# Final Exam

- Due Mar 16, 2020 by 11pm
- Points 100
- Submitting a file upload
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- Available Mar 16, 2020 at 7am - Mar 16, 2020 at 11:59pm 16 hours and 59 minutes

**This Final Exam will be from 8:30-10:20 on Monday March 16, 2020 and comprise 25% of your total grade.**

**ESS 412/512 Final Exam, open book, Monday March 16, 2020.**

**Due at 11 pm PDT on Monday, March 16, 2020, if you have any questions about a particular question (for example, if you do not understand how it is phrased or what is asked for), email me at jrhartog@uw.edu**

**Question 1.** (partly from the textbook, plus some additions)

a) The radii of the Earth, Moon, and Sun are 6371 km, 1737 km, and 6.951 x 105 km, respectively. From Figures 1.1, 1.5, and 1.6 in the textbook make a * rough* (estimate a single representative V

_{p}for each celestial body) estimate of how long it takes a P-wave to traverse the diameter of each body. Provide your answer in seconds as well as minutes.

b) Approximately, how long does it take for an S wave to traverse the diameter of the Moon?

c) What is the Poisson's ratio of rocks at the center of the Moon?

d) , the intrinsic (attenuation) quality factor for S waves for the Moon is estimated to be approximately 2400. What would the amplitude of an S-wave with period of 1s be, compared to its initial amplitude after traversing through the Moon ?

e) Read section 6.6.8 from the textbook (p. 172). Then compare the ShakeMaps from two Mw5.8 earthquakes, one in Virginia, and one in California. Given these two ShakeMaps, is Virginia or California more like Kazakhstan (which is where the Soviet test sites were)? Please explain. Is Q higher in California or Virginia?

**Question 2**

An earthquake in Oregon was recorded by several seismic stations and arrival times of P and S waves are available at each of those stations. Figure 2a shows the arrival time of the S-wave minus the arrival time of the P-wave (y-axis) versus the P arrival time (x-axis, measured in epoch seconds) recorded at the same seismic station for several seismic stations. The stations are located at different distances from the earthquake. The origin time of the earthquake, T_{0}, is not known yet, nor is its location (x,y,z). For this, and the next question, it will be helpful if you draw some simple sketches.

Figure 2a Figure 2b

is the arrival time of the P-wave at distance if we assume a constant (1)

is the arrival time of the S-wave at distance if we assume a constant (2)

a) Show that where denote the S and P *travel times* instead of arrival time.

b) Show that the slope of the line in Figure 2a let’s you determine the ratio . Hint: use equations (1) and (2) above.

c) At time t=, both the S-wave travel time and the P-wave travel time are 0. Thus, . Explain how you can determine the origin time from the data in Figure 2a.

d) Determine using the data from earthquake 1 in Figures 2a or 2b.

Figures 2a and 2b show the same data, but for 2b the origin time has been subtracted from the P-wave times so that it shows the P-wave travel time along the x-axis. The slope of the black line is used in the next exercise.

**Question 3**

Figure 3a shows the P wave travel time and the S wave travel time versus the distance from the closest station using the same data as in question 2. If we were to assume the P propagation velocity is 6.0 km/s and that the earthquake occurred at the closest station this represents the travel-time curve.

Figure 3a Figure 3b

a) If the earthquake was located right below the closest station, what would its depth be? Do both the P- and S- travel time agree with this result? (Use Vp/Vs=1.757)

b) Figure 3b shows the same data as 3a, except this time a reduction velocity of 9.0 km/s was used to plot the data. Assume that the event did happen just below the closest station. Consider the geometry in the Figure below. Estimate the incidence angle at a station that is 60 km away from the closest station. Determine the apparent horizontal velocity, is it close to 9.0?

**Question 4.**

The focal mechanism, derived from P-wave first motions, of earthquake 1 from Questions 2 and 3 is shown below.

a) What style of faulting does this focal mechanism indicate?

b) A few observations are labeled as "discrepant", what is meant by that in this context?

c) The normalized moment tensor that represents this double couple focal mechanism is given below in cartesian coordinates x,y,z, where x is positive towards North, y is positive towards East and z is positive down. , , , ,

This moment tensor in a coordinate system determined by its eigenvectors can be written as:

1 | 0 | 0 |

0 | 0 | 0 |

0 | 0 | -1 |

Where the components of corresponding eigenvectors in the x,y,z coordinate frame are:

Verify that this moment tensor represents a double couple source (section 9.2).

d) Which azimuth do the Tension and Pressure axes point in, respectively? Sketch the vectors in the x-y plane, and specify the azimuth clockwise from North. For each axis, specify whether the axis is dipping steeply or shallowly (Hint: The tension axis is the eigenvector associated with the smallest eigenvalue and the pressure axis is the eigenvector associated with the largest eigenvalue).

e) How can you use the beachball plot to verify your answer to d?

**Question 5.**

Examine the 1D velocity models a, b, and c and their resulting ray paths in the Figure below. Some of the ray paths have been labeled with a capital letter.

a) Sketch the Travel Time curve (T-X) for each model and mark where each labeled ray would plot on that curve.￼

b) Discuss the futility of this proposed work: *I plan to use P-wave first arrival times picked by the analysts of the PNSN seismic network to determine whether a homogeneous layer model or a linear velocity gradient model best represents the actual velocity structure of the crust in the Pacific Northwest.*

c) How could you modify the proposed study to make success more feasible (to derive a more realistic representation of the crustal structure)?