The Tusk was absolutely thrilled to see the publication last week of a paper concerning Carolina Bays in the distinguished journal, **Geomorphology**. Other than a brief role for the Carolina bays in the early papers of the Comet Research Group, and a much longer series of Geological Society of America posters laboriously researched and determindly published by Michael Davias et. al, Zamora’s A Model for the Geomorphology of Bays is the only peer-reviewed and published ‘ET origin’ work on bays in the last two decades — and it is a doozy.

Zamora builds on the work of Willam Prouty and Melton and Schriver in the first half of the 20th century, with an assist from Eyton and Parkhurst in the 70’s, and finally Davias and Kimbel’s efforts in recent years. Each of the researchers maintained that the bays were formed at once by a barrage of material from the midwest. But, just as the early researchers ultimately decided, those around today also dismiss bays as the ** direct impacts** of ET fragments of a comet or asteroid, and consider them to be the remnant features of

**from the ejecta and ballistic shockwaves of a northerly catastrophe. They are wise to do so.**

*secondary impacts*The correct theory must account for ALL the easily observed, unique characteristics of bays. [See list of 16 from Eyton and Parkhurst here] The “wind and wave,” gradual formation, theories that continue to hold sway in classrooms, and publications from Ivestor and Brooks, fail miserably to account for all the observed phenomena. Zamora checks each off with ease. When time permits I hope to address them one by one.

Significantly, Zamora’s work is multidisciplinary and, like Davias, assisted by geometry as well as geology. Here is a sample:

Ellipses are mathematical conic sections formed by the intersection of a plane and a cone. The elliptical geomorphology of the Carolina Bays and the Nebraska Rainwater Basins can be explained if the bays originated from slanted conical cavities that were later remodeled into shallow depressions by geological processes. A width-to-length ratio of 0.58 corresponds to a cone inclined at 35° using the relationship sin(θ) = W/L. The proposed conical cavities could have been made by impacts of material ejected at approximately 35° in ballistic trajectories from the point of convergence in the Great Lakes Region. The small variations of the width-to-length ratio correspond to slightly different angles that are consistent with possible ballistic trajectories

The bay rims to Zamora are the result of a complex mathematical equation. They are the final surface expression of thousands of conical, inclined ballistic shock cones, each traveling with a giant ice fragment blown from the ice sheet in a nine-minute supersonic arc from the frigid north to the Carolina coast. (I will work on that sentence but you get the idea). These icebergs from space slammed into the supersaturated unconsolidated clayey sands of the coastal plain and left behind the shock “ripples” and “flaps” that we recognize today as bay rims. Zamora even provides an equation relating the perfection and ellipticity of bays to the degree of unconsolidated sediments encountered by the ice bullets:

The LiDAR images also reveal that some terrains do not have elliptical bays. Davias and Harris (2015) describe six archetype bay shapes that may be determined by the geological characteristics of the terrain. The thickness of the layer of unconsolidated material required to produce an elliptical bay can be estimated by the formula tan(θ) × L/2, where L is the length of the major axis and θ is the angle of inclination. A conical cavity inclined at 35° corresponding to a bay with a major axis of 400 m would require a layer of unconsolidated material with a depth of approximately 140 m.

That makes sense to me, and accounts for the “classes” of similar bays, an aspect unexplained by wind and water enthusiasts, but first investigated and catalogued by Davias.

In addition to the present journal publication, Zamora makes his case in detail in a recently published book available from Amazon: Killer Comet: What the Carolina Bays tell us. I am reading it now and will update this post accordingly.

On the shoulders of genius, Zamora has provided defensible and superior answers to the many questions provoked by the appearance and distribution of Carolina bays. The geological community will largely ignore this paper, of course, but some will take note. And there is always reason for hope as the class of geologists who reject recent catastrophic explanations out-of-hand continue their long march from the tenured defense of the known, to retirement, and finally to death.

I am interested in where Antonio got that cone inclination from the Davias data. The way I look at it, he got his math wrong. I derived a very different values for the angle and the ratio. I come up with 43.652°, measured vis-a-vis the horizontal.

Michael Davias long ago shared his data with me, slightly before he completed the count of CBs. Davias ended up with 45,000, and what I have includes 43,900 of them (97.55% of the total). I’ve averaged their widths and lengths, and they came out to average W = 0.21743 km wide and L = 0.37514 km long – a ratio of 0.7235:1.000.

EXCEPT:The sine is not the right trig function to be using.How to explain this in 1,000 words or less? . . .

Technical stuff coming up:The geometry of it is such that the included angle between W and L in the right triangle with L as a hypotenuse ON THE GROUND and the W as the leg that makes the crater width*** – and because the impactor is assumed to be spherical, we can draw it as SQUARE to the angle made by the target surface and the incoming path, the angle θ. Thus we use NOT the sine value but the COSINE value.

