Transform the variables in equation (4.32) for X(p) to the spherical-Earth case by applying the flat-Earth transformation (4.45)–(4.46) and changing the equation from a dz integral to a dr integral....

Transform the variables in equation (4.32) for X(p) to the spherical-Earth case

by applying the flat-Earth transformation (4.45)–(4.46) and changing the equation

from a dz integral to a dr integral. That is, replace z with z = −a ln(r/a), u = uf

with the appropriate function of us, etc. Show that the result is the spherical-Earth

equation for (p) (equation 4.44). Hint: Remember that x = and to transform

the u on the right side of equation (4.40).