Earthquake Seismology The goal of these 3 questions is to help you think about raypaths, ray parameters, and some simple and direct ways to infer Earth's velocity structure. 1.(6 pts). a) Using the travel-times curves (Figure 3.5-4) for earthquakes at the surface and at a depth of 600 km, estimate the ray parameters in s/degree for direct P waves at 60° distance. b) Find angles of incidence at the earthquake source for these two rays by converting ray parameter values to s/radian and using the velocities estimated from Figure 3.5-1 (also attached). c) In words and with a sketch, explain how and why the angle of incidence for rays reaching a given distance varies with the depth of the earthquake. == 2. (8 pts). The travel-time curve for Pdiff (sometimes labeled just Pd), the P wave that diffracts along the core-mantle boundary, directly tells us the P-wave velocity at the base of the mantle. The Pdiff travel-time curve is linear, with a ray parameter p dT/dA = rcmb/Vemb, where rcmb is the radius of the core-mantle boundary, and Vcmb is the velocity at the base of the mantle. a) Measure the ray parameter (in s/degree) for the Pdiff phases shown in the record section of Figure P3.4 (attached). Pdiff is the one prominent phase seen on each seismogram. How does this value compare to the slope of the Pdiff travel-time curve in Figure 3.5-4? (Incidentally, I published a paper in 2004 using seismograms from these stations, which were part of MOMA, a PASSCAL experiment spanning the eastern US that predated EarthScope. Station CCM is in Missouri, and station HRV is in Massachusetts. My paper focused on surface waves, not core diffractions.) b) Convert the Pdiff ray parameter to s/radian, and find the velocity at the base of the mantle. c) Using values of dT/dA from Figure 3.5-4 for Pdiff and Sdiff, find the average ratio of P to S velocity (Vp/Vs) in the mantle. d) Compare the travel-times of PcP and ScS at zero epicentral distance for an earthquake at the surface (0 km depth). What is the average ratio of P to S velocity in the mantle (Vp/Vs)? 3.(4 pts) The travel-times for PcP, PKiKP, and PKIKP are shown in Figures 3.5-4 and 3.5-7 which are attached. You can use an outer core radius of 3482 km, and an inner core radius of 1217 km. a) b) Use the travel-times for PcP and PKiKP (Figure 3.5-4) at vertical incidence (incidence angle 0°) to estimate the average P-wave velocity in the outer core. Include a sketch that explains your reasoning. Use the travel-times for PKiKP and PKIKP (Figures 3.5-4 and 3.5-7) at vertical incidence to estimate the average P-wave velocity in the inner core. Include a sketch that explains your reasoning. Time (min) Figure 3.5-4: IASP91 travel time curves for a surface and deep source. 40 IASP91: 0 km source P'P' 40 IASP91: 600 km source SKKP PKKP 30 20 20 10 ScS SCP SKiKP S P PcP S diff SS SP SKS PKiKP PP P diff SKP PKP SKKS Time (min) PKKS SKKP 30 20 20 ScS PCS 10 SCP PcP ds P PKKP SS 20 40 60 80 100 120 140 160 180 Delta (°) 20 40 60 P'P' Sdiff SKKS SSKS PSKS SKS PKS SS SKP PPKP PP PKP PKiKP ор P diff 80 100 120 140 160 180 Delta (°) Figure 3.5-1: Comparison of the J-B and IASP91 earth models. 14 Velocity (km/s) 12 P 10 8 CMB S 6 + 2 Lower mantle Transition zone Upper mantle JB model IASP91 model ICB S Inner Outer core core 1000 2000 3000 4000 ☐ 5000 6000 Depth (km) Minutes after origin time 13 14 16 Figure 3.prob.4: Seismograms for homework problem #3.17. 17 CCM MM18 MM17 MM16 105 MM14 MM12 MM10 MM09 MM08 MM07 MM06 MM05 MM04 MM03 m MM02 MM01 HRV 110 Distance (°) 115 120 Time (min) Figure 3.5-7: Ray paths and travel times for major core phases. (98°) 22 PKP B(145°) PKP PKIKP D(1229) B(145°) C(153°) A(177°) F(180°) 20 20 PKIKP PKiKP B PKiKP 18 Pd 16 14 100 120 140 160 180 Distance (°) Pd (98°) C(153°)