins with Google Earth. He used great circle trajectories adjusted for the Coriolis effect to calculate the convergence point of the bays at Saginaw Bay. Previous attempts by others to find a focal point had failed because they had used straight lines on flat maps and they had ignored the flight time of the projectiles. Davias proposed that the Carolina bays formed from large bubbles in the ejecta blanket that left shallow cavities when the bubbles burst.

By 2015, Davias had used the orientation of 45,000 bays to derive a trigonometric equation to calculate the azimuthal orientation of the Carolina Bays and Nebraska Rainwater Basins just from their coordinates. This is very convincing evidence that Saginaw Bay is the convergence point of the bays.

Many researchers had described the Carolina Bays as either oval or elliptical. Melton and Schriever in 1933 and Prouty in 1952 characterized the bays as elliptical, but they did not perform a geometrical analysis to verify that the bays were mathematical ellipses. Using Google Earth with LiDAR overlays, I found that an ellipse with the same width-to-length ratio as a Carolina Bay fit the bay exactly after scaling and rotating the ellipse. This made it possible to conclude that the archetype shape of the Carolina Bays is elliptical and that the bays can be modeled as mathematical conic sections. Many bays have been deformed by terrestrial processes and human activity, but the bays that are well preserved have an elliptical shape. I will mention some exceptions later.

The elliptical geometry is a characteristic of small and large bays. The Carolina Bays are shallow elliptical depressions with raised rims on unconsolidated ground whose major axis is oriented toward the Great Lakes. The size of the bays varies from about one hundred meters to several kilometers in size. The bays are found on sandy soil close to the water table along the East Coast of the United States.

The Nebraska Rainwater Basins have been greatly degraded by wind and water erosion, but the ellipse-fitting procedure can still be used for the basins that have maintained well-defined borders. Comparison of the geometry of the Nebraska Rainwater Basins and the Carolina Bays revealed an interesting correlation.

The Carolina Bays and the Nebraska Rainwater Basins have the same ellipticity even though they have different axial orientations and they are separated by 2000 kilometers. The elliptical shapes correspond to cones inclined at about 35 degrees. The occurrence of elliptical features with identical geometry in Nebraska and in the East Coast radiating from a convergence point in Michigan requires a better explanation than just eolian and lacustrine mechanisms that cannot guarantee the shape or orientation of the resulting structures.

After three years of studying the bays, I developed the Glacier Ice Impact Hypothesis. I found four mechanisms that were necessary for the formation of the Carolina Bays. First, a meteorite impact on the Laurentide Ice Sheet ejected ice boulders. Then, the secondary impacts of the ice boulders liquefied unconsolidated ground close to the water table. Subsequent impacts of ice boulders created inclined conical cavities, and finally, the depth of the conical cavities was reduced by viscous relaxation to produce shallow elliptical bays.

The laws of physics are the mathematical foundation for calculating the characteristics of the Carolina Bays and the extraterrestrial impact. The bay geometry provides launch and impact angles, ballistic equations provide the speed, height and flight time of the trajectories, and yield equations correlating energy with crater size provide the mass and volume of the glacier ice projectiles. The energy of the extraterrestrial impact can be estimated by combining the information from all the bays.

The speeds required to launch ice projectiles from Michigan to the East Coast vary from 3 to 4 km/sec at angles of 35 to 45 degrees. All the ballistic trajectories are suborbital space flights with heights of 150 to 370 km and flight times of 6 to 9 minutes. Since the atmosphere extends only to about 100 km, a substantial portion of the trajectories is in the vacuum of space. Above 35 kilometers from the Earth's surface, the atmospheric pressure is below the triple point of water, and water cannot exist as a liquid. Any liquid water ejected above the atmosphere would have produced clouds of ice crystals that blocked the light of the Sun.

Knowing the speed of the ice boulders, we can use scaling laws relating energy to crater size for estimating the mass of the projectiles. The scaling laws were derived from detonations of chemical explosives and nuclear bombs in the 20th century. The University of Arizona had a program that implemented the scaling equations from the book by Prof. Jay Melosh. With this program, I calculated that a Carolina Bay with a diameter of 1 kilometer could have been created by an impact of an ice sphere with a diameter of 180 meters traveling at 3 km/sec with an energy of 3 Megatons.

The size and the energy of the ejected ice boulders can be used to estimate the characteristics of the extraterrestrial impact. Since there are at least half a million Carolina Bays, the combined energy [of ~6.35×1021  Joules] corresponds to an impact by an asteroid with a diameter of 3 kilometers. From the combined volumes of the glacier ice projectiles, we can also calculate that ~1.5×1012  [trillion] cubic meters of ice ejected by the extraterrestrial impact would cover half of the United States to a depth of half a meter.

