Lab_9_Earthquakes_2023

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ Lab 9: Earthquakes Purpose of the lab: ● Look at real seismic data and use it to locate an earthquake ● Learn how earthquake magnitude is calculated, and what controls strength of shaking ● Learn about earthquake frequency-magnitude relationships PART 1: Seismic data - staring at the wiggles Since the 1970s, seismologists have been installing high quality digital seismometers throughout the world; these instruments are now so sensitive we can detect magnitude ~3.5 earthquakes anywhere on the planet. The data come in the form of seismograms (a.k.a. wiggles), that record the ground motion at the location of the station as the ground moves up and down. The instruments are sensitive enough to detect vibrations much smaller than the width of a human hair (~75 microns, FYI). The earthquake signals travel through the Earth as waves, with magnitudes and frequencies that can tell us a great deal about the earthquake itself, as well as the Earth’s interior, through which they have travelled. A. Consider the seismogram below, which shows the vertical displacement recorded at a station in Taiwan from an earthquake in Papua New Guinea on May 14 th 2019. A full hour’s record (3600s) is shown at the top, and the insert shows a zoom-in on the highest amplitude part of the signal. i) Label on the zoomed-in record the following features of the wave: crest , trough , one period [3] ii) What is the period of the largest signals? (Hint: measure the time spanned by a few full oscillations and divide this time by the number of waves you measured across for a slightly more precise estimate.) ________________ seconds [1] iii) What is the frequency , , of these signals? Frequency is the inverse of period (1/period). ? ________________ Hz [1] iv) Calculate the wavelength , , of the wave as it travels over the ground, using the equation: λ where is the speed of the wave, which is about 4000 m/s λ = ?/? ? _________________ m [1] v) What is the maximum amplitude , , of these signals? 𝐴 Note: take the largest absolute amplitude, positive or negative - measure the distance from zero to the highest or lowest peak. ________________ microns [1] The amplitude of the waves is related to the magnitude of the earthquake. Stronger earthquakes shake the ground more (obviously) and make higher amplitude signals on the instrument. B. Estimate the magnitude , , of the earthquake using the following equation: 𝑀 𝑆 = 𝑀 𝑆 𝑙𝑜?10 0. 6 × ? × 𝐴 × 𝐷 5/3 ( ) Where A is the amplitude you already measured (in units of microns), f is the frequency, and D is the distance between the earthquake and receiver (see plot), in km. Please show your work. Magnitude, M S = ________________ [3] 1

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ C. Magnitude is measured on a logarithmic scale. To illustrate how this works, repeat the calculation you did above, but now pretend the amplitude you measured was actually 10x larger . What would the new magnitude be? Magnitude for 10x larger waves, M S = ________________ [2] What would the amplitude have been if the earthquake had been 1.0 magnitude units weaker than the true amplitude ? Wave amplitude for 1.0 unit weaker earthquake: ________________ microns [2] D. If this station cannot detect amplitudes smaller than 3 microns, what is the smallest magnitude earthquake it is capable of detecting at a distance of 4650 km? (Assume the frequency doesn’t change.) Smallest magnitude detectable at this distance: ________________ [3] 2

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ Modern seismic sensors measure motion of the ground in three dimensions, allowing us to pick apart these different wave arrivals on the basis of the arrival time and direction of ground shaking. G. The figure below shows a record of ground motion in three perpendicular directions (Z,R,T – see above), defined with respect to the seismic energy arrival direction. Use the information in the table to mark on the top of the figure each of the different wave arrivals –i.e., name the waves. [4] H. How long after the first wave arrival does the most energetic shaking start? ________________ seconds [1] This time difference is the principle behind earthquake early warning. The earliest-arriving waves are not very damaging but alert you to the occurrence of the earthquake and give you precious seconds to prepare for the later-arriving waves that shake the ground substantially. 4

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ PART 2: Locating an earthquake Seismologists use the arrival times (just like the ones that you measured above) to locate earthquakes. The arrival time allows us to work out how far away the earthquake is. By measuring these signals on several stations, we can triangulate the distances to locate the earthquake source. A. The figure below shows 200 seconds of seismic data recorded in early 2003 at four stations in the western US. Mark the arrival times of the first arriving wave (the first non-zero pulse of energy) at each of the stations. Report the arrival times here: [4] PFO: _____________ s WDC: _____________ s WUAZ: _____________ s COR: _____________ s B. What is the name of this first-arriving wave? (Note that since these signals are recorded much closer to the earthquake than the three-component seismogram above, all the waves look a lot stronger on this figure – and actually go way off scale!) _____________________ wave [1] 5

