Non-volcanic tremor (NVT) is an enigmatic seismic phenomenon that has become a topic of increasing interest, particularly in subduction zones. NVTs are emergent seismic signals of long duration and low amplitude (Obara, 2002). Previous studies have shown that NVTs are composed of repeating small low-frequency earthquakes, commonly accompanied by very-low-frequency earthquakes that, in both cases, involve shear failure and slip (Shelly et al., 2007; Bostock et al., 2015; Gomberg et al., 2016a, b). NVTs mainly occur along the plate interface, close to the shallow and deep edges of locked regions. This phenomenon can also be observed in other tectonic environments, such as in convergent margins (e.g., Taiwan; Tang et al., 2010) and continental transform faults (e.g., California; Nadeau and Dolenc, 2005; Shelly, 2010). Fluids are implicated in generating NVTs, similar to volcanic tremor processes (Obara, 2002). Pressure and temperature conditions in subduction zones, together with dehydration processes, control the occurrence of NVT (Yoshioka et al., 2008; Peacock, 2009). It has been reported that NVTs occur in regions of high pore-fluid pressure (Shelly et al., 2006). Other factors also contribute, including the composition of the overriding plate and processes such as metamorphism of subducting seamounts (Wada et al., 2008). Non-volcanic tremors commonly exhibit episodic activity, with periods of intense activity lasting from days to weeks, separated by quiescent intervals of months with few or no events (Obara, 2002). NVTs are also closely associated with slow earthquakes, with both phenomena sharing temporal and spatial occurrence (Rogers and Dragert, 2003). Another important feature of NVTs is their ability to be triggered by large earthquakes, such as the 2002 Denali earthquake (Mw=7.8) in Alaska (Rubinstein et al., 2007) and the 2003 Tokachi-oki earthquake (Mw=8.1) in Japan (Miyazawa and Mori, 2005), both of which triggered enhanced NVT activity.

Tectonic tremors have been reported along the Middle America Trench in Mexico, in the states of Guerrero (Payero et al., 2008; Cruz-Atienza et al., 2015; Villafuerte and Cruz-Atienza, 2017; Husker et al., 2019; Plata-Martínez et al., 2021; Chen et al., 2025), Jalisco-Colima (Ide, 2012), and Oaxaca (Brudzinski et al., 2010; Husker et al., 2019). In Guerrero, NVTs have been detected at approximately 200 km downdip, at depths of 40–50 km, and closer to the trench, at depths of 10–16 km (Plata-Martínez et al., 2021; Chen et al., 2025). Similarly, in Oaxaca, NVTs are located about 150–200 km from the trench at depths of 30–50 km (Brudzinski et al., 2010). In Western Mexico, NVTs occur in a narrow band oriented parallel to the trench, mostly at depths of 30–50 km (Ide, 2012). Much of the research on tectonic tremors has focused on locating events, generating catalogs, and their tectonic interpretation. Fewer studies, however, have examined the statistical characteristics of event occurrence. For example, Kao et al. (2010) determined the b-value of NVT sequences in northern Cascadia (Mw∼1.0–1.7), finding that the b-value of ∼1. Staudenmaier et al. (2019) estimated the b-value of NVTs in the San Andreas Fault (0.44<Mw<2.7), obtaining a b-value of 2.52. In contrast, other studies reported extremely high b-values (b>5 with 1.5<Mw<2.7; b=4.2 with 0.3<Mw<1.5) (Sweet et al., 2014; Bostock et al., 2015). In this article, we studied the statistical features of NVT sequences generated at the Mexican subduction zone. We analyzed the Gutenberg-Richter relationship, non-extensive statistics, and multifractality of magnitude and interevent-time distributions. Our results provide detailed statistical characterization of NVTs in subduction zones, which may contribute to a better understanding of their generation mechanisms.

The Mexican subduction zone (MSZ) is located along the border of three tectonic plates: the Cocos (CO), North American (NA), and Rivera (RI) plates, respectively (Fig. 1). Convergence rates predicted from the NUVEL1-A model (DeMets et al., 1994) fluctuate from 2.0 to 6.8 cmyr-1 for the RI-NA convergence in the north (Jalisco-Colima) to the CO-NA convergence in the south (Oaxaca), respectively (Fig. 1). The rupture areas of the previous largest earthquakes exhibit a seismic gap in the MSZ, known as the Guerrero seismic gap (GG). The GG is a 200 km long segment in the CO-NA plate boundary (Fig. 1). The gap is capable of producing an earthquake with a magnitude of 8.1–8.4 if the entire gap were ruptured in a single event (Singh and Mortera, 1991). The gap has not experienced a significant event (M>7) since 1911. The geometry of the subducted slab varies from north to south (Hayes et al., 2012). In the Jalisco region, the RI plate subducts at a steep angle (∼50°), and then the dip angle of the CO plate decreases gradually toward the southeast. In the Gurrero-Oaxaca region, the subducted slab is almost subhorizontal (Pardo and Suárez, 1995; Pérez-Campos et al., 2008). As mentioned above, non-volcanic tremors occur at certain regions within the subduction zone regime. They appear to signal the transition from creep to locking trench parallel segments (Chen et al., 2025).

