1 What is Richter magnitude? How does magnitude relate to the energy released by an earthquake? How can we compare the sizes of earthquakes? Earthquake Magnitude SSAC2005.QE531.LRW1.1 Prepared for SSAC by Laura Wetzel – Eckerd College, St. Petersburg, Florida © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved Core Quantitative Issues Orders of magnitude and logarithmic scales Supporting Quantitative Issues Scientific notation Ratios Logarithms Algebra: Rearranging equations Graphs, linear Graphs, semilogarithmic Peer-Reviewed

2 When rocks shift suddenly along a fault, they generate waves. These waves shake the ground, producing earthquakes. Seismographs record the wave amplitudes, which are used to calculate the earthquake magnitude and the energy released by the rupture. This presentation asks you to create spreadsheets and graphs to explore earthquake magnitude, wave amplitude, and energy release. Slides 3-4 briefly describe intensity and magnitude scales. Slides 5-7 ask you to create spreadsheets to calculate seismogram amplitudes corresponding to a variety of magnitudes. Slides 8-9 illustrate and further explain the concept of earthquake magnitude. Slides ask you to create more spreadsheets, this time to compare the energy released by earthquakes of various magnitudes. Slides ask you to create linear and logarithmic graphs to visualize how amplitude and energy increase with magnitude. Slides give the assignment to hand in. Preview

3 In 1935 Charles Richter developed a method to compare the sizes of California earthquakes based on waves recorded by seismographs. In his method, a single magnitude is assigned based on maximum wave amplitudes. (End note 1)End note 1 The intensity of shaking is one way to assess the size of an earthquake. A value is assigned based on damage reports and personal interviews of people who experienced the quake. The intensity depends on location; in general, the closer the observer to the earthquake, the higher the intensity. Intensity values assist in seismic hazard and historical earthquake analysis. Modern seismologists have modified his method and now analyze a large section of the waves recorded on a seismograph to calculate a seismic moment. The seismic moment is then converted to moment magnitude, which is the standard size reported by the U.S. Geological Survey. Source: neic.usgs.gov/neis/seismology/people/ neic.usgs.gov/neis/seismology/people/ Measuring Earthquake Size

4 This is a seismogram of the magnitude-9.1 Sumatra-Andaman Islands earthquake that occurred on December 26, The recording seismograph is located on the Cocos Islands in the Indian Ocean. To see more seismograms like this one, go to the Incorporated Research Institutions for Seismology website ( A seismogram is a graph of wave amplitude vs. time. In old seismographs, a pen drew the recording on a piece of paper. In new seismographs, the signal is recorded digitally. Seismograms

5 One way for us to explore earthquake magnitudes is to use a spreadsheet. Recreate this spreadsheet. We will consider earthquake magnitudes ranging from -1 to 9. Magnitudes above 2.5 can be felt by people. The magnitude scale is based on seismogram amplitudes; it is not a scale from 1 to 10. Earthquake Magnitude So far, the 1960 Chilean earthquake, with a magnitude of 9.5, is the largest earthquake seismically recorded. Given the properties of rocks, ~9.5 is probably the maximum possible magnitude.

6 How are earthquake magnitude and seismogram amplitude related? We will use scientific notation for seismogram amplitudes. The quantity that is normally expressed as 1 × is written as 1.E-07 in Excel. Recreate this spreadsheet. Each step in the magnitude scale represents a 10-fold increase in wave amplitude. This means the scale is logarithmic. Understanding Magnitude = Cell with an equation in it. = Cell with a number in it.

7 How large is the amplitude of a magnitude-8 earthquake compared to the amplitude of smaller events? A M8 earthquake produces waves 1000 times the size of those of a M5 earthquake. (Three steps in magnitude correspond to a fold increase in amplitude.) (End note 2)End note 2 Add three columns to your spreadsheet to calculate amplitude ratios. Understanding Magnitude

8 How does the amplitude of a magnitude-8 earthquake compare to the amplitude of smaller events? If we likened earthquakes to hills and mountain peaks, each peak is 10 times the height of the previous one. Mag. 8 = 10× larger than Mag. 7 = 100× larger than Mag. 6 Mag. 7 = 10× larger than Mag 6 Mag. 6 Understanding Magnitude

9 This is like comparing the elevation of Mt. Everest to the relief of a 300-ft hill! Understanding Magnitude How does the amplitude of a magnitude-8 earthquake compare to the amplitude of a magnitude-6 event? If we likened earthquakes to hills and mountain peaks...

