  Out-of-Time-Order Correlators (OTOCs) serve as a proxy for quantum
information scrambling, which refers to the process where information stored
locally disperses across the many-body degrees of freedom in a quantum system,
rendering it inaccessible to local probes. Most experimental implementations of
OTOCs to probe information scrambling rely on indirect measurements based on
global observables, using techniques such as Loschmidt echoes and Multiple
Quantum Coherences, via time reversal evolutions. In this article, we establish
a direct connection between OTOCs with global and local observables in the
context of NMR experiments, where the observable is the total magnetization of
the system. We conduct a numerical analysis to quantify the differences in the
evolution of both magnitudes, evaluating the excitation dynamics in spin ring
systems with 8 to 16 spins, using a many-body Hamiltonian and long-range
interactions. Our analysis decomposes the global echo into a sum of local
echoes and cross-contributions, leading to local and global OTOCs. The results
indicate that, after an initial transient period, local OTOCs determine the
global ones. To confirm the equivalence, we observe that the difference between
local and global OTOCs, as well as their fluctuations, becomes negligible as
the system size increases. This behavior aligns with that observed in highly
interacting or chaotic systems in several experiments.