This image helps to visualize the size and the energy of the ice projectiles that created the bays. The large bay on the left has a major axis of 950 meters. Yankee stadium measures approximately 180 meters in diameter. The stadium is about the same size as the glacier ice boulder that made the bay. The impact would have had an energy of about 3 megatons of TNT, corresponding to an earthquake of 7.54 magnitude. The smaller bay to the right has a major axis of 220 meters and was made by the impact of a 28-meter ice boulder with an energy of 13 kilotons of TNT, which corresponds to a 6.0 magnitude earthquake. This is comparable to the bomb dropped on Hiroshima, which had a yield of 15 kilotons. The correlation of the impact energy with earthquake magnitude shows that the glacier ice impacts that formed the bays had sufficient energy to liquefy saturated ground.

Seismic vibrations of magnitude 6.0 or higher liquefy saturated soil. The 2011 earthquake in Christchurch, New Zealand had a magnitude of 6.3 and produced significant liquefaction that swallowed cars. Even smaller aftershocks of magnitude 5.7 caused liquefaction. The 7.5 magnitude earthquake in Niigata, Japan liquefied the ground and toppled buildings.

The water table in North Carolina’s Coastal Plain is within 1.5 meters from the surface. This is where the Carolina Bays are found. The seismic waves of the extraterrestrial impact in Michigan traveling at 5 km/sec would have reached the Eastern seaboard approximately 4 minutes later. These shock waves may not have had enough energy to liquefy the soil after traveling more than 1000 kilometers. However, the saturation bombardment by the secondary impacts of glacier ice with energies of 13 kilotons to 3 megatons would have definitely liquefied the surface. Even if the initial impacts had struck solid unconsolidated ground, the impacts occurring shortly thereafter would have found soil liquefied by the seismic vibrations of the preceding impacts.

The Nebraska Rainwater Basins are also close to the water table. The bays occur in abandoned Platte River fluvial sands on terrain that is 600 to 700 meters above sea level. The seismic vibrations of the secondary impacts would have liquefied the ground, setting up the right conditions for the creation of conical cavities.

The conical shock wave of a projectile can be preserved if the projectile does not disintegrate as it travels through the medium and if the medium is viscous, but not elastic. If the projectile disintegrates, all the kinetic energy is released at once, creating a hemispherical shock wave that produces the typical bowl-shaped crater. If the medium is elastic, the conical cavity collapses after passage of the projectile, leaving only a tubular trail. In a viscous medium with low elasticity, the projectile travels until it is stopped by friction, creating a conical cavity.

I needed to test my hypothesis that ice impacts could create conical cavities. I found that impacts on a mixture of pottery clay, sand and water worked well. This allowed me to design experiments to evaluate impact conditions and viscous relaxation. One of my first observations was that the flanges around a conical impact cavity become the raised rims of a bay.

The raised rims of Carolina Bays correspond to overturned flaps around the crater. The thicker rims toward the distal end of the bays are formed by a plowing action in the direction in which the projectile is traveling.

Overlapping bays are formed from adjacent conical impacts as illustrated in the next slide. These pictures illustrate how adjacent conical craters become overlapping bays. Viscous relaxation decreases the depth of the craters. Shaking the container speeds up viscous relaxation by promoting liquefaction. During the formation of the Carolina Bays, the seismic vibrations of nearby impacts would have speeded viscous relaxation. The overlaps follow the principle of superposition. A bay that covers another one was created later in time.

One of the arguments used against the impact origin of the Carolina Bays is that their subsurface appears undisturbed. A projectile at ballistic speed penetrates a viscous surface by parting the layers of the target during the excavation phase. Viscous relaxation partially reconstitutes the stratigraphy because hydrostatic pressure increases with depth and promotes faster flow at the bottom of a cavity.

These photographs show an oblique conical cavity made by an ice projectile that went through a red layer in the medium. During viscous relaxation, the depth of the cavity is gradually reduced. The red layer remains at the same level and disappears from view when the cavity is filled from the bottom up.

In this experiment, a newly made conical cavity is covered with a thin layer of red sand to simulate exposure to sunlight. The subsurface of the cavity is not exposed to light at the time of impact or during viscous relaxation, so the OSL date of the subsurface would not be reset. Thus, the dates obtained from samples of the subsurface of the Carolina Bays would be the dates of the terrain, not the dates of bay formation. This explains the wide range of dates obtained by OSL for the Carolina Bays.

