An intriguing question in Space SE Optimal depth for underground flyby? asks about a theoretical spacecraft trajectory for a "slingshot maneuver" also known as a gravitational assist or "flyby" with the relaxed condition that the trajectory can go through the earth (presumably through a carefully constructed tunnel who's path is adjusted to account for Earth's rotation during the f̶l̶y̶b̶y̶ "flythrough".
There are answers there but currently the most rigorous numerical trajectories still assume a uniform density sphere. The answer will be much different if it can include the dramatic factor of 5 radial variation of Earth's density from say 2.5 (ignoring water) to over 13 g/cm3.
I found the plot below in Wikimedia which certainly looks like it's piecewise polynomial and perhaps even piecewise parabolic.
Sadly, it references only https://www.gps.caltech.edu/uploads/File/People/dla/DLApepi81.pdf as the source of the data and that link is of course broken (ones like this usually do) rather than a proper citation (name, year, journal, page number) or a doi link.
So I'd like to ask the following.
Question: Is there an approximate, piecewise continuous analytical model for Earth's radial density profile useful for numerical integration that can be used as a properly cite-able source for a Stack Exchange answer?
One could reverse-engineer this one, but it would be better to get at the source.
Earth's radial density distribution according to the Preliminary Reference Earth Model (PREM). 29 December 2010
update: This answer to Do there exist reasonable numbers on the density/radius/mass of the various geological layers of the Earth? provides one such model for Earth's core with two polynomials, but these end at a radius of 3480 km with nothing outside of that.