Earhquake Statistics


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Earhquake Statistics

  1. 1. Department of Earth Sciences KFUPM Introduction to Seismology Earthquake Statistics (pp. 371-396) Introduction to Seismology-KFUPM Ali Oncel [email_address]
  2. 2. Term-Paper Status Deadline: May 3 First Draft: Through the e-mail Introduction to Seismology-KFUPM
  3. 3. You have learned how to pinpoint the location of an earthquake by measuring the speed of seismic waves radiating away from the focus of the earthquake . Now, we can determine an earthquake's magnitude by measuring the strength of ground shaking as you did for global earthquakes . Learn how to do both these things by visiting the virtual earthquake web page. http://www.sciencecourseware.org/VirtualEarthquake/VQuakeExecute.html and completing the exercise . It should take you about 30 minutes . Turn in your certificate of completion at the beginning of class on Monday, 26 March. Homework: VIRTUAL SEISMOLOGY Introduction to Seismology-KFUPM
  4. 4. Recall: Homework due March, 28 <ul><li>Through the Interactive Data Module which is explained so far </li></ul><ul><li>http://atlas.geo.cornell.edu/ima.html </li></ul><ul><li>Prepare the focal mechanism map of the area for your term project as file *.jpg, send it to me via e-mail due next lecture. Also, try to provide a discussion about one paragraph on types of the faulting deformation through the region. </li></ul>Introduction to Seismology-KFUPM
  5. 5. Previous Lecture <ul><li>Interactive Mapping Tool of Cornell University </li></ul><ul><li>Interactive Mapping and Data Analysis </li></ul><ul><li>Learn how to select Regional data of focal mechanism </li></ul><ul><li>What is CMT? </li></ul><ul><li>global Seismotectonic zones and their relation to earthquake depths </li></ul><ul><li>seismicity patterns through the Continental Margins </li></ul><ul><li>Seismicity through the plates of convergent and divergent </li></ul><ul><li>Example: Mid-Ocean Ridge System  and Transform Plate Boundary </li></ul><ul><li>Seismicity through the Trunscurrent Fault </li></ul><ul><li>Seismicity through the Transform fault </li></ul><ul><li>Recommended Site for Fault Plane Solutions </li></ul>Introduction to Seismology-KFUPM
  6. 6. MAGNITUDE OCCURRENCE <ul><li>The Gutenberg and Richter (1944) cumulative frequency-magnitude law. The number of earthquakes in a region decreases exponentially with magnitude or : </li></ul>log 10 N c (m) = a - bm <ul><li>This is a whole process distribution , that means we use all the earthquakes in the data set or catalogue ( not aftershocks) </li></ul><ul><li>The magnitude of the quake expected to be largest in a year is : </li></ul>m 1 = a/b [i.e. N c = 1] Introduction to Seismology-KFUPM
  7. 7. Difficulties in practise <ul><li>Often observe non-linearity or roll-off at large </li></ul><ul><li>magnitude. </li></ul><ul><li>(2) Largest earthquake “catastrophe”. </li></ul><ul><li>(3) Often observe roll-off at lower magnitudes. </li></ul><ul><li>Why (1), (2) and (3)? Reasons? </li></ul>Introduction to Seismology-KFUPM
  8. 8. EARTHQUAKE OCCURRENCE <ul><li>Simple Poisson process or random model: </li></ul><ul><li>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. </li></ul>P (n,  t) = e -  t Probability Density n: number events in time t if  : the mean rate of occurrence Then, Poissonian probability : Introduction to Seismology-KFUPM
  9. 9. P(T) =  e -  T <ul><li>or the distribution of time intervals T between quakes: </li></ul><ul><li>Assumptions are: </li></ul>Introduction to Seismology-KFUPM The probability of a quake is identical for any interval along the time axis Stationarity (the mean rate  is not a function of time) iii) L im P {[N (t, t +  t)] > 1} = 0  t  0 Orderly events (probability of simultaneous events is zero) ii) N(t, t +  ) independent of N (  ,  +  ) Independent events i)
  10. 10. IMPLICATIONS ARE: <ul><li>The interval T may be measured starting anywhere. An interval T of 10 years from the last quake is exactly as likely as an interval of 10 years from now (independence + stationarity). </li></ul><ul><li>However, not all intervals T are equally likely. </li></ul> short intervals more likely than long ones. Events appear to cluster - pseudo-clustering. Earthquakes are not uniformly spaced in time.  corollary : uniformly spaced earthquakes in time implies a highly organised, non-random controlling process. [consider the traffic analogy] [consider apparent changes in seismicity] Introduction to Seismology-KFUPM
  11. 11. 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 Introduction to Seismology-KFUPM
  12. 12. COMPLETENESS Depends on data availability. The usual and obvious bias is against small shocks in the earlier years. During the instrumental era it is a function of network density and detection threshold. In the pre-instrumental era (historical) it is a function of population density, culture and survival rate of documents. Introduction to Seismology-KFUPM