Pasta Quake

Separate 1 piece of spaghetti, 32 pieces of spaghetti, and 1000 pieces of spaghetti.

Hold up one piece of spaghetti. Bend it between your hands until it breaks. Notice the work it takes to break the spaghetti. Call this a 5 on the pasta magnitude scale.

Hold up a bundle of 32 pieces of spaghetti. Bend the bundle until it breaks. Notice the work it takes to break the bundle. If the pasta magnitude scale were like the earthquake magnitude scale, this would be a pasta magnitude 6 break.

Hold up 1,000 pieces of pasta (the remainder of the package). Bend the bundle until it breaks. Notice the work it takes to break the bundle. This is a pasta magnitude 7 break.

The currently used magnitude scale for the energy released in an earthquake is officially named the moment magnitude scale, written M_W. It is an exponential scale. An increase of one unit on the scale represents an increase in energy released by a factor of 32. An increase of two units represents an increase in energy release 1,000 times larger. This means that to dissipate the energy of one magnitude 7 earthquake, you would need to have 1,000 magnitude 5 earthquakes. An increase of 0.2 on the magnitude scale represents a doubling of energy released.

An earthquake with M_W = 6.0 releases 6.3 x 10¹³ joules (63 terajoules) of energy, about the energy of a small atomic bomb. The largest earthquake measured so far, the Great Chilean earthquake of 1960, had M_W = 9.5.

An older standard known as the Richter scale was also an exponential scale. Each increase of one unit on the Richter scale represented an order of magnitude (i.e., x10), increase in the amplitude of the motion of the ground. The moment magnitude scale has been adjusted to match the Richter scale for magnitudes under 8. For magnitudes above 8, the Richter scale becomes meaningless.

The increase of energy by a factor of 1,000 for a two-unit increase in magnitude is set by the exponential nature of the moment magnitude scale. According to this definition, an increase of one unit will release 31.6 times the energy, the square root of 1,000. Since adding one unit twice is the same as multiplying by the energy increase twice, 31.6² = 1,000.

Our understanding of the phenomenon explored in this Science Snack is built on the work of many scientists.

Dr. Sarah Jaye Oliva is a geophysicist who earned her PhD at Tulane University in Louisiana. She sees geophysics as a marriage of her two favorite fields: physics and the earth. Sarah studies seismology and modeling to understand earthquakes, volcanoes, and their related hazards. Growing up in the Philippines, Sarah experienced what it was like living on the Pacific Ring of Fire, which is known for its earthquakes and volcanoes. She studied physics and materials science as an undergraduate in the Philippines and came to the United States to pursue her graduate studies. Sarah is passionate about teaching and science communication, especially with regards to STEM outreach. The Science Snack Pasta Quake is one that Sarah uses in her own outreach work with K–12 audiences!

The equation for energy released, E, in terms of moment magnitude, M_W, is:

E = E₀ 31.6^M_W or also E = E₀ 10^(1.5*M_s)

Where E₀ is an energy constant = 6.3x10⁴ J, the energy of a magnitude 0 earthquake.

Note 10^1.5 = 31.6