[Geology2] Prediction of large earthquake probability improved
Prediction of large earthquake probability improved
- Date:
- January 30, 2017
- Source:
- Universitat Autònoma de Barcelona
- Summary:
- Scientists have developed a mathematical law to explain the size distribution of earthquakes, even in the cases of large-scale earthquakes such as those which occurred in Sumatra (2004) and in Japan (2011).
As part of the "Research in Collaborative Mathematics" project run by the Obra Social "la Caixa," researchers of the Mathematics Research Centre (CRM) and the UAB have developed a mathematical law to explain the size distribution of earthquakes, even in the cases of large-scale earthquakes such as those which occurred in Sumatra (2004) and in Japan (2011).
The probability of an earthquake occurring exponentially decreases as its magnitude value increases. Fortunately, mild earthquakes are more probable than devastatingly large ones. This relation between probability and earthquake magnitude follows a mathematical curve called the Gutenberg-Richter law, and helps seismologists predict the probabilities of an earthquake of a specific magnitude occurring in some part of the planet.
The law however lacks the necessary tools to describe extreme situations. For example, although the probability of an earthquake being of the magnitude of 12 is zero, since technically this would imply the earth breaking in half, the mathematics of the Gutenberg-Richter law do not consider impossible a 14-magnitude earthquake.
"The limitations of the law are determined by the fact that the Earth is finite, and the law describes ideal systems, in a planet with an infinite surface," explains Isabel Serra, first author of the article, researcher at CRM and affiliate lecturer of the UAB Department of Mathematics.
To overcome these shortages, researchers studied a small modification in the Gutenberg-Richter law, a term which modified the curve precisely in the area in which probabilities were the smallest. "This modification has important practical effects when estimating the risks or evaluating possible economic losses. Preparing for a catastrophe where the losses could be, in the worst of the cases, very high in value, is not the same as not being able to calculate an estimated maximum value," clarifies co-author Álvaro Corral, researcher at the Mathematics Research Centre and the UAB Department of Mathematics.
Obtaining the mathematical curve which best fits the registered data on earthquakes is not an easy task when dealing with large tremors. From 1950 to 2003 there were only seven earthquakes measuring higher than 8.5 on the Richter scale and since 2004 there have only been six. Although we are now in a more active period following the Sumatra earthquake, there are very few cases and that makes it statistically a poorer period. Thus, the mathematical treatment of the problem becomes much more complex than when there is an abundance of data. For Corral, "this is where the role of mathematics is fundamental to complement the research of seismologists and guarantee the accuracy of the studies." According to the researcher, the approach currently used to analyse seismic risk is not fully correct and, in fact, there are many risk maps which are downright incorrect, "which is what happened with the Tohoku earthquake of 2011, where the area contained an under-dimensioned risk." "Our approach has corrected some things, but we are still far from being able to give correct results in specific regions," Corral continues.
The mathematical expression of the law at the seismic moment, proposed by Serra and Corral, meets all the conditions needed to determine both the probability of smaller earthquakes and of large ones, by adjusting itself to the most recent and extreme cases of Tohoku, in Japan (2011) and Sumatra, in Indonesia (2004); as well as to determine negligible probabilities for earthquakes of disproportionate magnitudes.
The derived Gutenberg-Richter law has also been used to begin to explore its applications in the financial world. Isabel Serra worked in this field before beginning to study earthquakes mathematically. "The risk assessment of a firm's economic losses is a subject insurance companies take very seriously, and the behaviour is similar: the probability of suffering losses decreases in accordance with the increase in volume of losses, according to a law that is similar to that of Gutenberg-Richter, but there are limit values which these laws do not take into consideration, since no matter how big the amount, the probability of losses of that amount never results in zero" Serra explains. "That makes the 'expected value of losses' enormous. To solve this, changes would have to be made to the law similar to those we introduced to the law on earthquakes."
Story Source:
Materials provided by Universitat Autònoma de Barcelona. Note: Content may be edited for style and length.
Journal Reference:
- Isabel Serra, Álvaro Corral. Deviation from power law of the global seismic moment distribution. Scientific Reports, 2017; 7: 40045 DOI: 10.1038/srep40045
Universitat Autònoma de Barcelona. "Prediction of large earthquake probability improved." ScienceDaily. ScienceDaily, 30 January 2017. <www.sciencedaily.com/releases/2017/01/170130100131.htm>.
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Posted by: Lin Kerns <linkerns@gmail.com>
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[californiadisasters] On This Date In California Weather History (January 31)
2002: Temperatures plummeted on 1.30 and on this day.
It was 13° F at Shelter Valley, 17° F at Campo, 22° F at Ramona and 28° F at Escondido.
Crops were damaged in northern San Diego County.
1999: Four funnel clouds were reported in the Valley: two north of Bakersfield, one near the Fresno Yosemite International Airport and another near Merced.
1995: Fresno recorded 0.01" of precipitation.
This marked the 21st day of the month to record measurable precipitation, a record for any month of the year.
1984: High of 82° F in Bakersfield, tied for warmest high ever in the month of January (also on January 16, 1932).
1979: A winter storm that started on 1.30 and ended on this day spread 2"-4" of rainfall in 24 hours over much of coastal Southern California, and 2" of snow in Palm Springs.
