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# Earhquake Statistics

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### Earhquake Statistics

1. 1. Introduction to Seismology Introduction to Seismology-KFUPM Earthquake Statistics (pp. 371-396) Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM STUDENT PRESENTATION DAY Earthquake Seismology-May 9, 2007 Introduction to Seismology-KFUPM Magnitude Occurrence The Gutenberg and Richter (1944) cumulative frequency- magnitude law. The number of earthquakes in a region decreases exponentially with magnitude or:…………….. log10 Nc(m) = a - bm Charles F. Richter (source:Michigan Technological University) 4 log10 Nc 3 The magnitude of the quake 2 expected to be largest in a 1 year is:……………………… 4 5 6 7 8 m m1 = a/b [i.e. Nc = 1] Magnitude This is a whole process distribution, that means we use all the earthquakes in the data set or catalogue (not aftershocks)………………………………………… 1
2. 2. Introduction to Seismology-KFUPM Frequency-Magnitude Statistics Magnitude-Frequency Relationship Earthquake Earthquake Number 1918-2005 Magnitude Classification per year >8 Great 3 (N) 7.5 7-7.9 Major 20 Log (N 5.5 Log N = -1.0M + 8.4 Log 3.5 6-6.9 Strong 180 1.5 5-5.9 Moderate 1800 -0.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 4-4.9 Light 10000 Magnitude 3-3.9 Minor 90000 Source: Fowler, 2005 2-2.9 Very Minor 1000000 The b value is a coefficient describing the ratio of small to large earthquakes within a given area and time period. It is often shown to be the same over a wide range or magnitudes. It is the slope of the curve in the Gutenberg-Richter recurrence relationship (Source, Bullen and Bolt, 1987). … … … … … … … … … … . . N= Number of earthquakes M= Magnitude Worldwide b-value is are between 2/3 and 1 Introduction to Seismology-KFUPM Magnitude Versus Energy Comparison of frequency, magnitude, and energy released of earthquakes and other phenomena. The magnitude used here is moment magnitude, Mw (After Incorporated Research Institutions for Seismology)………………………………………………….. Introduction to Seismology-KFUPM Seismic Moment and Fault Length Seismic moment is a measure of earthquake size related to the leverage of the forces (couples) across the area of the fault slip. It is equal to the rigidity of the rock times the area of faulting times the amount of slip. The dimensions of seismic moment are dyne- cm (or Newton-meters). 2
3. 3. Introduction to Seismology-KFUPM Frequency-Seismic Moment Statistics Introduction to Seismology-KFUPM Frequency-Magnitude Statistics Introduction to Seismology-KFUPM Frequency-Magnitude Statistics 3
4. 4. Introduction to Seismology-KFUPM Time Variation of Seismic Moment Introduction to Seismology-KFUPM Variation in b value along the Fault Zones Calavaras Fault North Anatolian Fault Zone Oncel and Wyss, 2000 Introduction to Seismology Introduction to Seismology-KFUPM Illustration courtesy IRIS Consortium http://geology.about.com/library/bl/blquakestats.htm Earthquake Statistics (pp. 371-396) Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM 4
5. 5. Introduction to Seismology-KFUPM Previous Lecture Magnitude Occurrence The Gutenberg-Richter Law Beno Gutenberg Charles Richter Magnitude versus Energy Seismic Moment and Fault Length Frequency-Seismic Moment Statistics Frequency-Magnitude Statistics Spatial-variation of b-value along the Fault Zones Introduction to Seismology-KFUPM How to find the asperities by b-value? Calavaras Fault North Anatolian Fault Zone Oncel and Wyss, 2000 Source Characterization for Simulating Strong Ground Motion Source: Kojiro Irikura, AGU 2003 5
6. 6. 10000 Relation between Rupture Area (km^2) 1000 Rupture Area and M0 100 Outer Fault Parameters Somervill et al. (1999) What is Asperity? Kagoshima(3/26) Yamaguchi Iwate (Miyakoshi et al., 2000) 10 Kobe (Sekiguchi et al, 2000) Kocaeli (Sekiguchi and Iwata, 2000) How to find the asperities ? Chichi (Iwata and Sekiguchi, 2000) Tottori (Sekiguchi and Iwata, 2000) 1 1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28 Seismic Moment(dyne-cm) 10000 Somervill et al. (1999) Kagoshima(3/26) Yamaguchi Iwate (Miyakoshi et al., 2000) Combined Area of Asperities (km^2) Kobe (Sekiguchi et al, 2000) Kocaeli (Sekiguchi and Iwata, 2000) 1000 Chichi (Iwata and Sekiguchi, 2000) Relation between Tottori (Sekiguchi and Iwata, 2000) Combined Area of 100 Asperities and M0 10 Inner Fault Parameters 1 1.00E+24 1.00E+25 1.00E+26 1.00E+27 1.00E+28 Seimic Moment(dyne-cm) Somerville et al. (1999) and Miyakoshi et al. (2001) Source: Kojiro Irikura, AGU 2003 Repetition of Asperities Spatial Distribution of Moment Releases during 1968 Tokachi-oki Earthquake and 1994 Sanriku-oki Earthquake (Nagai et al., 2001) 1944 6
