Cratering as a Geological Process Part 1 (a) Simple in addition to complex craters; (b) Fu
Rodgers, Larry, Music Writer has reference to this Academic Journal, PHwiki organized this Journal Cratering as a Geological Process Part 1 (a) Simple in addition to complex craters; (b) Fundamental concepts of stress waves, plastic waves, in addition to shock waves; (c) Impact in addition to crater modifying processes Importance of Crater Studies: Principal process in shaping planetary surfaces.Principal means of determining relative in addition to as long as some planetary bodies the absolute ages of planetary surfaces.Major impact events may have affected the tectonic, chemical in addition to biological evolution of planetary bodies (e.g., initiation of plate tectonics; alternate mantle convection; extensive melting in the mantle; removal mantle in addition to crustal materials of target planets during major impacts, extinction in addition to possible delivery of organism of planets).Crater morphology may tell us about the rheological structures of the crust in addition to mantle of planetary bodies.Large impacts may have affected planetary rotations in addition to orbits. Basic Classification: (1) Simple craters: strength controlled as long as mation process with smooth bowl shapes; relatively higher depth-to-diameter ratios.(2) Complex craters: gravity-dominated modification process, clear sign of wall in addition to floor modifications expressed as central peaks, peak-ring structures; relatively low depth-to-diameter ratios (i.e., relatively shallower basins than simple craters).(3) Multi-ring basins: having peaks in concentric rings on flat floors.
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Moltke Crater (D = 7km):Simple crater with a bowl-shaped interior in addition to smooth walls. Such craters typically have depths that are about 20 percent of their diameters (Apollo 10 photograph AS10-29-4324.)Tycho crater (D = 83 km): Complex crater with terraced rim in addition to a central peak.Bessel Crater (D = 16 km h = 2km) A transitional-type crater between simple in addition to complex shapes. Slumping of material from the inner part of the crater rim destroyed the bowl-shaped structure seen in smaller craters in addition to produced a flatter, shallower floor. However, wall terraces in addition to a central peak have not developed. (Part of Apollo 15 Panoramic photograph AS15-9328.)
Mare Orientale (D = 930 km)A lunar multiring basinAn outer ring has a D = 930 kmThree inner rings with D= 620, 480, in addition to 320 km.Radial striations in lower right may be related to low-angle ejection of large blocks of excavated material.Young lava flowTransition size from simple to complex craters on various planetary bodies: Europa: 5 km Mars: 8-10 km Moon: 15-20 km Venus: No craters with diameters < 10 km are scarce, possibly due to thick atmosphere; dominantly complex craters in addition to multi-ringed basins. Earth: 2-4 km Mercury: 10 kmSimple-to-complex crater transition occurs when the yield strength is related to the gravity (g), density (rho), transient crater depth (h), in addition to a constant c that is less than 1:orWhere Dtr is the transient crater diameter that can be related to the final crater diameter byThat is, D is proportional to yield strength (Y) in addition to inversely proportionally to density (rho) in addition to gravity (g). Transverse in addition to longitudinal waves are related to bulk modulus K0, shear modulus m, in addition to density r0.Wave-induced longitudinal in addition to transverse or perpendicular stress components arePoissons ratio=UL is particle velocityC is wave velocityRelative importance of longitudinal in addition to transverse waves:Transverse waves are not important in the cratering process, because the shear strength of materials limits the strength of the wave.The strength of the longitudinal waves have no limit, the strength of compression has no upper bound. In most cratering modeling, transverse waves are neglected.Compressional in addition to tensional waves are converted at a free surfaceFree surfaces require both normal in addition to shear stresses are zero, but the particle velocity can be non zero.UL at the free surfaces as long as compressive wave is: UL = sL /CL r0For tensional waves, sL in addition to CL have the opposite sign, in addition to thusUL = sL /CL r0Thus, at the interface, UL is doubled. De as long as mation generated by this process is called spalling. Three stages of cratering: Contact in addition to compression stage (initiation of shock waves) Excavation stage (shockwave expansion in addition to attenuation; crater growth; ejection of impactor in addition to target materials) Post-impact modificationReflection at an interface from high-velocity material to low- velocity material: Reflected wave is tensile waves in addition to the rest continues into the low-velocity material as compressive wave. Reflection at an interface from low-velocity material to high- velocity material: Reflected wave is compressive wave in addition to the rest continues into the high-velocity material as compressive wave. Plastic Yielding at HEL the Hugoniot Elastic LimitWhen stress in the stress wave reached the plastic limit, irreversible de as long as mation will occur. This plastic yield strength affects both the speed in addition to shape of the stress wave. The onset of this behavior is indicated by a characteristic kind in the Hugoniot P-V plot. The corresponding pressure is known as the Hugoniot Elastic Limit (HEL).In the continuum in addition to fracture mechanics sense, when the differential stress sL sp = - Y, Y is the yield strength, the material begins to experience plastic flow.Shear stress t = - (sL sp)/2 Pressure P = - (sL + 2sp)/3 HELAt the failure point, when t = - Y/2, the longitudinal stress equals to HEL, that is Idealized cross section of a simple craterOnce the wave-induced stress reaches HEL, the shear stress t = - (sL sp)/2 remains constant, in addition to thus the increase in sL in addition to sp must also maintain in such a way that its difference is the same as -2t. When P is much greater than t, we neglect the differential stress term in addition to corresponding stress wave becomes strong pressure wave.Cautions as long as the HEL:For porous medium, there might be two HEL points, one as long as the collapse of the pores, in addition to the other as long as the onset of ductile flow. Yield strength may not be constant, but a pressure-dependent envelope. Yield strength may be rate-dependent. Elastic Wave: sL < sHEL Longitudinal wave depends on both bulk in addition to shear muduli Plastic Wave: sL = sHEL Longitudinal wave depends almost completely on the bulk modulus. The wave propagates much slower than the elastic wave in addition to at a speed of the bulk wave speed defined byCB = [K(P)/r0]1/2 Where bulk modulus increases with pressure. Thus, the bulk speed of plastic wave is much higher under high-pressure condition. This segment is called strong or shock wave, which is a plastic wave travels faster than elastic waveStrong compressive waves: The Hugoniot EquationsConservation of massConservation of momentumConservation energy
P = P(V, E) is equation of state as long as shock waves. There are two ways to represent the equation of state as long as shock waves (P-V in addition to U-up plots)Shock pressure as a function of specific volumeShock wave velocity as a function of particle velocity
Release wave or rarefaction waveThe high-pressure state induced by an impact is transient, ranging from 10-3 to 10-1 sec as long as projectile of 10 m in addition to 1 km size.The high-pressure in a shock wave is relieved by the propagation of rarefaction, or release waves from free surfaces into the shocked materials. This type of wave from strong compression generally moves faster than the shock wave in addition to is proportional to the slope of the adiabatic release curve on the P-V diagramStage 1: Contact in addition to compression (shockwave generation in addition to projectile de as long as mation): this stage only lasts a few seconds. Rarefaction waves cause projectile to trans as long as m into vapor in addition to melts instantaneously. From OKeefe in addition to Ahrens (1975)Impact of 46-km-diameter projectile at a speed of 15 km/s 1 s after the impact.
Isostatic adjustment after a large impact removing crust in addition to uplift mantle
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