  In the present paper, we analyze the signatures of long-range persistence in
seismic sequences along Circum-Pacific subduction zones, from Chile to
Kermadec, extracted from the National Earthquake Information Center (NEIC)
catalog. This region, known as the Pacific Ring of Fire, is the world's most
active fault line, containing about 90$\%$ of the world's earthquakes. We used
the classical rescaled range ($R/S$) analysis to estimate the long-term
persistence signals derived from a scaling parameter called the Hurst exponent,
$H$. We measured the referred exponent and obtained values of $H>0.5$,
indicating that a long-term memory effect exists. We found a possible fractal
relationship between $H$ and the $b_{s}(q)$-index, which emerges from the
non-extensive Gutenberg-Richter law as a function of the asperity. Therefore,
$H$ can be associated with a mechanism that controls the level of seismic
activity. Finally, we concluded that the dynamics associated with
fragment-asperity interactions can be classified as a self-affine fractal
phenomenon.