7. 7. What is Annual Mean? HOMEWORK Due to May 12: Make it under EXCEL and prove SOLUTION? Introduction to Seismology-KFUPM Difficulties Knopoff, 2000 Southern California (3) Log N (2) (1) Magnitude (1) Often observe non-linearity or roll-off at large magnitude………………………………………….. (2) Largest earthquake “catastrophe”…………………. (3) Often observe roll-off at lower magnitudes Why (1), (2) and (3)? Reasons? Introduction to Seismology-KFUPM Inadequate Sample Size Causing Deviation From a L in ea r Frequency- Magnitude Relation 7
8. 8. Introduction to Seismology Introduction to Seismology-KFUPM Illustration courtesy IRIS Consortium http://geology.about.com/library/bl/blquakestats.htm Earthquake Statistics (pp. 371-396) Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM Previous Lecture Asperity based Source Characterization Relation between Rupture Area and Seismic Moment Repetition of Asperities Frequency of Earthquakes in California: Firs Paper on Earthquake Statistics Roll-off pattern in Magnitude distribution: Possible Reasons Introduction to Seismology-KFUPM Incompleteness in Data Mc Threshold Magnitude, (3) which indicates data completeness Log N (2) (1) Magnitude (1) Often observe non-linearity or roll-off at large magnitude………………………………………….. (2) Largest earthquake “catastrophe”…………………. (3) Often observe roll-off at lower magnitudes Why (1), (2) and (3)? Reasons? 8
9. 9. Introduction to Seismology-KFUPM Earthquake Completeness Significance? What is Time- or Space Variation in Earthquake Completeness? Time-space analysis of e a r t h q u a k e completeness indicates the best value of Mc, which is 2.9, resulted analysed data of consecutive moving window……………… Oncel and Wilson, 2007 Introduction to Seismology-KFUPM Mainshocks for Turkey: 1900 and 1997 45 EURASIAN PLATE Long-term BLACK SEA B:Central Earthquake 42 A:Western NAFZ C:Eastern Completeness 39 ANATOLIAN AGEAN This method takes into SEA 36 account unequal completeness periods for different magnitude 33 AFRICAN PLATE ARABIAN PLATE ranges (Weichert, 23 28 33 38 43 48 Magnitude 1 9 8 0 ) … … … … Completeness Number of Earthquakes Range Period Western Central Eastern Zone Zone Zone 4.0 - 4.5 1/1976 - 12/1992 119 24 10 4.5 - 5.0 1/1965 - 12/1992 62 27 28 Oncel and 5.0 - 5.5 1/1950 - 12/1992 23 14 15 LaForge, 1998 5.5 - 6.0 1/1930 - 12/1992 11 10 6 6.0 - 6.5 1/1915 - 12/1992 9 5 1 6.5 - 7.0 1/1890 - 12/1992 6 6 1 7.0 - 7.5 1/1850 - 12/1992 8 4 2 7.5 - 8.0 1/1800 - 12/1992 1 1 0 Introduction to Seismology-KFUPM DESIRABLE PROPERTIES OF EARTHQUAKE CATALOGUES Homogeneity: if parameters are redetermined then uniform redetermination magnitudes determined uniformly or calibrated against each other intensity values on same scale all parameters to known accuracy, e.g. hypocentres Complete: ideally complete down to small magnitudes, but certainly of known completeness………………….. Duration: catalogue to cover a long time span, ideally greater than the largest return periods………………. Source material: known and referenced if there are multiple sources for some earthquakes and parameters are not uniformly re-determined then a stated hierarchy of preferences amongst sources…………………….. Computer readable: simple format…………………. 9
10. 10. Introduction to Seismology-KFUPM http://neic.usgs.gov/neis/epic/epic_rect.html Use rectangular coordinates of your term project and make a small program under EXCELL for tabulating earthquakes through the catalogue “Significant Worlwide Earthquakes” for different magnitude range “∆M=0.5” as done for North Anatolian Fault Zone. Add an explanation regarding longer-term of earthquake occurrence “4000 thousand years”? Finally, determine Magnitude-Frequency Relation?......................... Homework Due to May 19 Introduction to Seismology-KFUPM Source: Stein and Wysession, 2003 P is typically about 1. Introduction to Seismology-KFUPM EARTHQUAKE OCCURRENCE Simple Poisson process or random model: Assume that an earthquake or event in a given magnitude range and a given volume of the Earth’s crust is assumed to be found equally in any unit time interval, and it is independent of any other earthquake……………………….. n: number events in time t if λ: the mean rate of occurrence (λ t ) n P (n, λt) = e -λt n! Then, Poissonian probability : Probability Density 10
