Click Here for Figure 1 - 2 - 3 - 4 - 5

(In figures the parameters are as follows: meteorite radius = 5m, density = 4g/cm3, and Speed = 30,000m/s when parameters must be used)

Click Here for Table 1

Introduction - Meteorite Study and Application

Natural particles of solid matter that are too small to be regarded as planets are traversing our universe constantly. When these particles sometimes plunge into the earth's atmosphere while still large enough to retain their identity once they have landed they are called meteorites (Nininger, 1961). Literally millions of such impacts have bombarded the earth in it's 4.6Ga history. From the theorized production of magma oceans to the extinction of the dinosaurs, the earth has been constantly bombarded.

Although frequently obscured by time, evidence of meteorite impacts is abundant. Impact induced mineral assemblages, and partially melted breccia are sure signs of these interstellar bombs, while impact craters and shatter cones represent convincing landforms.

In the past much work has been done deciphering the physics and quantifying the mechanics involved in meteorite impacts. From the flight to final impact topics like diffusion, turbulence of flight, geometry, rotation of flight, aerodynamic pressure, drag and energy transfer, ablation, radiation, target density, atomic collision, potential energy of atomic interaction, shock wave propagation, shock wave detachment, cratering, melting, and oblique impacting have been evaluated using physical quantitative models. This approach has been quite successful for small meteorite impacts, however for large scale impacts, our ability to understand the processes involved decreases as the size of the meteorite increases (Melosh, 1980). For this reason, to gain a basic understanding of the sheer magnitude and striking spectacle that is a meteorite impact, it may be more effective (if not more understandable) to focus on simple energy relationships.

This paper will discuss some of the geologic features that are characteristic of meteorite impacts then try and semi-quantitatively access some of these phenomenon using basic energy balances, and finally apply these to a "real-world" problem.

History of Meteorite Study and Products of Impact

The first evidence of meteorite impacts was the unique suite of minerals present surrounding what were thought to be volcanic centers. Most early workers were reluctant to accept the possibility that some of these "volcanic centers" were impact craters. Without any real proof impact theory was mostly considered mostly as a curious phenomenon associated with other planets, and as a science meteorite study did not advance until the mid 1900's. The discovery of Coesite in the early 1950's marked the turning point in meteorite study by bringing about the general acceptance of impact cratering. Loring Coes determined that at extremely high pressures and temperatures (40kb at 700C- 1700C) silica took on a dense, heavy form that later was named coesite (Mark, 1987). Coesite had never been found in any naturally occurring rock, until close examination of the Coconino sandstone within the Arizona (Barringer or Meteorite) crater in the 1950's. At the time of this discovery, scientists became so excited at the prospect of finding more impact sites that vigorous reinvestigation of possible impact sites took place immediately. Years later the mineral Stishovite, an even higher temperature, higher pressure polymorph of quartz, was found in the Arizona Crater (Mark, 1987).

The Arizona crater was also at the center of a unique debate concerning diamonds. In 1955 experiments were completed by F. P. Bundy and others that indicated extreme pressures and temperatures were needed to form a diamond. The speculation that followed was that tiny diamonds, found in iron associated with the Arizona Crater, likely formed as a result of a high pressure and temperature impact (Mark, 1987). Opponents argued that needed heat and pressure could not have been achieved in such an impact, and that the diamonds were probably formed in space, during the formation of the meteorite itself (Mark, 1987). Today diamond formation is characteristic of most meteorite impacts, and along with other high temperature, high pressure minerals has been accepted as evidence for a meteorite impact. Nearer the impact itself, pressures and temperatures become high enough to melt pre-existing rock.

Impactite is a term used to describe any rock that formed as a result of melting during impact. Although, impactites go by many different names their presence is important for one reason - they define the most intense melting or shocked zone of an impact. Names like suevite and tagamite along with many others distinguish between the chemical composition and degree of melting within these rocks. Impactites are commonly quite brecciated and phenocrysts have a "shattered" appearance. Pseudotachylite is a general term referring to impact related breccia commonly showing some melting and/or flow textures. It is commonly used when discussing the Sudbury Complex of Canada and the Vredefort Dome of South Africa (Mark, 1987). The name pseudotachylite exemplifies the early confusion of an impact site with a volcanic center.

Adding to the evidence of meteorite impacts, is a unique feature called a shatter cone. According to Dietz a shatter cone is a "conical fragment of rock characterized by striations that radiate from the apex." (Mark 1987). These cones are a rock feature that is a result of the high pressure, high velocity shock wave produced from an impacting meteorite. The mechanics that produce these cones are poorly understood, and only nuclear tests generate enough heat and pressure to even slightly mimic shatter cone formation. In 1959 the first man-made shatter cone was produced during an underground nuclear explosion. Years of hunting for and careful mapping of shatter cones and their orientations shows that the apex of these cones (from all sides of an impact site) combine to point out the exact center of impact. Consequently, in the early 1960's shatter cones and impact minerals were both considered adequate criteria for suggesting an impact site (Mark, 1987).

