  We measure the effects of transverse wakefields driven by a relativistic
proton bunch in plasma with densities of $2.1\times10^{14}$ and
\unit[$7.7\times10^{14}$]{electrons/cm$^3$}. We show that these wakefields
periodically defocus the proton bunch itself, consistently with the development
of the seeded self-modulation process. We show that the defocusing increases
both along the bunch and along the plasma by using time resolved and
time-integrated measurements of the proton bunch transverse distribution. We
evaluate the transverse wakefield amplitudes and show that they exceed their
seed value (\unit[$<$15]{MV/m}) and reach over \unit[300]{MV/m}. All these
results confirm the development of the seeded self-modulation process, a
necessary condition for external injection of low energy and acceleration of
electrons to multi-GeV energy levels.