11. 11. Introduction to Seismology-KFUPM The distribution of time intervals T between quakes: P(T) = λ e-λT Assumptions are: i) Independent events N(t, t + ∆) independent of N (τ, τ + ∆τ) ii) Orderly events (probability Lim P {[N (t, t + ∆t)] > 1} = 0 of simultaneous events is ∆t → 0 zero) iii) Stationarity (the mean rate The probability of a quake is identical for λ is not a function of time) any interval along the time axis Introduction to Seismology Introduction to Seismology-KFUPM Source: Fenton, Adams and Halchuk, 2006 Earthquake Statistics: Example from regions of low seismic areas Ali Oncel oncel@kfupm.edu.sa Department of Earth Sciences KFUPM Introduction to Seismology-KFUPM Previous Lecture Earthquake Completeness: Threshold Magnitude (Mc) Spatial-Temporal detection of Mc for Modern Catalogue (1992-1999): Example from North Anatolian Fault Zone Long-term detection of Mc: Example from NAFZ based on approach of unequal observation periods for different magnitudes Earthquake Catalogues: Desirable Properties 11
12. 12. Recall: MAGNITUDE OCCURRENCE Introduction to Seismology-KFUPM The Gutenberg and Richter (1944) cumulative frequency- magnitude law. The number of earthquakes in a region decreases exponentially with magnitude or:…………………. log10 Nc(m>M) = a - bm b=βx log e log e=0.4343 4 The magnitude of the quake log10 Nc 3 expected to be largest in a 2 year is:……………………….. 1 m1 = a/b [i.e. Nc = 1] 4 5 6 7 8 m Magnitude This is a whole process distribution, that means we use all the earthquakes in the data set or catalogue (not aftershocks)…………………………………………………. Seismicity of Stable Cratonic Cores (SCC) Greenland Siberia Arabia N. America India Africa S. America Australia Antarctica Modified after Fenton, Adams, Halchuk, 2006 Introduction to Seismology-KFUPM Earthquake catalogue completeness 12
13. 13. Introduction to Seismology-KFUPM Magnitude-Frequency (per 50.7 x 106 km2) plot for the worldwide SCC seismicity data set Introduction to Seismology-KFUPM Stable Craton Once a decade a M6.5 log10 Nc(m) = 3.68 – 0.947 m Introduction to Seismology-KFUPM Worldwide rates of stable cratonic core seismicity 13
14. 14. Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM Introduction to Seismology-KFUPM 14
15. 15. west east stable Plattsburgh 2002 NY Introduction to Seismology-KFUPM Seismicity of east Saudi Arabia west stable Source: Al-Amri., 2005 15
16. 16. Rupture on a Introduction to Seismology-KFUPM Fault Total Slip in the M7.3 Landers Earthquake Introduction to Seismology-KFUPM Slip on an earthquake fault START Surface of the earth Depth Into the earth 100 km (60 miles) Distance along the fault plane Introduction to Seismology-KFUPM Slip on an earthquake fault Second 2.0 16
17. 17. Introduction to Seismology-KFUPM Slip on an earthquake fault Second 4.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 6.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 8.0 17
18. 18. Introduction to Seismology-KFUPM Slip on an earthquake fault Second 10.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 12.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 14.0 18
19. 19. Introduction to Seismology-KFUPM Slip on an earthquake fault Second 16.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 18.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 20.0 19
20. 20. Introduction to Seismology-KFUPM Slip on an earthquake fault Second 22.0 Introduction to Seismology-KFUPM Slip on an earthquake fault Second 24.0 Introduction to Seismology-KFUPM Bigger Faults Make Bigger Earthquakes 1000 100 Kilometers 10 1 5.5 6 6.5 7 7.5 8 Magnitude 20
21. 21. Introduction to Seismology-KFUPM Bigger Earthquakes Last a Longer Time 100 Seconds 10 1 5.5 6 6.5 7 7.5 8 Magnitude 21