  We study the characteristics of chaos evolution of initially localized energy
excitations in the one-dimensional nonlinear disordered Klein-Gordon lattice of
anharmonic oscillators, by computing the time variation of the fundamental
frequencies of the motion of each oscillator. We focus our attention on the
dynamics of the so-called `weak' and `strong chaos' spreading regimes [2010,
EPL 91 30001], for which Anderson localization is destroyed. Based on the fact
that large variations of the fundamental frequencies denote strong chaotic
behavior, we show that in both regimes chaos is more intense at the central
regions of the wave packet, where also the energy content is higher, while the
oscillators at the wave packet's edges exhibit regular motion up until the time
they gain enough energy to become part of the highly excited portion of the
wave packet. Eventually, the percentage of chaotic oscillators remains
practically constant, despite the fact that the number of excited sites grows
as the wave packet spreads, but the portion of highly chaotic sites decreases
in time. We show that the extent of the zones of regular motion at the edges of
the wave packet in the strong chaos regime is much smaller than in the weak
chaos case. Furthermore, we find that in the strong chaos regime the chaotic
component of the wave packet is not only more extended than in the weak chaos
one, but in addition the fraction of strongly chaotic oscillators is much
higher. Another important difference between the weak and strong chaos regimes
is that in the latter case a significantly larger number of frequencies is
excited, even from the first stages of the evolution. Moreover, our
computations confirmed the shifting of fundamental frequencies outside the
normal mode frequency band of the linear system in the case of the so-called
`selftrapping' regime where a large part of the wave packet remains localized.
