  Context. The origin of blazar variability, seen from radio up to gamma rays,
is still a heavily debated matter and broadband flares offer a unique testbed
towards a better understanding of these extreme objects. Such an energetic
outburst was detected by Fermi/LAT in 2008 from the blazar PKS 1502+106. The
outburst was observed from gamma rays down to radio frequencies.
  Aims. Through the delay between flare maxima at different radio frequencies,
we study the frequency-dependent position of the unit-opacity surface and infer
its absolute position with respect to the jet base. This nuclear opacity
profile enables the magnetic field tomography of the jet. We also localize the
gamma-ray emission region and explore the mechanism producing the flare.
  Methods. The radio flare of PKS 1502+106 is studied through single-dish flux
density measurements at 12 frequencies in the range 2.64 to 226.5 GHz. To
quantify it, we employ both a Gaussian process regression and a discrete
cross-correlation function analysis.
  Results. We find that the light curve parameters (flare amplitude and
cross-band delays) show a power-law dependence on frequency. Delays decrease
with frequency, and the flare amplitudes increase up to about 43 GHz and then
decay. This behavior is consistent with a shock propagating downstream the jet.
The self-absorbed radio cores are located between about 10 and 4 pc from the
jet base and their magnetic field strengths range between 14 and 176 mG, at the
frequencies 2.64 to 86.24 GHz. Finally, the gamma-ray active region is located
at (1.9 +/- 1.1) pc away from the jet base.