In the late 1960's NASA became preocupied with the possibility of a meteorite or tiny space particle puncturing equipment, and becoming a hazard in space (Cosby and Lyle, 1965). The consequences of such an interstellar encounter were feverishly investigated by NASA scientists and workers for years to come. Thus NASA's research, seemingly misguided now, paved the way for present day meteorite impacting study.

The physical appearance of craters was not enough to convince more than a handful of scientists that meteorites had bombarded our earth in the past and will continue to do so in the future. The tangible evidence, high temperature/high pressure minerals, impactites, and shatter cones, was the sole and overwhelming factor that triggered the field of meteorite study.

Cratering in Theory

The largest and most terrific impact feature is the meteorite crater. The theory of cratering is logical, however, the mechanics of the process is quite unique and intricate. Imagine the consequences of an impact that produces more energy than 1000 atomic bombs the size of those dropped on Japan to end WWII (Grieve and Personen, 1992).

An iron-rich meteorite traveling over 50 km/s enters the earth's atmosphere as a fiery ball with a thin layer of melt due to the heat from air friction. Travel through the earth's atmosphere is approximately the same as traveling through 4 feet of solid rock (LeMaire 1980). When this meteorite comes in contact with the earth a fantastic shock wave is produced in both the meteorite and surface rocks. This is referred to as the compression stage by Melosh (1980), or the "early stage" by Holsapple and Schmidt (1987). During this process the target material is accelerated downward by the shock. Because the tremendous pressures produced within the target by the shock wave are adjacent to the "outer limit" of impact, which is still only subjected to the earth's atmospheric pressure, material is catastrophically forced out the sides of the impact area. This squishing of material out the sides of the impact is called jetting. The material ejected forms a hydrodynamic jet that has a velocity several times that of the meteorite itself, and is composed of an incandescent liquid or superheated vapor spray (Melosh, 1980). A complicated system of shock waves and rarefaction waves envelop the target and projectile. One of the main results of this process is the transfer of kinetic energy from the meteorite to the target in the form of internal and kinetic energy. The rarefaction waves catch up with the initial shock wave several projectile distances from the impact, greatly reducing the shock intensity. After only a fraction of a micro-second, the compression stage ends with the complete transfer of energy in the form of a shock wave and latent heat.

The crater excavation stage (Melosh, 1980) overlaps somewhat with the compression stage. This stage is likened to an atomic explosion, and is characterized by rapid crater expansion. Materials leave the crater in two ways, ballistically, or plastically (Melosh, 1980). The most highly shocked rock nearer the surface is unloaded so rapidly it has a net upward force that propels the rock from the opening crater. Slightly deeper rock is pushed laterally from the crater. During this stage, depending on exact P/T conditions the target rock may be melted, partially melted, brecciated, or vaporized. Commonly a large amount of impact melt is formed. Several authors have attempted to calculate the decay rate of the shock wave, one estimate by Gault and Heitowit (1963) (form Melosh, 1980) indicates that pressure decrease was proportional to the 1/radius2.6. Another estimate given by Hollsapple and Schmidt (1987), indicates the shock decreases at a rate of 1/radius6 to 1/radius2. Crater growth finally stops when the net upward propelling force at the crater rim is not large enough to eject any more material.

The final stage of crater growth, the modification stage, lasts only 20 s to 30 s (Melosh, 1980). Small simple craters (basically craters that are symmetrically bowl shaped) don't undergo much modification, but they may fill themselves, at least partially, with impact breccia or melt from the impact. Large craters, however, often undergo tremendous modification (they are called complex craters). This modification often produces raised centers and double rings. Although the exact mechanism for is debated, Melosh (1980) indicates that gravitational collapse is the main driving force. At least three main theories for central uplift of craters exist, but it seems intuitively obvious that the rebound from shock is the most likely of these. This process could be likened to the initial upward movement of water droplets when a stone is tossed in a pool. The development of a second ring around a complex crater is also is poorly understood. Ideas like "frozen" shock waves, fault scarps, and material differences have all been suggested (Melosh, 1980), however second rings appear to be related to normal faulting found around impact sites.