On this day snow fell heavily in Palm Springs and eight inches fell at Lancaster.
All major interstates into LA (I-5, I-15, and I-10) were closed.
Snow drifts shut down Interstate 10 on both sides of Palm Springs, isolating the city.
Schools were closed and hundreds of cars were abandoned.
A snow and rain mix was reported in Borrego Springs.
Mt. Laguna received two feet of snow and Julian one foot.
Winds up to 60 mph blew in the San Diego Mountains.
A tornado touched down in Santa Ana, and possibly occurred elsewhere.
Golf ball size hail and widespread snow were also reported during the storm.
4.82" of rain fell in National City, 4.25" in La Mesa, 3.30" at SDSU, and 3.78" in El Cajon.
Flooding occurred along Silver Strand highway, in Fashion Valley, also in Spring Valley, Lemon Grove, Lakeside and Carlsbad.
Lake Hodges overflowed.
Numerous power outages resulted.
2.57" of rain fell in San Diego on this day, the seventh wettest calendar day on record and the wettest January day.
56" of snow fell in Big Bear Lake from this day to 2.2, the greatest storm snowfall on record.
26" fell on this day, the greatest daily snowfall on record for January and the second greatest daily amount on record.
This snowfall also occurred on 2.17.1990.
It snowed 1.5" in Palm Springs, the second greatest daily snowfall on record.
The only other daily measurable snowfall on record was 2" (the greatest daily amount on record) on 1.11.1930.
1979: Significant snow fell in the Kern County desert from the 30th into the 31st.
Total accumulations from this event included 9" at China Lake NAS and Mojave with 8" at Randsburg and 4.5" at Inyokern.
1976: It was 83° F at Paso Robles setting a record high for the month.
1963: Big Sur received 9.23" of rain -- its greatest one day rainfall.
Source: NWS San Francisco/Monterey, Hanford, Reno, Las Vegas, & San Diego
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Posted by: Kim Noyes <kimnoyes@gmail.com>
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Monday, January 30, 2017
[californiadisasters] On This Date In California Weather History (January 30)
It was 13° F at Shelter Valley, 17° F at Campo, 22° F at Ramona and 28° F at Escondido.
Crops were damaged in northern San Diego County.
2000: Snowburst: 10" of snow fell at Lodgepole and 13" at Tuolumne Meadows in under 12 hours.
1998: High surf caused coastal damage (SoCal).
1993: A funnel cloud was observed over Mission Bay.
1985: Bakersfield had its' 21st day this month with dense fog, a record for January and tying December 1985 for the most days in any month.
1979: A winter storm that started on this day and ended on 1.31 spread two to four inches of rainfall in 24 hours over much of coastal Southern California, and two inches of snow in Palm Springs.
Golf ball size hail and widespread snow was also reported during the storm.
Flooding occurred along Silver Strand highway, in Fashion Valley, also in Spring Valley, Lemon Grove, Lakeside and Carlsbad.
Lake Hodges overflowed.
1976: High of 84° F at Ash Mountain (Tulare Co.).
1969: Fresno recorded 0.04" of rain, bringing the total to 8.56" for the month.
This made January 1969 the wettest month ever at Fresno. In all, 22 days recorded precipitation.
1968: 10.9" of snow fell at Reno, NV.
1963: Snow and rain continued to fall on Northern California.
A massive traffic jam clogged Highway 99 12 miles north of Redding when trucks and cars got stuck attempting to drive up a hilly stretch without chains.
24" of new snow covered the Mt. Shasta Ski Bowl; skiing conditions were excellent.
1962: Monterey reported a high temperature of 81° F.
1957: The high temperature of 32° F on this day in Victorville is the lowest high temperature on record.
This also occurred on 12.15.1957 and 12.11.1972.
1937: 14" of snow fell at Carson City, NV, with 10.1" of snow being reported at Reno, NV.
1916: Heavy rain that began on 1.25 and ended on this day exacerbated the flooding earlier in the month.
Monthly rainfall totals for 1.1916 ranged from 7.56" at San Diego to 57.91" at Dorman's Ranch (in the San Bernardino Mountains, 2,500 feet elev.).
5" fell in less than 12 hours in San Diego.
Extensive flooding occurred all over Southern California, the worst to date and it resulted in 28 total deaths in the region, 22 in San Diego County.
This is the most destructive and deadly weather event in San Diego County History.
The Lower Otay Dam broke sending a 40-foot wall of water downstream, killing 15.
A few others drowned in Mission Valley and in the San Luis Rey River.
The Sweetwater Dam also broke.
Every large bridge in San Diego County but one was seriously damaged or destroyed.
Four drowned in Orange County, two in a cottage floating down the Santa Ana River.
Two drowned in San Bernardino County.
Total damage was nearly $8 million (1916 dollars).
Source: NWS San Francisco/Monterey, Hanford, Reno, Las Vegas, & San Diego and the Redding Record-Searchlight
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Posted by: Kim Noyes <kimnoyes@gmail.com>
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Please join our Discussion Group at http://groups.yahoo.com/group/californiadisasters_discussion/ for topical but extended discussions started here or for less topical but nonetheless relevant messages.
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[californiadisasters] 2000 Alaska Air 261 Disaster, Tuesday, 31 January 2017
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