U.S. Earthquake Frequency Estimation - Ratemaking for

Unusual Events

CAS Ratemaking SeminarNashville, Tennessee

March 11-12, 1999

Stuart B. Mathewson, FCAS, MAAA, M.EERIICAT Managers

Introduction

• Tough to price high severity, low frequency coverage

• Often priced without actuarial involvement

• Catastrophe portion of property coverage an obvious example

• Property actuaries now have tough problems

Introduction

• New methods to analyze catastrophes allow for much better rate making

• The frequency estimates are key• Among major perils, earthquake frequency is

most problematic• This is a brief survey of methods, sources

and current issues in seismic frequency

One Look at the Problem

Another Look at the Problem

Experts

• Seismologists and Geologists– Seismological Society of America (SSA)– U. S. Geological Survey (USGS)– Cal. Div. Of Mines & Geology (CDMG) – Southern California Earthquake Center (SCEC)– Earthquake Engineering Research Institute

(EERI)– Others for Central U.S., Pacific NW, etc.

Seismologists’ Methods

Seismologists’ Methods

• Slip Rate Analysis– Plate Tectonics

• For seismicity at plate boundaries• Scientists can measure the rate at which one

plate moves in relation to another

Plate Tectonics

Seismologists’ Methods

• Slip Rate Analysis– Measure overall slip– Amount of slip correlated to amount of

energy released - measured by Magnitude– Observe displacement in historical event– Calculate return time for that event

Seismologists’ Methods

• Slip Rate Analysis– Simple example

• San Andreas Fault moves about 2 inches per year

• 1906 San Francisco earthquake had maximum displacement of about 20 feet

• This gives a return time of 120 years

Seismologists’ Methods

• Slip Rate Analysis– Real world much more complicated

• Faults are not simple lines at the plate boundary• For instance, Southern California has a complex

system of faults• Even Northern California is not simple• Scientists actually apportion the amount of

accumulated slip

California Faults

Seismologists’ Methods

• Slip Rate Analysis– Works well where plate tectonics gives a

measure of slip– Other approaches necessary elsewhere, or

as supplement to slip rate

Seismologists’ Methods

• Gutenberg-Richter Relationship– Log relationship between magnitude and

frequency– log N = a - b*M– Fitted to actual experience– Used to project large events beyond

historical record

Gutenberg-RichterGutenberg-Richter Relationship

0.000

0.001

0.010

0.100

1.000

6.0 6.5 7.0 7.5 8.0 8.5

Mw

Rat

e

Observed GR, Mx=8.12

Seismologists’ Methods

• Paleoseismic research– Washington-Oregon

• Oregon - Study of buried soils beneath marshes to show evidence of subsistence

– 16 disturbance events over 7,500 years– Return times of nearly 500 years, if all

disturbances caused by earthquakes

Seismologists’ Methods

• Paleoseismic research– Washington-Oregon

• Washington - Study of buried soils beneath marshes to show evidence of subsistence

– one very large shallow earthquake about 1,000 years ago on fault through Seattle

Juan de Fuca Plate

Seismologists’ Methods

• Paleoseismic research– Washington-Oregon

• Pacific Northwest has potential for a great subduction earthquake

• Great Subduction Earthquake of January 27, 1700

• Japanese tsunami records and local traditional stories

Seismologists’ Methods

• Paleoseismic research– New Madrid

• Great earthquakes of 1811-12• Trench and date sand blows• Dated large events at 900 and 1300 A.D.,(in

addition to 1811-12) with two others possible in last 2,000 years

• Magnitudes of events not known, but large enough to cause sand blows ( > 7.5 ? )

Seismologists’ Methods

• Paleoseismic research– New Madrid

• This implies a return time of 500 for large events - maybe 7.5

• Some were larger than others - scientists’ estimates of 400-1,100 year for 8.0+

• An additonal event between 1400-1600?

