U.S. Earthquake Frequency Estimation - Ratemaking for Unusual Events CAS Ratemaking Seminar Nashville, Tennessee March 11-12, 1999 Stuart B. Mathewson, FCAS, MAAA, M.EERI ICAT 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

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-Richter

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 Trench and date sand blows Dated large events at 900 and 1300 A.D.,(in addition to ) 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 ?

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

USGS Open-File Report – 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 ( )60% –San Jacinto ( )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

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

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 Enigma

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.