The cratering process represents the greatest release of energy per unit time known to man. The mechanisms are complex, and the results are spectacular. It is little wonder we do not fully understand the cratering process. In the past, experiments that model cratering by shooting projectiles at great speeds into different materials (Hollsapple and Schmidt) have been performed. Although these experiments paved the way for further research and modeling, they are fundamentally flawed. We simply do not have the ability to shoot projectiles at hyper-velocities equivalent to those of meteorites, and the extrapolation or scaling from moderate velocities to hyper-velocities is not adequate. Experimental limitations coupled with the huge number of mechanical factors involved in theoretical calculations is a real problem. Perhaps it is better to grossly oversimplify all of these problems, and try to rely on the fact that some of these factors may, in effect, cancel each other out. Therefore the simplest way to look at a meteorite impact may also be the best.

Quantifying the Cratering Process

First we will consider the kinetic energy of a meteorite. The variables mass and velocity become unknowns, however, we can put realistic limits on each of these. For example a meteorite must be traveling at least 11 km/s. This is equal to the minimum velocity needed for a projectile shot from earth to overcome gravity and reach space. Logically, anything falling from space to earth must achieve the same velocity. According to Middleton and Wilcock (1994), 72 km/s is near the upper limit of meteorite speed. The density of an iron meteorite is 8000 kg/m3 and for a stoney meteorite is 3500 kg/m3. Although the diameter of a meteorite remains an unknown variable, it's density must lie between these two endmembers. Let us assume that the meteorite is roughly spherical in shape. Now taking an iterative approach, we can plug in various reasonable speeds, reasonable densities + reasonable diameters (thus reasonable masses) into the formula,

1/2Mv2 = Total Kinetic Energy.

Consequently, we will receive a reasonable total kinetic energy estimate over a wide range of conditions (Table 1).

This is a valuable approach to cratering, because slight variations in the angle of impact can be (for the most part) entirely neglected. In other words an impact at 75 degrees is approximately the same as using a diameter 3/4 as big as the original diameter or using a density that is 3/4 the original density of the meteorite.

Because most impact features (melts, shatter cones, etc.) are often hidden under sediment or eroded away, the only real impact features we can measure directly is a crater. Can one estimate the size a meteorite from the size of its crater? The answer is yes, to a first approximation. Lets assume for a minute that 100% of the meteorite's energy goes into the formation of a simple crater. This can now be likened to the energy needed to excavate a bowl shaped volume (a simple crater). In other words Energymeteorite = Potential Energyexcavation . The potential energy is equal to the volume of rock that will be displaced (V) multiplied by that rocks density (d), the gravity of the planet the meteorite is impacting (in this case, earth) (g) and the height of excavation (h). If we call the hemispherical radius of the crater, R, and we let the height needed to move the rock (h) be equal to R, it is easily seen that Energymeteorite = K * Rcrater4 , where K is a constant equal to 2/3 pi * d * g (Table 1).

Of course not all of a meteorite's energy is used to crater, in fact some of it is used to produce a huge shock wave, and most is lost as latent heat (Melosh, 1985). These are two important considerations, but how can we consider them? Holsapple and Schmidt (1987) and Melosh (1985) treat this problem at length. Melosh (1985) estimates that about 80% - 95% of the meteorite's energy is expended as a shock wave and heat, leaving only a small percent to excavate a crater. Calculating the energy of the shock wave, and the amount of heat produced is not straight forward. Calculations for shock propagation speed and particle velocity depend heavily upon the property of the target rock itself. The amount of heat produced and the resulting amount of melt is also very complicated to calculate and varies only roughly as a function of impact energy (or crater diameter) (O'Keefe and Ahrens, 1994). Because of these problems, the seemingly easily calculated relationship Emeteorite = Ecratering + Eheat + Eshock wave doesn't do us much good.

It makes more sense to now borrow some results from experimentation and models that will allow us to calculate a melt volume given a crater diameter, and to describe the mechanical behavior of a shock wave. O'Keefe and Ahrens (1994) show us that for an "average" impact 4% to 6% of the diameter of the crater is equal to the thickness of the melt layer produced. Melosh (1985) indicates that the initial shock wave travels at 6 - 20 km/s. And Holsapple and Schmidt (1987) indicate that the initial particle velocity is about 1/2 that of the meteorite's velocity at impact, the initial pressure of shock is approximately equal to dtarget*v2meteorite, and the pressure of shock decays at a rate equal to 1/R6 to 1/R2, where R is the radius of the impact crater. Melosh (1980) indicates that initial impact pressures for an 11.2 km/s to 30 km/s impact are around 1 to 10 Mega bars.

Let us look first at the melt volume produced upon cratering. It can be easily calculated because we can relate it to the crater diameter (O'Keefe and Aherns, 1994). The first step is straight forward. Let us say 5% of the diameter of the crater is equal to the melt thickness. Now using this information we can calculate the volume of melt produced. We simply calculate two bowl-shaped objects. First we calculate the volume of a bowl with the diameter of the original crater, next we calculate the same volume of a bowl with a diameter that is d-(2*0.05d). Subtracting the two volumes gives the total melt volume (Table 1). The other parameter left to calculate is the pressure (P) of a shock wave at a given distance from the impact site.