10 Create this spreadsheet to determine the seismic moment for a range of magnitudes. How is magnitude related to energy? One advantage of moment magnitude (M W ) is its direct relationship to the amount of energy released during an earthquake. The energy released is related to the seismic moment (M o ) and is expressed in dyne-cm. Rearrange this equation to solve for M o. Understanding Magnitude

11 How is magnitude related to energy? E = M o. 2 × 10 4 The radiated energy (E) is related to the seismic moment (M o ) and is also expressed in dyne-cm. The following equation is a good approximation for the relationship between radiated energy and seismic moment. Add one column to your spreadsheet to calculate radiated energy.

12 How large is a magnitude-8 earthquake compared to smaller events in terms of radiated energy? A M8 earthquake radiates ~32,000 times the energy of a M5 earthquake. This means that ~32,000 M5 earthquakes must occur to produce the energy radiated in one M8 earthquake. (End note 3)End note 3 Add three columns to your spreadsheet to calculate energy ratios. Working with Magnitude

13 How large is a magnitude-8 earthquake compared to smaller events? To plot seismogram amplitude and energy on the same graph, multiply all amplitudes by 1 × Combine your magnitude, amplitude, and energy columns into one spreadsheet for magnitudes 5 through 9. Working with Magnitude Note: At the end of this module, you will be asked to hand in copies of this spreadsheet and the three graphs that you will create on the following slides.

14 How large is a magnitude-8 earthquake compared to other events? Create two graphs showing amplitude vs. magnitude. Draw one with a linear and one with a logarithmic scale. Add trendlines. Hint: After creating the linear scatter graph, click on the Y-axis. Select Scale and click the box on the bottom labeled Logarithmic scale. Working with Magnitude Linear Scale Logarithmic Scale

15 How large is a magnitude-8 earthquake compared to other events? Create a graph showing both amplitude and energy vs. magnitude. Note that energy increases at a much faster rate than amplitude. Working with Magnitude

16 Hand in copies of the master spreadsheet in Slide 13 and the three graphs you created in Slides Thus far, you have explored general relationships between earthquakes. Next, apply your knowledge to some real events. Hand in answers to the following questions, including copies of all new spreadsheets and graphs. 1.Create a spreadsheet to calculate the seismic moments for these earthquakes. 2.Create linear and logarithmic scatter graphs illustrating magnitude on the X-axis and seismic moment on the Y-axis for these earthquakes. End of Module Assignments

17 3. Compare the moments of the Loma Prieta, San Francisco, and Sumatra earthquakes. a. _______ Loma Prieta earthquakes = 1 San Francisco earthquake b. _______ Loma Prieta earthquakes = 1 Sumatra earthquake c. _______ San Francisco earthquakes = 1 Sumatra earthquake End of Module Assignments

18 4. Create a scatter graph with magnitude on the X-axis and fatalities on the Y-axis. 5. Create another scatter graph of magnitude vs. fatalities, but omit the Sumatra earthquake. (To do this, you can copy your original graph and reset the Y-axis maximum to ) 6. Briefly describe two reasons why earthquake magnitude and the number of fatalities are not directly correlated. For example, the Alaskan earthquake has a high magnitude, but relatively few fatalities. Details of Interest: The 2004 Sumatra earthquake produced a devastating tsunami. A fire caused by the 1906 San Francisco earthquake destroyed most of the city. The 1989 Loma Prieta earthquake rattled the San Francisco Bay area during the World Series. The 1964 Alaska earthquake struck Anchorage on Good Friday. For more information, see End note 4.End note 4 End of Module Assignments

19 End notes 1.For more information on earthquake magnitude, visit the following US Geological Survey website: Return to Slide 3. to Slide 3. 2.The wave amplitude and magnitude relationships are actually more complicated than discussed thus far. Earthquakes produce a group of waves with many periods. Waves with short periods of ~1 second are the fastest and are the first to arrive at a seismic station. These waves reach a maximum amplitude at a magnitude of ~6. Waves with longer periods of ~20 seconds reach maximum amplitudes at a magnitude of ~8.2. This is why seismologists compute the seismic moment by using long sections of seismograms, which capture very long period waves. These very long period waves have higher amplitudes even at the highest magnitudes. Seismologists first calculate the seismic moment, which, in turn, is used to calculate the moment magnitude. Return to Slide 7.Return to Slide 7 3.How large is an 8.7-magnitude earthquake compared to a 5.8-magnitude earthquake? See the US Geological Survey website: Return to Slide to Slide 12 4.For more information on these and other earthquakes, consult the US Geological Survey file Preferred Magnitudes of Select Significant Earthquakes. Return to Slide 18. Preferred Magnitudes of Select Significant EarthquakesReturn to Slide 18