Moment magnitude scale

The moment magnitude scale ( Mw) is one of the preferred magnitude scales that are used in seismology to determine the magnitude of earthquakes. Especially with heavy quake, the disclosure relates to a Erdbebenmagnitude today usually on this scale. The end of the scale is the value of 10.6 corresponding to the assumption that at this value the earth's crust would completely fall apart.

Development of the scale

The first magnitude scales which were developed for the quantitation of earthquakes based on the measurement of the maximum amplitudes of the seismic waves in seismograms. These amplitudes were placed in a linear relationship with the release of energy, increasing the strength of various earthquake was comparable. In particular, the well-known Richter scale, however, is valid only in a very limited distance range. Moreover, most magnitude scales of saturation at very strong earthquakes - that is, that the increase of the energy released in the upper range of the scale in less and less leads to an increase in the magnitude. A comparison of earthquake intensities is therefore no longer guaranteed.

To overcome this limitation, Hiroo Kanamori in 1977 led a new magnitude scale, which is based on the seismic moment introduced in 1966 by Aki Keiiti. This is the scalar product of the size of the fracture area in the ground, the average displacement of the stone blocks and the shear modulus of the rock. Since the seismic moment not entering saturation undergoes the torque magnitude as opposed to the other magnitude scales no saturation and is therefore suitable to quantify seismic with great energy release.

Method

The scalar seismic torque can = 0 Hz are determined from, for example, the asymptote of the displacement amplitude spectrum at frequency f. The torque magnitude is thereby connected to the surface wave magnitude scale (). After Gutenberg and Richter, the following relationship between the radiated seismic energy () and the magnitude:

It follows for the seismic moment in units of joules:

When this equation is solved for the magnitude and this is replaced by, the moment magnitude is measured as the dimensionless parameter, given by the expression

Is defined.

Although the seismic moment of the surface wave magnitude of this method is determined, which, like other scales reaches saturation, the seismic moment itself is not affected, since it is not derived from the maximum amplitude, but from the amplitude spectrum. For determining from the seismogram there are different inversion methods today. The calculated seismic moment depends on the details of the inversion method used, so that the resulting magnitude values ​​may differ slightly.

Magnitude value and comparability

Interskalarer comparison

At two quakes in their intensity (ie, the votes seismic energy) to compare, it should be noted that this is a logarithmic scale, the earthquake magnitude thus grows exponentially with the scale value. Thus, a quake of magnitude 4 is not twice as strong as a quake of magnitude 2 (see below). A similar difference between the two magnitude values ​​always means an equal ratio of the corresponding intensities ( the liberated in the earthquake energies):

Examples:

• 0.2 scale points correspond approximately to a doubling of energy
• 0.66 scale points correspond to a tenfold increase
• 1 point on the scale corresponds to a factor of 31.6
• 2 scale points correspond to a factor of 1000

Comparison with TNT equivalents

To make the meaning of the magnitude value plausible that radiated when the earthquake seismic energy is sometimes compared with the effect of conventional chemical explosive TNT. The seismic energy is obtained from the above formula by Gutenberg and Richter to

Or converted into Hiroshima bombs for large magnitudes:

For the comparison of the seismic energy (in Joules ), with the corresponding explosion energy, a value of 4.2 x 109 joules per metric ton of TNT applies. The table illustrates the relationship of the seismic energy and moment magnitude.

Comparability with other scales

The moment magnitude is only partly comparable with other magnitude scales, the same as is already evident from the different determination. The closest match of the torque magnitude scale (Mw) is the surface wave magnitude scale ( MS) which is 5 to 8, only small deviations in the range of about magnitude. 8 starts with a magnitude above the saturation which is reached at about 8.5. A good agreement has the torque magnitude with the Richter scale (ML ) in Magnitudenbereich below 6.5. However, it is not comparable with the ambient wave magnitude scale (MB), which is only match exactly with a magnitude of 7.0, and saturated at about 8.0, as well as with the short-period space wave magnitude ( MB), the only when the magnitude 5.0 is exactly the same and 6.8 reached its saturation already at about magnitude.