Project VESE (very expensive seismic experiment) deployed 60 seismometers in a
linear array extending 240 km away from a large surface explosion. Despite careful
picking of the resulting seismograms, the first-arrival P-wave travel times (plotted
in Fig. 5.16 and also given in the supplemental web material) show considerable
scatter.
Fit these points with a series of straight lines and compute the ray parameter p
and the delay time τ for each line. The first of these lines should go through the
origin (zero time and range). Be sure to take into account the reduction velocity of
8 km/s in computing p. Using equation (5.12), invert these results for a layer-cake
P-velocity model of the crust and uppermost mantle. List your model in a table,
starting with the surface layer and continuing downward, with each line consisting
of a depth (km) and a velocity (km/s). Specify the velocity discontinuities between
layers by listing the depth twice, with the first line containing the velocity in the
upper layer and the second line the lower layer velocity. Make sure that the first
column of your table is absolute depth and not layer thickness. For example, a
three-layer model with a 2 km thick top layer of 4 km/s, a 4 km thick middle layer
of 6 km/s, and a bottom layer of 8.1 km/s would be written as:
What is the Pn crossover distance? How thick is the crust in your model? How
much uncertainty would you assign to your crustal thickness estimate? Note: Not
everyone will get the same answer to this exercise! It’s fun to plot the different
models to see how well they agree.