Our estimates of the b-value showed that the b-values for NVTs at the Mexican subduction zone range from 1.25 to 2.42, with completeness magnitudes (Mc) between 1.10 and 1.80. Sequences 1 and 3 have the highest b-values, indicating a possible distinct characteristic of the down-dip Guerrero segment of the Cocos plate. They are followed by sequence 2, located at the interface between the Rivera and Cocos plates. The lowest b-value is found for sequence 5 in the Guerrero Gap region (Fig. 2 and Table 2), which unfortunately cannot be corroborated by sequence 6 at the same region, as it does not include magnitude data. The q-value from the non-extensive statistical analysis fluctuates from 1.39 to 1.65. The q-values show an apparent inverse relationship with the b-value, since the sequences located near the trench (2 and 5) have higher q-values than those located down-dip (1 and 3), which exhibit similar q-values. Bootstrap resampling (1000 iterations) was used to estimate uncertainties in b-values, Mc, and q-values (Tables 2 and 3). Smaller sequences (e.g., sequence 5, N=101) exhibit larger relative uncertainties, which are now explicitly reported. A Monte Carlo analysis incorporating these uncertainties confirms a strong negative correlation between b- and q-values, with mean Pearson coefficient r=-0.94 (95 % CI: -0.999 to -0.743), supporting the inverse relationship observed across the NVT sequences.

Multifractal indicators of the original time series show that the multifractal spectra are mostly right-skewed (magnitude sequences 1 to 4, interevent time sequences 1, 2, and 6). In contrast, left-skewed spectra correspond to interevent time sequences 3 and 4. Sequence 5 exhibits a symmetric multifractal spectrum. Results for the degree of multifractality (Δα) indicate that interevent time series have a higher multifractal strength than magnitude time series. On the other hand, the singularity parameter (Δf) indicates that the singularities are weaker for magnitude sequences 2 and 3, as well as interevent time sequences 1–2 and 6. Conversely, the singularities are stronger for interevent time sequences 3 and 4. Estimates of the Hurst exponent (H) depict a long-term persistence signature (H>0.5). By comparing the multifractal spectra (Fq(s), h(q), τ(q), α(q), and f(α)) obtained from the original, shuffled, and surrogate time series, we observe that multifractality is not completely removed in all cases. However, in several sequences, the multifractal indicators become statistically indistinguishable from those derived from surrogate data. Statistical tests based on IAAFT surrogates show that p-values associated with the multifractal indicators (A, Δα, Δf, and H) vary significantly across sequences. Magnitude sequence 5 and interevent time sequences 1, 4, and 5 exhibit relatively high p-values, indicating no statistically significant differences with respect to surrogate data. In contrast, magnitude sequence 1 shows consistently low p-values across multiple indicators, suggesting statistically significant deviations from surrogate behavior. For the interevent time sequences 2, 3, and 6, low p-values are observed for key parameters, such as Δα, and, in sequence 3, for H as well, indicating significant differences relative to the surrogate series. In magnitude sequences 2 and 3, the results are mixed: some indicators yield low p-values, while others remain high, preventing a clear classification based solely on the statistical tests. Overall, the results indicate that the statistical significance of multifractality varies across sequences and depends on the specific indicator considered.

Regarding the inter-event time distributions, a comparison of the fitted probability density functions (PDFs) with the empirical distributions from sequences 1 to 4 showed that the Lognormal distribution provided the best fit. In contrast, for sequences 5 and 6, the Gamma distribution yielded the best fit for the interevent time data. In all cases, the least well-fitting distribution is the Exponential distribution (Fig. 10 and Table 5). Finally, event duration observations exhibit large scatter, resulting in linear scaling relationships with low coefficients of determination (0.03<R2<0.34) (Fig. 11 and Table 6). This scatter is intrinsic to the genesis of NVTs or is associated with the detection process, as it is present in all reported sequences.

