Geologic Data and Seismic Hazard Analysis Illustrated Through Development of a Hazard Curve

Transcription

1 Geologic Data and Seismic Hazard Analysis Illustrated Through Development of a Hazard Curve What we are going to do: Go through the steps through which data describing active earthquake faults is incorporated into development of seismic hazard maps. We are going to go through it ignoring formal uncertainties to emphasize the logic and elements that go into it. The path we will take: The approach begins with a geologists map showing the distribution and location of active faults in the vicinity of a site where one wants to quantify the seismic hazard. The map we will use is shown in figure 1. Because the map is schematic and not quite to scale, each fault is annotated to show the geologists measure of a) the mapped length of the fault, b) the type of mechanism of the fault (normal, strike-slip, or reverse) c) and the shortest distance of the fault (km) to the site for which hazard is being computed, and the d) name of the fault (number of the fault in this case) You have been provided an Excel Table with column headers. Fill in the appropriate length for each fault in column C. Fill in the appropriate mechanism for each fault (SS=strike-slip, R=Reverse, N=Normal) in column B Geologists (or geodecists) provide information describing the faults slip rates in a region. The slip rate of each fault on the map is presented here: Fault Source Slip Rate (cm/yr)

2 Place the respective fault slip rate into column K of the accompanying Excel table. Additionally, assume the dip of normal faults, reverse faults, and strike-slip faults are 60, 30, and 90. Enter the appropriate value for each fault in column E. We ll assume that all earthquakes are large and break through the entirety of the seismogenic thickness (column E).. We ll assume a value of 20 km for our map area. Enter the value of 20 km for seismogenic thickness (column E). The actual width of each fault will depend on the dip of the fault and the seismogenic thickness. Write a formula using these values for each fault to compute the width of each fault and enter in Column G. We will later use the value of crustal rigidity µ. In principle, it is this value that controls the velocity of shear waves and given to us by seismologists. We will use the value of 3 x dyn-cm. Enter this for each fault in column H of the Excel Table. The next step entails estimating the size of an earthquake that can be produced by each fault. There are various ways to do this. Commonly it is done using observations (regressions) that show the average amount of slip that occurs during an earthquake is proportional to the length of the respective earthquake rupture. More specifically, we will use regressions of rupture length versus slip reported in Figure 7a of Wesnousky ( provided to each of you). The regressions show that the proportionality and form of the relationship between earthquake rupture length and coseismic offset (slip) differs for earthquakes of normal, thrust, and strike-slip mechanism. For this exercise, we will use the linear regressions in Figure 7a of Wesnousky (2008) for normal and reverse faults, and the Power Law curve for strike-slip earthquakes. In the Excel Table use the equations to predict the coseismic slip expected from the length of each fault (column C) and enter it for each fault in column D (labeled expected slip). The size of an earthquake may be measured in units of seismic moment Mo. The value of Mo = µ * L * W * D, where µ is the rigidity (column H), L the fault length (column C), W the fault width (column G), and D the average (expected) slip (column D). Write this formula in Excel and place the result in column I.

3 The magnitude of an earthquake is related to the seismic moment of an earthquake by the relationship LogMo = 1.5M Use this relationship and your estimate of seismic Mo in column I to estimate the magnitude expected for rupture of each fault. The rate of seismic moment release Modot is calculated in the exact same manner as seismic moment but instead the fault slip rate is entered in place of displacement D. Modot = µ * L * W * slip rate (column K). The moment rate is a measure or proxy of the average rate of strain accumulation along the fault. Enter the formula and calculate Modot for each fault and enter it in column L. At the heart of seismic hazard analysis are estimates of how often earthquakes occur on faults. We will keep things simple and assume each fault produces only one size earthquake proportional to its fault length. With that assumption, the time between the occurrence of earthquakes T may be calculated by dividing the value of Mo(exp) in column I by the value of seismic moment rate in column L. Calculate the repeat time T for each fault and enter into column M. Now, Take the inverse of T, which is the frequency of occurrence of earthquakes on the fault, and enter it into column N. At this stage, you have constructed your seismic source model. The next step is to determine the level of shaking (i.e. strong ground motion) that earthquakes on each fault can produce at the site of interest. By studying historical earthquakes, various investigators have been able to establish empirical relationships between the 3 variables: earthquake magnitude M, distance from site to earthquake source r, and measured levels of ground motion. We are going to use a regression from a paper by Joyner and Boore (1997). In this exercise, the measure of ground motion we will use is peak ground acceleration on rock. The pertinent equation and coefficients are shown here.

4 where Vs is the average shear wave velocity in the 30m below the site of interest. We will assume Vs = 5000 m/s, that which might be expected for a seismic station situated on granite. and where r = sqrt(d 2 + h 2 ), and the value d is the closest distance of the fault to the site of interest (and the coefficient h is a fictitious depth that arises in development of the regressions curve.. Use this equation with your estimate of Mw at each site (column J) to compute the level of peak ground motion that each fault can produce at the fault, and enter it into column P. Now for each fault you have the expected level of Peak Acceleration (column P) that it will produce at the site and the frequency at which it will occur (column N). Examination of column P should reveal that Predicted ground motions range from.05g to 1.2g. For each expected (or predicted) level of Peak Acceleration, it is important to recognize that all levels of ground motion up to and equal to the predicted level of ground motion will be exceeded at the time of an earthquake. With this information, you are now posed to compute the cumulative frequency that peak ground accelerations of 0.05g to 1.2g will occur at the site due to the repeated occurrence of earthquakes on all of the faults. Toward this end, you will see beginning in column Q in row 9 and continuing to column AF the labels of 0.05g to 1.2 g. Below each, list the expected frequency of each fault to exceed each level of acceleration. As an example, I have filled in the appropriate values for fault #14. Note that values.025 are placed in each column from.05g to 0.6g. This is because the earthquake that ruptures the length of fault #14 will produce accelerations exceeding these values with an annual frequency of.025. Follow this same approach for the remainder of the faults. In row 37 of column P I have annotated Sum of the frequencies=. To the right in row 37, now sum the frequencies of expected acceleration for each level of ground motion from earthquakes on all of the faults. I have listed the sum for >.05g that I obtained. You can use this to make sure you are on the right track. When all values are summed, you have computed the data needed to formulate a hazard curve. A hazard curve is a plot of the expected frequency of occurrence of ground motion (peak ground motion in this case) versus the value of strong ground motion. On log-log paper, construct such a plot with the values you have computed. You should note that the frequency of occurrence of small ground motions is greater than that predicted for large ground motions. With that plot, answer the following questions. 1. What is the peak value of strong ground acceleration that you expect to occur each 100 years? 1000 years?

5 What uncertainties have been ignored? Materials A map showing a site of interest within a distribution of active faults, each capable of producing large earthquakes (Figure 1)