Refractions Head Waves Diving Waves Refraction Tomography Velocity

Refractions: Head Waves, Diving Waves, Refraction Tomography Velocity z Diving Waves (exist vertical dv/dz>0)

Head Waves vs Diving Waves Velocity Head Wave z Velocity z Diving Waves (exist vertical dv/dz>0) Velocity z Interference Head waves

Diving Waves, linear V(z) grad. and Triplications Velocity x x Direct Wave z z Refraction t p = sin i(z)/v(z) = 1/vmax Direct Wave V(z)=vo+ kz A simple velocity gradient produces a refraction that takes a circular path, having a hyperbolic sine (or Error Function) shape in the t-x plot. Velocity x 3 arrivals at dash x Direct Wave z Direct Wave Reflection Head Wave p = sin i(z)/v(z) = 1/vmax t Reflection Refraction

p = sin i(z)/v(z) = 1/vmax Slowness = inverse apparent Vx p = sin i(z)/v(z) = 1/vmax Limit of thin horizontal layers P = sin. O 1/v 1 = sin. O 2/v 2=sin. O 3/v 3=1/v 4 v 1 v 2 v 3 v 4

Diving Waves, linear V(z) grad. and Triplications Velocity x x Direct Wave z z Refraction t p = sin i(z)/v(z) = 1/vmax Direct Wave V(z)=vo+ kz A simple velocity gradient produces a refraction that takes a circular path, having a hyperbolic sine (or Error Function) shape in the t-x plot. Velocity x 3 arrivals at dash x Direct Wave z Direct Wave Reflection Head Wave p = sin i(z)/v(z) = 1/vmax t Reflection Refraction

Diving Waves, linear V(z) grad. and Triplications Velocity 3 arrivals at dash x x Direct Wave Reflection z t Head Wave d Refraction Reflection p = sin i(z)/v(z) = 1/vmax Synthetics 40 s Gulf California Data 40 s Direct Wave T-dx 10 s Direct Wave Reflection T-dx 10 s 80 s 10 deg Reflection 80 s Refraction 10 deg Refraction 40 deg

T(x, z) for a linear V(z) grad. Identify with circular arc: Thus: Source-receiver offset: Linear velocity variation: Constancy of apparent horizontal wave-number:

Time: T(x, z) for a linear V(z) grad. One can solve for Plugging Eq. (1) and (3) into Eq. (2), we finally get: From Asymptote:

Layered Medium & Critical Angle CSG 0 Model 0 3 km/s Sea floor Post-critical reflection ray Time (s) Z (km) Post-critical reflections 4. 0 3. 5 0 X (km) 6 1. 5 km/s 0 X (km) 6

Sahdow Zones: http: //www. iris. edu/hq/programs/education_and_outreach/visualizations/tutorial http: //www. youtube. com/watch? feature=endscreen&v=JZy. Ys 0 t. So 4 k&NR=1 Shadow Zones and Caustics Shadow Zone II: http: //www. youtube. com/watch? v=v_1 Qc. I 3 BWRk Velocity x z F z Caustic: Phase change results, large Amplitude, ray area zero, surface weak focus, Discontinuity of traveletime slopes x t Shadow Zone F Shadow Zone: An area on Earth's surface where no direct seismic waves from a particular earthquake can be detected.

Shadow Zones and Caustics Romaowicz Lecture 1 hour: http: //earthquake. usgs. gov/learn/animations/animation. php? flash_title=Shadow+Zone+Flash+Animation &flash_file=shadowzone&flash_width=220&flash_height=300 Shadow Zone: An area on Earth's surface where no direct seismic waves from a particular earthquake can be detected.

Head Wave, Diving Wave, post-Crit. Reflections 1. Head Waves: Horizontal layered medium Vx = Vrefrac. Slope dx/dt in data = Vrefract. . refract More generally: Refraction tomography. 2. Post Crit. Reflections: Strong Amplitude More generally: Refraction tomography. Phase Change 3. Diving Waves: Phase Changes, Triplication Strong Amplitudes, Interfer. Head Waves, Shadow http: //www. nature. com/nature/journal/v 427/n 6974/full/nature 02231. html Zones, Caustics

Refraction Tomography t 1 = L 11/v 1 + L 12/v 2 + L 13/v 3 + …. + L 1 n/vn t 2 = L 21/v 1 + L 22/v 2 + L 23/v 3 + …. + L 2 n/vn

Refraction Tomography http: //www. youtube. com/watch? v=Hrto 0 n. IP 8 nk&feature=related Cool=falling blobs Cool colors = +v 670 km discontinuity Hot=rising blobs Hot colors = -v Any planet with a radius over ~1500 km cannot conduct its internal heat away within the age of the universe, so it must convect viscously to release its heat, or it would melt and then convect as a fluid. http: //www. youtube. com/watch? NR=1&v=ve 7 N 25 R 2 h 4 c&feature=endscreen

3 D Marine: http: //www. youtube. com/watch? v=YNk. Jq. J 2 VAk. Q&feature=related Bedrock Depths from the Wells here! Humboldt County Lander County The bedrock is expected to be at depth of several hundred meters from ground surface 677 m Pershing County 3. 36 km Buffalo Valley Mine #124 680 ft(200 m) #125 320 ft(97 m)

Buffalo Valley North central Nevada Buffalo Valley Mine Seismic Line Pershing County

Survey Site

Seismic Recording Unit

Seismic Source

Comparison of Tomographic and Seismic Image Tomographic Image m/s Z (m) 0 300 Seismic Refractor Image A C Amplitude Z (m) 0 B 300 0 X (m) 2500

#125 320 ft (97 m) Z (m) 0 Interpretation of Tomogram and A Seismic Refractors B C #124 300 0 680 ft (200 m) 900 ft (273 m) X (m) 2000 m (ch 48 of Line C) 845 ft (256 m) 2500 150 m off from the end m/s