Seismologists’ Methods

• Paleoseismic research– Southern California

• Trenching– Landers EQ (7.3) - Multiple faults, some not

broken for over 10,000 years– San Andreas fault - one site showed 10 events

over 2,000 years, but they show clustering

Sources

Sources

• USGS Open-File Report 88-398– 1988 study of probabilities on major faults

in Northern and Southern California• Probabilities of certain events in next 30 years

– Bay area ( 7.0 ) 50%– So. San Andreas ( 7.5 - 8.0 ) 60%– San Jacinto ( 6.5 - 7.0 ) 50%

Sources

• USGS Circular 1053– 1990 study updating probabilities on major

faults in Northern California• Bay Area ( > 7 ) 67%

– Hayward North 20% => 28%– Hayward South 20% => 23%– Peninsula S. A. 20% => 23%– Add Rogers Creek => 22%

Sources

• SCEC paper “Seismic Hazards in Southern California: Probable Earthquakes, 1994 to 2024”– Updated study on Southern California

Earthquakes• Southern California ( > 7 ) 80-90%

New Hazard Maps

• Series of maps covering the U.S. (USGS) and California (USCG/CDMG) showing probabilistic maps of peak accelerations– Various return times – Shown as exceedance probabilities– Examples -- Peak ground accelerations with

10% probability of exceedance in 50 years

Non-California Sources

• For other areas including Central US, Pacific Northwest, South Carolina, Salt Lake City, etc.

• Sources listed earlier, plus local universities and state geologists

Ratemaking Issues

• Loss Costs are very sensitive to model frequencies

• Eg., sensitivity to New Madrid 8.0+ assumption

Current Thoughts

Current Thoughts

• Gutenberg-Richter vs. Characteristic Earthquake– Seismologists disagree on this– Gutenberg-Richter seems to apply for a

region, maybe not a single fault– But, how big a region?

Current Thoughts

• Simplistic example – Characteristic earthquake = 7.0– GR ranges 6.0 to 7.5

Mag Freq Loss6.0 0.08 106.5 0.04 307.0 0.02 1007.5 0.01 300

Total 0.15 7

Current Thoughts

• “The Paradox of the Expected Time until the Next Earthquake,” by Sornette and Knopoff– Paper in SSA Bulletin challenges

conventional wisdom– The chances of a quake in an area may

not increase with time since the last one– Clusters

Current Thoughts

• The Enigma in the SCEC report - D.D.Jackson at EERI, 1998 (and earlier)– The SCEC estimates give much higher

estimates of probability than the historical record (150 yrs ) suggest -- by a factor of 2

The EnigmaSouthern California 1850-1996

0.000

0.001

0.010

0.100

1.000

6.0 6.5 7.0 7.5 8.0 8.5

Mw

Rat

e

Observed GR, Mx=8.12

Phase 2

Current Thoughts

• The Enigma in the SCEC report - D.D.Jackson at EERI, 1998 (and earlier)– Why?

• Non-earthquake creep - latest research => No• Lucky? - Maybe, but not too likely• Or …….

The Solution to the Enigma?

Current Thoughts

• The Enigma in the SCEC report - D.D.Jackson at EERI, 1998 (and earlier)– Jackson suggests that earthquakes larger

than the Ft. Tejon earthquake of 1857 are possible and necessary to use up the strain

– Perhaps an 8.6 earthquake is possible every 1000 years (Richter)

Current Thoughts

• The Enigma in the SCEC report - D.D.Jackson at EERI, 1998 (and earlier)– Good news? Maybe– If there is one huge event, we would then

project significantly fewer 6’s and 7’s

Current Thoughts

• 1998 SSA Meeting– Researchers disputed ‘great earthquake’

theory– Historical record may be skewed

Conclusion

• Earthquake frequency is key to model-driven rates, but carries much uncertainty

• Scientific community has done much to help

• Scientists are still not in agreement

Conclusion

• Work will continue to progress, and estimates will change

• We, as ratemakers, must understand assumptions in models … and the sensitivities.