RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 7, ES6004, doi:10.2205/2005ES000193, 2005

On the estimation of elastic stresses in the mantle at the time moment of a large meteorite fall

S. M. Molodensky
Institute of Physics of the Earth, Russian Academy of Science, Moscow, Russia

Contents


Abstract

[1]  Simple relations are obtained for estimating stresses in the mantle at the time moment of a large meteorite fall from values of the velocity and mass of the meteorite and the sizes of its crater. It is shown that the fall of the Chicxulub meteorite, the largest over the last 100 Myr, produced stresses of the order of 0.1-1 MPa.


Backmatter

[2]  Jones et al., [2002] proposed a hypothesis according to which the fall of a large meteorite (such as the Chicxulub meteorite 10-16 km in diameter, which fell 65 Myr ago at a velocity of about 11 km s -1 and produced a crater 180-300 km in size) can activate convection in the lower mantle and provoke the formation of plumes in the D'' layer. An attempt to estimate the order of magnitude of elastic stresses arising at the time moments of such events is made in the given paper.

[3]  The main uncertainty involved in the estimation of elastic stresses is related to the question of which part of the kinetic energy of a meteorite is converted into heat and which part, into the energy of seismic vibrations. It is natural to divide the fall process into two phases: (1) the phase of inelastic impact (accompanied by the fracture of material in a region comparable in size with the crater) and (2) the phase of elastic interaction of the resulting fragments with the mantle.

[4]  As follows from the law of conservation of momentum, the average velocity of fragments in the first phase is determined by the relation

eq001.gif(1)

where ( m1, r1 ) and ( m2, r2 ) are the mass and average radius of the meteorite and the crater, respectively, and v1 is the velocity of the meteorite fall. Accordingly, the ration of the total kinetic energy of fragments to the initial energy of the meteorite is

eq002.gif(2)

[5]  The phase of elastic interaction of fragments with the mantle outside the crater can be described by the elastic energy balance

eq003.gif(3)

where

eq004.gif(4)

is the volume density of elastic energy, l and m are the Lamé coefficients, u is the displacement vector, eik is the stress tensor, and

eq005.gif(5)

is the k th component of the Poynting vector in a Cartesian coordinate system (summation over repeated indices is assumed in (4) and (5)). Neglecting the depth dependence of the elastic moduli, we may assume that the elastic energy in mantle is concentrated in a spherical layer centered at the impact point and bounded by spheres of radii R1 and R2; the thickness of the layer R2-R1 is determined by (i) the finite time of the interaction of fragments with the lower boundary of the crater and (ii) the diffusion of the wavefront associated with the dispersion of seismic wave velocities. In the case of body waves, the velocity dispersion is only due to the inelasticity of the medium (the velocities depend on the period of vibrations and are independent of the wavelength). Given the quality factor values characteristic of the Earth's mantle ( Qmsim102-103 ), the velocity dispersion is dVp/Vpsim dVs/Vssim 10-2, and the value of the wavefront dispersion due to the velocity dispersion is of the order of dRsim R1dV(p,s)/V(p,s) sim 10-2R1. It is easy to show that this effect is negligible compared to the first effect. To estimate the finite time of the interaction of fragments with the inner boundary of the crater dt, note that elastic strains at the lower boundary of the crater assume have ultimate (failure) values typical of rocks: e maxsim 10-3cdot10-4. In accordance with the law of conservation of momentum, we have for the interaction process of fragments with the inner boundary of the crater:

eq006.gif(6)

where the average interaction force is of the order of

eq007.gif(7)

Hence, we have dtsim m1 v1/(me max r22) and

eq008.gif(8)

[6]  In accordance with the equation of the energy balance in the second phase of the process, the stresses in the wavefront region efr are determined by the relation

eq009.gif(9)

where

eq010.gif(10)

is the volume of the spherical layer in which the energy of elastic vibrations is concentrated. Accordingly, the maximum stresses in the mantle at the distance R1 from the center of the crater can be estimated as

eq011.gif(11)

sim mr3/21 r2-1/2 R-11 (v1 e max/(2pVp, s))1/2.

Setting R1 = r2 in this formula and equating the result to the known value of elastic stresses at the lower boundary of the crater me max, we obtain

eq012.gif(12)

which yields

r2 sim r1 (v1/ (2pVp, s e max))1/3.

With characteristic values of ultimate tangential stresses of rocks of the order of 10-3-10-4 and v1 sim pVp, s sim 10 km s -1, this formula yields the estimate r2sim(10-25)r1 relating the sizes of a meteorite and its crater and agreeing well with data on the Chicxulub meteorite. To obtain numerical estimates of stresses that developed in the D'' layer at the time moment of the Chicxulub meteorite fall, one can use either formula (11) giving r2/r1 sim (10-25) or the aforementioned geological data according to which r2/r1 sim (180-300) km/(10-16) km~ 10-30. Given e maxsim 10-3-10-4 and msim 1011 dyn cm -2, we obtain in both cases mefr sim 106-107 dyn cm -2 = 0.1-1 MPa.

[7]  This value is about an order of magnitude smaller than the tectonic stresses developing in the crust and upper mantle before an earthquake.


References

Jones, A. P., G. D. Price, P. DeCarli, N. Price, and C. Hayhurst (2001), Modelling impact decompression melting: a possible trigger for impact induced volcanism and mantle hotspots, in: Abstracts, ESF Workshop on Impact Markers in the Stratigraphic Record, Eds.: F. Martinez-Ruiz, M. Ortega-Huertas, I. Palomo, p. 57, Universidad de Granada, Granada.


Received 12 November 2005; revised 21 November 2005; accepted 1 December 2005; published 14 December 2005.

Keywords: stresses in the mantle, geodynamics.

Index Terms: 8164 Tectonophysics: Stresses: crust and lithosphere; 8168 Tectonophysics: Stresses: general; 1236 Geodesy and Gravity: Rheology of the lithosphere and mantle.


RJES

Citation: Molodensky, S. M. (2005), On the estimation of elastic stresses in the mantle at the time moment of a large meteorite fall, Russ. J. Earth Sci., 7, ES6004, doi:10.2205/2005ES000193.

Copyright 2005 by the Russian Journal of Earth Sciences
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