Because the Carolina Bays do not have the characteristics of extraterrestrial impacts, some authors have proposed that the bays have a similar origin as thermokarst lakes that form when underground ice in permafrost melts and creates a sinkhole. However, the thermokarst lakes do not have the regular elliptical structure of the Carolina Bays, and their alignment is toward lower terrain, rather than to a common focal point.

Raymond Kaczorowski performed wind experiments to simulate the formation of Carolina Bays. The shape of his initial pool was modified by the wind, but it did not produce the elliptical geometry characteristic of the bays. This image is from his 1977 thesis, which was distributed within the Geology Department of the University of South Carolina but was never published in a peer-reviewed journal. Nevertheless, Kaczorowski’s thesis has been widely referenced in publications proposing the eolian and lacustrine formation of the Carolina Bays. The eolian hypotheses have never explained the detailed physical mechanism by which “blowouts” could produce perfect ellipses in Nebraska and the East Coast.

Michael Davias has identified six basic shapes of Carolina Bays. These distortions of idealized ellipses are caused by characteristics of the terrain that prevent the formation of perfect conical cavities. The distorted shapes also result when the stratigraphy and topology of the terrain modify the process of viscous relaxation for the conical cavities.

Conical cavities cannot be made on ground that does not have sufficient depth of unconsolidated material. A conical cavity inclined at 35 degrees corresponding to a bay with a major axis of 400 meters requires an unconsolidated layer 140 meters deep. An ice projectile impacting a hard layer would disintegrate explosively and create a hemispherical shock wave and a circular crater, like these bays near Barclay, Maryland in the Delmarva Peninsula.

Thirty-five million years ago, a meteorite struck the Chesapeake Bay and created a tsunami that washed away the loose surface sand of the Delmarva peninsula. Shallow depth of unconsolidated material can explain why the bays in Delmarva are circular, like these bays near Mappsville, Virginia.

These Carolina Bays are found close to the banks of the Savannah River. They are examples of bays that were distorted by the topography of the terrain, which is indicated by the color gradient. The orchid color in the center corresponds to an elevation of 58 meters above sea level and the green color toward the bottom corresponds to an elevation of 43 meters above sea level. The bays have a flattened shape toward higher terrain.

These distorted bays have an elliptical end and a flattened end. Five points are necessary to fit an ellipse. The shape of these bays can be explained by noting that the flattened ends of the ellipses are adjacent to areas of higher elevation, and that mud slides could have changed the shapes of the bays.

The experimental model can be used to confirm the mechanism of bay deformation. An elliptical impact cavity is modified when the terrain is inclined. The distortion of the bay is caused by soil flowing downhill after the formation of the conical cavity, but the soil flows faster on the uphill side due to the steeper gradient into the cavity. The resulting structure has an elliptical end and a flattened end similar to the bays near the Savannah River. Notice that the ice projectile is less dense than the liquefied soil, and it floats at the distal end of the ellipse. This may make it possible to find clasts carried by the glacier ice boulders near the surface of the bays, rather than deep at the apex of the conical cavities.

The Glacier Ice Impact Hypothesis explains all the characteristics of the Carolina Bays and Nebraska Rainwater Basins, including their radial orientation and their elliptical shape with specific width-to-length ratios. The use a physical model that produces conical cavities explains 1) the mechanism by which overlapping bays are formed, 2) the reason why the stratigraphy of the bays appears undisturbed, and 3) the reason why the OSL dates of the terrain are not the dates of bay formation.

This is a timeline of the events proposed by the Glacier Ice Impact Hypothesis and deduced from ballistic equations and scaling laws. The meteorite impact on the Laurentide Ice Sheet ejected chunks of glacier ice in suborbital trajectories during 30 seconds of excavation time. Seven minutes later, the ice boulders re-entered the atmosphere killing fauna and destroying their habitat. When the ice bombardment stopped, solid ground was covered with half a meter of ice, and unconsolidated ground was covered with Carolina Bays. The sound of the extraterrestrial impact, traveling at 340 meters per second, reached the East Coast one hour after the impact.

The Glacier Ice Impact Hypothesis proposes that the Carolina Bays were produced by a saturation bombardment of glacier ice chunks ejected by an extraterrestrial impact on the Laurentide Ice Sheet. Water ejected above the atmosphere would have produced a fog of ice crystals in low Earth orbit that blocked the light of the Sun. Thus, the formation of the Carolina Bays has to coincide with an extinction event on the eastern half of the United States and the onset of a global cooling event. This combination of conditions happened approximately 12,900 years ago. Look at the density of the Carolina Bays and consider their energy of formation. There was no place to hide from the impacts of the giant ice boulders. Any animals that miraculously survived the barrage would find themselves in a desolated, mud-covered landscape where death by starvation was certain.

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