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: __________ Seismologists actually no longer use the Richter scale for big earthquakes. This is because (a) the scale was designed for SoCal, which is quite different from most of the planet, and (b) the scale saturates at ~M 7.5, meaning a M 9.1 gives the same reading as a M 7.6, which is pretty silly. Instead, we use the Moment Magnitude ( M w ) scale, which actually reflects the energy release by the earthquake. The formula for moment magnitude is: where is the distance the fault slips 𝑀 ? = 1 + 0. 66 𝑙𝑜?10 𝑠 𝐴 ( ) 𝑠 (in m) and is the area (in m 2 ) of fault that breaks. (FYI here we’ve assumed a shear rigidity of 30 GPa, in case you’re wondering!) 𝐴 E. The San Andreas is long but is a vertical fault, so only ~20 km of down-dip width is cold enough to break in an earthquake (i.e. below 20 km depth, the rocks are too warm to fail in a brittle earthquake and instead deform in other ways). Imagine a 500 km length of the fault breaks, slipping 10 m (this huge earthquake is unlikely but not impossible). What magnitude would this earthquake be? Hint: Area is width multiplied by length … and don’t forget to convert values from km to m. Please show your work. Mw = _____________________ [3] F. Subduction zone faults slope at a much shallower angle, so as much as ~200 km of down-dip width can break in earthquakes. Imagine a 500 km length of the Cascadia subduction zone fault breaks, slipping 10 m. What magnitude would this earthquake be? (Please show work) Mw = _____________________ [3] Earthquakes emit multiple types of waves, which travel at different speeds, have different kinds of vibrations, and take different paths through the Earth. See table: 3