(a) Plot the transfer function (i.e., \(\Delta g_{f a} / H\) ) versus the
absolute value of the wavenumber on a semilog plot. Use elastic thicknesses of
0 and \(30 \mathrm{~km}\). Assume \(s=5 \mathrm{~km}\) and \(b_{m}=\) \(6
\mathrm{~km}\). Why does the transfer function approach zero at high
wavenumbers? Why does it approach zero at low wavenumbers? Explain what
happens when the elastic thickness is zero. (Be sure to do all calculations in
mks units.)
(b) Generate a topography profile for a Gaussian topography given by
\(h(x)=h_{0} \exp \left(-\frac{x^{2}}{2 \sigma^{2}}\right)\) where \(h_{0}=5
\mathrm{~km}\) and \(\sigma=20 \mathrm{~km}\).
(c) Use MATLAB to calculate the gravity profile for this topography and the
two values of elastic thickness. The correct answers will have peak gravity
values of \(5.67 \times 10^{-4} \mathrm{~m} \mathrm{~s}^{-2}\) and \(2.34 \times
10^{-3} \mathrm{~ms}^{-2},\) for elastic thicknesses of 0 and \(30
\mathrm{~km}\), respectively.
