“…Therefore, in this paper, we primarily utilize the WKB method as a cross-check, specifically for determining fundamental modes. For higher overtones, we commonly resort to the PS method-a fully numerical approach renowned for its power in determining QNFs [29,30,64,[66][67][68][69][70][71][72][73]. Nevertheless, it is essential to note that, like many numerical methods, the PS method may be time-consuming compared to the semi-analytic WKB method.…”