Basic trig, it is a case of the near side over the hypotenuse– and that is COSINE, not SINE. The lower this W/L ratio, the steeper the impact angle.This is easily visualized by looking at a hypothetical vertical impact and a hypothetical (basically) horizontal impact. The former would have a W/L = 1.000, and the latter would have W/L of essentially zero. The lower the angle relative to the ground, the greater L becomes. This is what the COSINE does, not the sine.

(*** This is NOT the bolide diameter, but the crater width.)

(I could be wrong, but, folks, I don’t think so. My main gig in my early engineering years was solving scads and scads of triangles – probably upwards of 100,000 –

LONGHAND. And I HAD to get them right. And I’ve checked and double-checked this before writing this comment.)Given that we are given W and L, I determined that the direct method is that W/L gives the COSINE, not the sine.

The Sine would work if the angle was taken OFF THE VERTICAL, but to GET to the vertical, you have to go round about, if you started with W and L. But W/L itself does NOT give you the angle off the vertical. W/L can only lead directly to the angle measured off the surface. Because L is measured ON the surface, not on the vertical. And W cannot HELP but be related geometrically to the WIDTH of the bolide. Again, because L is measured on the surface, not on the vertical, working off the vertical is WRONG.

The cosine should be used, and then the arccosine angle should be derived, and then that angle subtracted from a 90° vertical impact angle. This fits my trig sketch and fits the way the impactors come in and are discussed.

It ALSO agrees with the 20° downward angle always referred to in, say, Chelyabinsk. The reference 0° position is not the vertical, but the horizontal (the ground). The 20° was measured versus a horizontal path (a 0° path parallel to the ground).

Thus Zamora’s angle has been gotten wrong. He also got a different value than my 43,900 CBs gave. He got And I don’t think the 1,000 other craters Davias has identified and measured is going to change my angle much. My average angle is 43.652° measured off the horizontal. This is based on arccos (0.27143km/.37514km). (I feel comfortable going to 5 decimal places on such a large population in the database, even though Davias only took the L and W values to 2 places.)

——

(Can I be wrong because this is an ellipse and maybe there is something magical about ellipses? An ellipse is defined as “

the locus of all points P such that the sum of the distances from P to two fixed points F, F1 (foci) are constant.”Yeah, and in the real world, every one of those points has the same coordinates (relative to the intersection of the major and minor axes, A and B) as if you took a circle and stretched everyone of P’s Y coordinates in one direction by the ratio of A/B. I learned this from experience. Note that this intersection point of A and B is NOT the intersection of the right angle cone’s axis and the plane cutting across it.)

It’s not all harsh critiquing, though… I will post at least one positive comment, too. . . .

Steve,

It is not clear to me what triangle and included angle you are considering when you say

“The geometry of it is such that the included angle between W and L in the right triangle with L as a hypotenuse ON THE GROUND and the W as the leg that makes the crater width …”

My understanding is that the included angle between W and L is 90°, since W and L are twice the semi-major and major axes of the ellipses, as shown in the figures in the paper. That is, L is the maximum dimension of the ellipse, but it seems like you are viewing L differently. A diagram would be helpful. I have no doubt that you are very knowledgeable about ellipses and impact craters, but I am not understanding your interpretation here.

To check Zamora’s result, I did a calculation based on a very simple model. I assumed that a spherical object sweeps out a cylinder as it approaches and impacts the surface of the Earth, which is represented by a plane, where the cylinder is inclined at angle θ to the plane. I simply calculated the intersection of the cylinder and the plane, to represent the shape of the impact crater. The result is that the intersection is an ellipse with eccentricity cos(θ), and sin(θ) = W/L, which agrees with Zamora.

I have not yet closely read Zamora’s paper, but I notice two things. (1) He gives an incorrect definition of ellipticity, and (2) the ballistic equation he cites is not the correct equation in this case. It assumes that gravity is constant over the trajectory and the trajectory is over a flat surface, neither of which is true. At best is is an approximation, which may be good enough for his argument, but it is not accurate. The ballistic equation describes a parabola, but the suborbital trajectory of the ice boulders is elliptical.

Interesting paper. Only addressed the physical processes involved in forming the bays – no small task that. Will have to reconcile the formation dating issue somewhere along the line. Cheers –

I’m happy for Mr. Zamora that he got this published and it is a neat idea. In fact that what was first drew me to look for in impact feature in the disputed area on the Laurentide ice sheet. I’m still not all that interested in this hypothesis anymore, but it certainly was NOT Saginaw Bay.

One could possibly surmise that the Black Sturgeon River geomorphological feature might do it, but even that’s a stretch given the evidence.

The big problem with Darwin’s Valentine is that any evidence of it would be long gone and the sedimentary evidence thus far is inconclusive.

I’ve been away a long time and am just catching up?

Does Mr. Zamora offer any value for velocity of these, ‘Ejected Ice Fragments’??

I’ve been away a long time and am just catching up?

Does Mr. Zamora offer any value for velocity of these, ‘Ejected Ice Fragments’??