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ E. Using the map and the wave speeds from the table above, estimate how long after the earthquake the S-waves would have arrived in Santa Barbara (do not use the travel time curve for this question)? ________________ seconds [2] F. Buildings are particularly vulnerable to the strong side-to-side motions of Love waves. If the first-arriving waves instantly trigger a warning, how long do you have from this warning to Drop, Cover, and Hold On before the substantial Love wave shaking starts if you were in Santa Barbara for this event? (Hint, use the wave speeds in the table above on page 3) ________________ seconds [3] G. Looking back to the seismic waveforms recorded at the four stations what trend do you notice in the amplitudes of the waves between the different stations? How do you explain this answer? _________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________ [3] PART 3: Quantifying the shaking The July 2019 Ridgecrest earthquake sequence in eastern California included one of the largest earthquakes in the state in the last century, and the largest in the age of widespread instantaneous internet access. The USGS now collects earthquake “Did You Feel It?” (DYFI) responses from the public, including information that allows estimation of the intensity of shaking at each location. The three factors that affect how strong shaking will be at a given location are: 1) Magnitude of the Earthquake 2) Distance from the Earthquake 3) Local geology and regional plate structure (local geololgy can cause very local amplification, while regional structure controls how the energy decays with distance throughout a region.) A. The intensity map on the basis of DYFI reports is shown above and is available in color from the TAs. This map shows DYFI responses averaged by zip code. Describe how the shaking intensity varies with distance from the earthquake. _________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________ [2] 7

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ B. Consider the Intensity vs. Distance plots to right. Fill in the table with the average reported intensity for each earthquake at each distance. [3] TABLE OF INTENSITY Distance: 20 km away 100 km away 300 km away C. How do the magnitudes of these two earthquakes compare ? (see titles of Intensity vs. Distance figures) [1] Magnitude of Ridgecrest, CA: ____________ Magnitude of Mineral, VA: ____________ In large part, the difference in how strongly earthquake waves are felt at large distances is controlled by the plate structure. The following figure shows the strength of measured surface wave dissipation across the continental US (averaged over many earthquakes). Red colors mean the waves run out of energy quickly at a certain location, as the energy is absorbed by the Earth. Blue means relatively little wave absorption. Dissipation depends on several factors, but a major one is the temperature of the uppermost mantle (i.e. the thickness of the lithosphere). D. On the 8

EARTH 2 Your name: ___________ Lab day & time: ______________ TA name: __________ PART 4: Frequency vs. Magnitude Luckily for us, there is an inverse relationship between frequency and magnitude of earthquakes in a given location. So, as you go up in magnitude, there are fewer and fewer earthquakes in a certain time (i.e., they are less frequent – note, this has nothing to do with the frequency content of the waves, in Hz!). The table below reports the number of earthquakes in each magnitude range since 1970 (i.e. 50 years ago) within the states of California and Nevada. Magnitude M ≥ 2 M ≥ 3 M ≥ 4 M ≥ 5 M ≥ 6 M ≥ 7 M ≥ 8 Number 52330 * ~26000 2499 ? ? 27 4 ? ? A. Spot the trend: Considering the number of earthquakes greater than M ≥ 3, M ≥ 4, M ≥ 6, and M ≥ 7 describe in your own words the trend in how magnitude and frequency (i.e. the number of occurrences) relate to each other. Note – for this question it is NOT helpful to consider the M ≥ 2 box! _________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________ [2] Estimate the number in the M ≥ 5 and M ≥ 8 boxes and write them in the table above. [2] B. Assuming the rates of occurrence stay about the same, approximately how many M ≥ 6 earthquakes do you expect to occur in these two states in the next century? Number of M ≥ 6 from 2020-2120: ________________ [1] Assuming the overall frequency-magnitude statistics stay constant, how many M ≥ 8 earthquakes can we expect in this region in the next century? Number of M ≥ 8 from 2020-2120: ________________ [1] C. Now consider the M ≥ 2 box. If the frequency magnitude statistics extend consistently to small magnitudes, approximately how many earthquakes would you have expected to have been recorded in since 1970? Number of M ≥ 2 since 1970: ________________ [1] Can you suggest why the observed number is so different from the value you propose above? Hint: Consider your answers to Part 1. Question D, Part 3. Question A., and everything you know now about how we detect earthquakes. _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________ _____________________________________________________________________________________________________________________ [3] 10