EAS 434 Reflection Seismology
HW: Travel times and Amplitudes
Due 10/7/02
Let’s develop some useful MATLAB tools:
1. a) Write a MATLAB m-file to compute the travel time curves for the direct
wave, critically refracted wave, and reflected wave for a single layer overlying a
half space. (Just compute times, don’t worry about amplitudes yet). Attach a
listing of the m file here.
b) Use this program to compute and plot these three arrivals for the following
earth model (cross section):
_______________ surface
V0 = 6 km/sec
----------------------- z1 = 35 km
V1 = 8 km/sec
c) What is the cross-over distance for the model above?
2. a) Write a MATLAB m-file to compute the respective velocities and thicknesses
for a two layer model.
b) Use this program to solve for the structure corresponding to the travel times in
dataset 1 (following). First determine how many layers you think are involved.
Then pick the arrival times for each trace; use least squares to determine the slope
and intercept time for the best fitting line segments (it would be nice to have this
as an option in your MATLAB code). Note: The distance from the shot to the
nearest geophone is 5 m. The spacing between geophones is 5 m.
3. a) Write a MATLAB m file to compute the respective velocities, thicknesses and
dip for a single dipping layer.
b) Use this code to analyze the dataset 2 below (a reversed refraction survey)
Dataset 1
Dataset 2
Data Source:
http://www.earth.ox.ac.uk/~tony/watts/teaching/mendips/2002/mendips_seismic_r
efraction_data.html
4. a) Write a MATLAB m-file to determine the average velocity from the surface to the
depth of the 3 prominent reflections at t0 = 5.1 sec, 1.3 sec and 1.9 sec in Dataset 3
below: Use the T2-X2 method. What are the corresponding depths to these reflectors.
Dataset 3
b) While you are at it, what velocity structure (be specific) is indicated by the first
(refracted) arrivals? How do those velocities and thicknesses compare with those
estimage from the reflected arrivals?
5) Write a MATLAB routine (m-file) to compute and plot the amplitude At of a vertically
incident seismic P wave reflected from a flat interface at depth, normalized to a
reference amplitude at a reference travel time (e.g. A0 = 1 at t = 500 m). Include
spherical divergence, anelastic attenuation, and the normal incidence reflection
coefficient. Use this code to compute and plot relative amplitude versus travel time
for the following interface at z1, where z1 = 500, 1000, 1500….. 5500 meters.
__________S=R___________ z0 = 0
Vp = 4000 m/sec,  = 2.4 gr/cc, Q =500
________________________ z1
Vp = 6000 m/sec,  = 2.7 gr/cc, Q =1000
Vp is the P wave velocity,  = density and Q = attenuation factor. The attenuation
constant  is related to Q by the equation  = f/QVp, where f = frequency of the
seismic wave.
Assume your seismic source is at the surface, the receiver is co-incident with the
source, and the dominant frequency for your seismic signal is 50 Hz.
6) Plot relative amplitude versus travel time for the above model using f = 1, 10, and 100
Hz, respectively. Which frequency gives best penetration?
7) a) Modify your program to include a finite source-receiver offset x. Keep the nearvertical approximation for the reflection coefficient but compute and plot the relative
amplitude of the reflected signal as a function of offset for the parameters in the
above problem for z = 5000 m and 0≤x≤1000 m.
b) While you are at it, compute and plot the two way travel time for the reflection in
part a) as a function of offset.