Kelly Kiloton Index of Earthquake Moment Magnitudes

The Richter Earthquake Magnitude Scale, which was perfected by Charles Richter of Cal Tech in 1935, has always been misleading for people who are not used to thinking logarithmically. In this case, it's log-10: every whole position is 10 times greater than the one before. Therefore, if 4.0 is taken to be the equivalent of 10 units, 5.0 is 100.

But according to a new way of measuring earthquakes, based on the seismic "moment of force," translated to the equivalent energy released by an explosion of TNT, the Richter Scale is converted from a log-10 to a 2/3 log-10 scale. In this scale, every positional increase, e.g. Richter 4.0 to 5.0, goes up by a factor of 31.62, which we can round to 32. Thus, R 2.0 corresponds to the detonation of 1 ton of TNT, R 3.0 = 32t, R 4.0 = 1000t, R 5.0 = 32,000t, 6.0 = 1,000,000t, 7.0 = 32,000,000t, and so on. This "Moment Magnitude" is represented by M_w. The "w", introduced by Hiroo Kanamori in 1977, presumably stands for "work"; it refers to "elastic strain energy." The formula used here is: Tonnage = 10^(1.5R-3).

The Kelly Kiloton Index (KKI), formulated in 2006 by H. A. Kelly of UCLA, in consultation with Geoffrey Mess of the UCLA Math Department, aims at giving a "realistic" picture of earthquake energy. It uses the kiloton (= 1000 metric tons = 2,200,000 lbs) as the basic unit. Here is the KKI range for Richter 6.0 to 6.9 and for 7.0 to 7.9:

Richter	6.0	6.1	6.2	6.3	6.4	6.5	6.6	6.7	6.8	6.9
KKI	1000	1400	2000	2800	4000	5600	8000	11,000	16,000	22,000

Richter	7.0	7.1	7.2	7.3	7.4	7.5	7.6	7.7	7.8	7.9
KKI	32,000	45,000	63,000	90,000	125,000	180,000	250,000	355,000	500,000	710,000

The increase for every 2 positions, say, from R 6.0 to R 8.0, is not x 100, as it would be on a log-10 scale, but x 1000. So, since 6.0 is 1000, 8.0 is KKI 1000 x 1000 = 1,000,000. Similarly, 8.1 is KKI 1400 x 1000 = 1,400,000, and so on. See below for a complete table.

Here is how some past earthquakes register on the Richter Scale and the Kelly Kiloton Index:

Assisi 1997 Northridge (LA) aftershock 1994 Sylmar (LA) 1971 Northridge (LA) 1994 Loma Prieta Peak (SF) 1989 Pakistan 2005 San Francisco 1906 Sumatra 2004 Chile 1960

Richter 5.6 Richter 5.9 Richter 6.6 Richter 6.7 Richter 7.1 Richter 7.6 Richter 8.3 Richter 9.2 Richter 9.5

KKI 250 KKI 710 KKI 8000 KKI 11,000 KKI 45,000 KKI 250,000 KKI 2,800,000 KKI 63,000,000 KKI 180,000,000

So, the Loma Prieta Earthquake (from San Francisco to Santa Cruz) of 1989 was more than 5 times bigger than the Sylmar quake of 1971, and 4 times bigger than the Northridge quake of 1994. But the San Francisco quake of 1906, just over one position larger on the Richter scale, was 62 times bigger than Loma Prieta, and the recent Sumatra quake of 2004, just two Richter positions higher, had 1400 times the energy. It should be clear that small quakes do not do much in the way of defusing or diffusing the pent-up energy that the big ones have in store for us.

Complete Conversion Table

Richter Scale	Kelly Kiloton Index
2.0 2.5	.001 (1 ton) .0056 (5.6 tons)
3.0 3.5	.032 (32 tons) .180 (180 tons)
4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9	1 (1000 tons) 1.4 2 2.8 4 5.6 8 11 16 22
5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9	32 45 63 90 125 180 250 355 500 710	Assisi 1997 Northridge (LA) Aftershock 1994
6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9	1000 1400 2000 2800 4000 5600 8000 11,000 16,000 22,000	Sylmar (LA) 1971 Northridge (LA) 1994
7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9	32,000 45,000 63,000 90,000 125,000 180,000 250,000 355,000 500,000 710,000	Loma Prieta (SF) 1989 Pakistan 2005
8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9	1,000,000 1,400,000 2,000,000 2,800,000 4,000,000 5,600,000 8,000,000 11,000,000 16,000,000 22,000,000	San Francisco 1906
9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9	32,000,000 45,000,000 63,000,000 90,000,000 125,000,000 180,000,000 250,000,000 355,000,000 500,000,000 710,000,000	Sumatra 2004 Chile 1960
10.0	1,000,000,000