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 Mw.  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

 

10001400
2000
2800
4000
5600
8000
11,000
16,000
22,000

 

 

 

Sylmar (LA) 1971
Northridge (LA) 1994

7.0
7.17.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9

 

32,000
45,00063,000
90,000
125,000180,000
250,000
355,000
500,000
710,000


Loma Prieta (SF) 1989

 


Pakistan 2005

8.0
8.18.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9

 

1,000,000
1,400,0002,000,000
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
9.29.3
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