General Properties of Waves Reflection Seismology Geol 4068 Questions and answers to first lecture homework September 8, 2005

Q. 1 What is the P-wave velocity of the following earth materials measured near the surface of the earth: basalt, granite, peridotite, gabbro and iron Homework 1-due September 8, 2005 at 9.30 a.m. Answer. +/- 10% basalt-- 5 km/s granite km/s peridotite km/s gabbro km/s SOURCES must be referenced!!!

Q. 2 If following a surface explosion, a “ray” of sound enters the blue synform, what will the angle of refraction at point A for the following interface geometry? Apply Snell’s Law with the values provided. Explain your work clearly and succinctly. Hint: simplify the geometry of the geology We can assume that the explosion is at the center of a circle and that the synform describes, approximately the shape of a circle. With this assumption, we start by noting that lines of radius intersect the circumference of a circle at right angles. If so then the incident angle of refraction is 90 degrees. At this normal incidence, reflected rays will return along the same path as the incident ray. Not all the energy of the ray is is returned entirely to the place where of the explosion took place. Some energy may be transmitted through the boundary.

Q. 2

Q. 3 If the lowest frequency your body size can register is about 8 times your greatest dimension, does this value change whether you are in water or in air? What are these values? Will your body “feel” or register these waves? Or, is your body too small? Assume your are 2 m tall ! Assume sound travels at (I) 1500 m/s in water and (II) 330 m/s in air. Assume you are 2 m high. Consider that the dominant frequency in your signal is (a) 10 Hz, and (b) 400 Hz,

Matlab code

Q. 4 What is the critical angle between water and basalt? This is a typical scenario in oceanic spreading ridges. Assume a P-wave velocity of 1500 m/s First, let’s study Snell’s Law for this case at critical conditions, i.e., when the angle of refraction 90 degrees and Snell’s Law reduces to: sin(incident angle) / V in first medium = sin(90deg.) / V in second medium (1)

Note carefully, that your calculator may either return arcsin in radians or degrees. Always consider you units, sin(critical angle)/V in first medium = 1/V in second medium (2) sin(critical angle) = V in first medium/V in second medium critical angle = angle whose sine is: V in first medium/V in second medium (3) In other words, critical angle = arcsin(V1/V2)

Now, taking V1=1500 m/s and V2=5000 m/s we obtain that arcsin(1500/5000) = degrees We can also plot the data out for the general case to understand the behavior better: Matlab code