We start the discussion by comparing our b-value estimates with previous studies. The b-value associated with NVTs has been determined in both crustal and subduction environments, with the latter being the most common. In crustal regions, for example, along the San Andreas Fault (Parkfield segment), Staudenmaier et al. (2019) calculated a b-value of 2.52 for NVT episodes. For subduction zones, it has been found that the b-value of NVTs ranges between 1 and 5 (Kao et al., 2010; Rabbel et al., 2011; Gallego et al., 2013; Sweet et al., 2014; Bostock et al., 2015). The Cascadia subduction zone, particularly in Vancouver Island, exhibits both low and high b-values (b∼1 and 4.2<b<5, respectively) (Kao et al., 2010; Sweet et al., 2014; Bostock et al., 2015). In Chile, the b-value of NVT sequences was determined to be 2.4 (Gallego et al., 2013). Regarding b-value estimations of NVTs at the Cocos plate, Rabbel et al. (2011) estimated a value of 1 in the region of Costa Rica. Our results show that the b-value varies from 1.25 to 2.42 for the NVTs detected in the Mexican subduction regime studied. We observed that in the down-dip segment, NVT sequences have the highest b-values (2.22–2.42), while in the interplate coupling region, the b-value ranges from 1.25 to 1.41 (Table 2). High b-values may indicate a greater degree of fracturing, as they reflect a larger proportion of small-magnitude events relative to larger ones. In general, the b-values obtained for the coupling region do not differ significantly from those reported for tectonic earthquakes. For example, for the Cocos plate, the b-value for tectonic seismic events has been observed to lie in the interval of 0.8–1.3 (Nishikawa and Ide, 2014).

Temporal variations in seismic network geometry can significantly influence the magnitude of completeness (Mc) for NVT sequences. Sequences 1–3 (Ide, 2012; Idehara et al., 2014) were recorded using temporary networks such as MARS and MASE, where changes in station coverage over time affected event detection and Mc estimates (N=1908, 1411, 6776; Mw ranges -0.27 to 3.65, -0.40 to 3.21, -0.80 to 2.00). Sequence 4 (Husker et al., 2019) was analyzed using limited station coverage, constraining the detection of low-magnitude events, although magnitudes were not estimated (N=23408). In contrast, sequences 5 (Plata-Martínez et al., 2021) and 6 (Chen et al., 2025) used submarine seismometers, allowing reliable detection of events, despite Chen et al. (2025) not reporting magnitudes (N=101 and 637; Mw ranges 0.10 to 2.70 and not reported, respectively). These examples demonstrate that temporal changes in network configuration, station density, and instrument type may directly affect Mc and, consequently, influence b-value calculations and their interpretation for NVT catalogs.

In terms of the non-extensive statistical analysis, our estimates of the q-value for NVTs in Mexico are consistent with previous reports from subduction zones, where q-values range from 1.61 to 1.69 (Scherrer et al., 2015). These results agree with our findings, in which the q-value varies from 1.64 to 1.65. Our results also show that down-dip interplate sequences have lower q-values (1.39) (Table 3). High q-values in coastal regions may be explained by greater stress heterogeneity, associated with plate coupling and asperity distribution, compared to down-dip regions, where different conditions, such as pressure, temperature, and rock structure prevail.

Regarding the multifractal analysis, our results indicate that both magnitude and interevent time NVT sequences exhibit multifractal structures similar to those observed in tectonic earthquakes (interevent time, Michas et al., 2015; magnitude, De Freitas and França, 2024). Tests based on surrogate data show that only one sequence exhibits intrinsic multifractality, while four sequences display apparent multifractality and five sequences yield inconclusive results. De Freitas and França (2024) also reported that seismicity in some subduction zones shows apparent multifractality, whereas others exhibit intrinsic multifractality, which is consistent with our findings. The estimated Hurst exponent (H) values further illustrate the heterogeneity of the sequences, ranging from 0.65 to 1.06 (Table 4). Several sequences fall within the range typically associated with persistent behavior (0.5<H<1.0), while some sequences, including magnitude sequences 1, 2, and 5, reach or slightly exceed H=1.0. Values above unity should be interpreted with caution, as they may indicate non-stationary or trending behavior, rather than purely long-range dependence. Nonetheless, these high values may reflect strong temporal correlations in certain sequences.

