Seismic magnitude

SEISMIC IMPACT MAGNITUDE

INTRODUCTION

When an object hits the ground, the kinetic energy (ie the energy of motion) is changed into a number of different forms. Some goes into excavating a crater (for a hypervelocity impact), some goes into heat, light and sound, and some goes into seismic energy. The latter is in the form of sound waves that travel through the Earth and are registered on distant seismographs.

ENERGY AND SEISMIC MAGNITUDE

The kinetic energy of a body (in Joule) is given by

where m is the body mass in kg
and v is the velocity of the body in metres per second

Empirical research has shown that about 5% of this energy is converted into seismic energy.

The (approximate) relationship between seismic energy (E_s) and seismic magnitude (Richter scale) is

₁₀

where E_s = 0.05 K

CALCULATIONS

The tables below use the above formulae to calculate the volume, mass, kinetic energy, seismic energy and seismic magnitude of a impactor with the specified radius, density and velocity. The first table is for a stony body and the second for an iron body. Note that the kinetic energy is given both in Joule and in kilotons of TNT explosive equivalent.


Impactor density 3600 kg/m^3  velocity 20 km/sec

Radius  Volume     Mass    Kinetic Energy   Seismic-En  Mag
  [m]    [m^3]     [ton]   [Joule/kT TNT]    [Joule]
  1.0      4.2      15.1   3.0E+12     0.7   1.5E+11    4.3
  2.0     33.5     120.6   2.4E+13     5.7   1.2E+12    4.9
  5.0    523.6    1885.0   3.8E+14    89.8   1.9E+13    5.6
 10.0   4188.8   15079.6   3.0E+15   718.1   1.5E+14    6.3
 20.0  33510.3  120637.1   2.4E+16  5744.6   1.2E+15    6.9


Impactor density 8000 kg/m^3  velocity 20 km/sec

Radius  Volume     Mass    Kinetic Energy   Seismic-En  Mag
  [m]    [m^3]     [ton]   [Joule/kT TNT]    [Joule]
  1.0      4.2      33.5   6.7E+12     1.6   3.4E+11    4.5
  2.0     33.5     268.1   5.4E+13    12.8   2.7E+12    5.1
  5.0    523.6    4188.8   8.4E+14   199.5   4.2E+13    5.9
 10.0   4188.8   33510.3   6.7E+15  1595.7   3.4E+14    6.5
 20.0  33510.3  268082.3   5.4E+16 12765.8   2.7E+15    7.1

The graph below gives the seismic magnitude for impactors of two different velocities and two different densities:

ASA Australian Space Academy