Using the relationship provided by Hollsapple and Schmidt (1987), Pinitial = dtarget*v2meteorite, we can calculate the initial pressure (Table 1). Using a decay rate of about 1/r3, Where r is the radial distance from the point of impact (not a radius), we can roughly calculate the pressure of the shock wave at a distance, (d) from the crater. To accomplish this, first we set Pinitial = K*1/r3initial , where K is a proportionality constant. When P is at it's greatest we can assume r is approximately equal to the radius of the meteorite itself (at impact the initial pressure would be roughly constant at the perimeter of a spherical shape about the size of the meteorite). Now for various Rmeteorite and Pinitial values (dependent upon initial velocity and target density) a K value can be calculated. Using this K value, we can plug a P value into the above equation and find the distance from the impact site where the shock wave would reach this pressure (Table 1). Converesly, we could plug in a distance, r, to the above equation and find what the shock pressure, P, would be at this distance.

Implications of Results

The calculations above show us that even a small meteorite impact can release the energy equivalent of a nuclear arsenal (many megatons of TNT). More importantly, these calculations are not only simple and useful in quantitatively understanding impact cratering, but also provide us with a better qualitative understanding of the same processes. Table 1 is a summary of results, however, figures 1, 2, 3 and 4 better help to show changes in specific parameters. Respectively, change in total energy is plotted against the speed and the radius of a meteorite, crater diameter is plotted against melt volume for a simple crater, and total pressure is plotted against the energy of a meteorite. Perhaps, more than all the others figure 5 provides the best insight into the magnitude of cratering. Figure 5 is a plot of pressure stability zones for the assemblages coesite, stishovite, quartz; diamond, graphite; impact melt, melt breccia; and shatter cones versus the distance from an impact site.

Conclusions, Application to Sudbury, Canada

It is essential for the equations derived earlier to apply to real situations. We will review cratering concepts and apply equations by focusing on a "real" problem dealing with the Sudbury Igneous Complex (SIC), of Ontario, Canada.

The single largest magmatic nickel source in the world is Sudbury Canada (SIC - Sudbury Igneous Complex). For decades scientists have agreed that Sudbury is the site of a large meteorite impact, however, a debate over the ultimate source of the nickel ore continues today. Did the magma that brought with it the nickel-bearing sulfide ore form from the fractionation of an impact melt, or from a mantle derived melt? This is the question being debated.

Early supporters of a mantle derived source for nickel rely largely on the fact that all other known large nickel deposits have a deep mantle-derived source, and impact melting could not have reached such depths. Norman (1994) argues that the SIC need not be formed from an impact melt, and an endogenous magmatic process is all that is required. He points to concentrations of PGE's and Re-Os isotopic compositions as further evidence to disqualify an impact melt.

Lately, the impact melt theory has received much support. Deutsch (1994) and Deutsch et al. (1994), strongly support an impact melt source for nickel at Sudbury. Isotopic evidence and melt volume calculations seem to support this viewpoint.

Deutsch et al. (1994), lists the parameters estimated for the Sudbury impact by various authors.

1) Meteorite = 14 km, 2) Crater = 110 km , 3) Density of Meteorite = 3000 kg/m3, 4) Melt Volume = 12,500 km3 .

Using these parameters we can apply the principles we developed earlier (above) to try and solve the Sudbury problem. We can also learn how the results reported by Deutsch et al. (1994) match our own. Assuming a radius of about 5 km for a theoretically spherical meteorite, and a density of 3000 kg/m3, my calculated crater diameter is 57 km and my calculated melt volume is 15,500 km3. The estimates given by Deutsch et al. (1994), although based on visual evidence and more sophisticated modeling calculations, are the same order as my results. I assumed that 50% of energy went into cratering as a marker (it may be closer to 15% or possibly higher than 65%).

Further, If we assume that a percent of the meteorite's composition is incorporated in the melt (say 20%), then a spherical stoney meteorite with a 0.05% nickel content , a radius of 5 km, and a density of 3000 kg/m3 could supply approximately 1.6 billion kilograms of nickel. The average grade of ore at Sudbury is about 3%, so the meteorite itself could account for 52 billion kilograms of nickel ore. During the best nickel production year ever, Sudbury produced 209,000,000 kg of nickel, but amounts around 120,000,000 kg/year are about average (Giblin, 1984, p. 5). Assuming this is correct, the nickel from the meteorite alone could supply 13 solid years of average nickel production. If you assume the entire meteorite was incorporated into the melt a figure like 60 to 70 years of production could be accounted for. This appears to be adequate to explain the formation of the greater portion of Sudbury ores. An impact melt then seems like the only logical way this deposit could have formed.

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