(COMPUTER) Consider MARMOD, a velocity-versus-depth model, which is
typical of much of the oceanic crust (Table 4.1). Linear velocity gradients are
assumed to exist at intermediate depths in the model; for example, the P velocity
at 3.75 km is 6.9 km/s. Write a computer program to trace rays through this model
and produce a P-wave T(X) curve, using 100 values of the ray parameter p equally
spaced between 0.1236 and 0.2217 s/km. You will find it helpful to use subroutine
LAYERXT (provided in Fortran in Appendix D and in the supplemental web
material as a Matlab script), which gives dx and dt as a function of p for layers
with linear velocity gradients. Your program will involve an outer loop over ray
parameter and an inner loop over depth in the model. For each ray, set x and t to
zero and then, starting with the surface layer and proceeding downward, sum the
contributions, dx and dt, from LAYERXT for each layer until the ray turns. This
will give x and t for the ray from the surface to the turning point. Multiply by two
to obtain the total surface-to-surface values of X(p) and T(p). Now produce plots
of: (a) T(X) plotted with a reduction velocity of 8 km/s, (b) X(p), and (c) τ(p). On
each plot, label the prograde and retrograde branches. Where might one anticipate
that the largest amplitudes will occur?