High H values have previously been linked to fault-zone properties (Cisternas et al., 2004). While we hypothesize that they could reflect limited volumes of perturbed regions containing fluids, this interpretation remains speculative. The observed H values are statistically comparable to those reported for regional seismicity and aftershock sequences: southern Italy (0.5–0.92, Telesca et al., 2001), Taiwan and Greece (∼0.8, Chen et al., 2008; Gkarlaouni et al., 2017), and the San Andreas Fault (∼0.87, De Freitas et al., 2013), with Izmit aftershocks reaching 0.95 (Cisternas et al., 2004). Although fundamental differences exist between aftershock relaxation and NVT generation, the similarity in scaling behavior suggests comparable long-term memory in the underlying processes. The surrogate analysis indicates that the physical origin of multifractality is not uniform across sequences. Magnitude sequence 1 and interevent time sequences 2, 3, and 6 show statistically significant deviations from surrogate data, suggesting contributions from temporal correlations and potential nonlinear interactions, whereas other sequences are consistent with apparent multifractality arising from broad distributions or finite-size effects. Overall, these results support the interpretation that the observed multifractal behavior arises from a combination of mechanisms, whose relative influence varies across sequences and depends on their temporal organization.

The interevent time analysis showed that NVT sequences 1 to 4 are well described by a Lognormal distribution, while sequences 5 and 6 are better fitted by a Gamma distribution (Table 5). Although the Lognormal distribution provides the best fit for sequences 1 to 4, it can also occur in purely tectonic settings (Mesimeri et al., 2019), and thus its presence alone does not imply mixed tectonic-volcanic behavior. Our interpretation of “mixed behavior” is supported by additional indicators, including magnitude ranges, q-values, and variability in short- and long interevent times. Traversa and Grasso (2010) showed that a Gamma distribution mainly describes volcanic seismicity, although some episodes deviate from it, while purely tectonic activity can be captured by Exponential, Gamma, or Lognormal distributions (Corral, 2006; Passarelli et al., 2015; Post et al., 2021). Our results align with both global (Mw≥7, Bantidi, 2022) and regional (0.1<Ml<5.1, Mesimeri et al., 2019) studies, where Lognormal distributions often provide the best description of interevent times. For sequences 5 and 6, the statistical preference for the Lognormal distribution is less clear, likely due to smaller sample sizes (Table 1), which increases uncertainty in the fits. Overall, the observed differences between down-dip and interplate coupling regions are consistent with this interpretation, with the Gamma distribution better explaining observations in the latter, likely reflecting the lower number of detected events.

Finally, the scaling relationship between tremor duration and magnitude for all NVT sequences exhibits substantial scatter. Although positive slope coefficients are consistently observed in log⁡(τ)=a+bMW, the low coefficients of determination (R2=0.03–0.34) indicate a weak dependence of duration on magnitude, in contrast to the more robust scaling observed for regular earthquakes. Part of this variability may be related to observational limitations, as tremors lack clear phase arrivals and their parameters (e.g., duration, magnitude, and amplitudes) are more difficult to constrain (Staudenmaier et al., 2019). However, the persistence of this scatter across all sequences, despite similar tectonic settings and depths, suggests that it is not primarily controlled by first-order structural differences. Instead, this weak scaling likely reflects the complex and heterogeneous nature of tremor generation. Consistent with previous studies (Schwartz and Rokosky, 2007), this behavior suggests that tremor duration and magnitude may be governed by partially independent processes, highlighting that NVT does not follow simple earthquake-like scaling relationships. Although the relationship between slow earthquakes and tectonic tremors is not fully understood, there is evidence that NVTs are modulated by slow dislocations on the plate interface (Villafuerte and Cruz-Atienza, 2017).

We investigated the statistical features of reported NVT sequences along the Mexican subduction zone, analyzing the Gutenberg-Richter relation, non-extensive statistics, and multifractal behavior of magnitude and interevent time series. The estimated b-values range from 1.25 to 2.42, consistent with previous reports worldwide, with the highest values observed in down-dip regions. In contrast, q-values are lower in these regions compared to coastal areas (1.39<q<1.65), in agreement with the inverse relationship between b and q proposed in previous studies (b=2(2-q)/(1-q)). Although quantitative differences exist, both approaches consistently indicate that higher b-values correspond to lower q-values. Both magnitude and interevent-time series exhibit multifractal behavior, similar to tectonic earthquakes. Our results show that the origin of this multifractality is not uniform across sequences, but rather arises from a combination of mechanisms whose relative importance varies. In several cases, the observed behavior is consistent with apparent multifractality associated with broad probability distributions, whereas in others, statistically significant deviations from surrogate data indicate contributions from long-range correlations and possible nonlinear dynamics. Overall, the results suggest that no single mechanism dominates and that the multifractal properties reflect the heterogeneous temporal organization of the sequences.

Most NVT sequences are well described by a Lognormal model, while a few are better fitted by a Gamma distribution. Although lognormal fits are common, they can also occur in purely tectonic settings; therefore, their presence alone does not imply mixed tectonic-volcanic behavior. Evidence from magnitude ranges, multifractal parameters, and interevent-time variability supports the interpretation of mixed statistical characteristics. These findings highlight the complex temporal patterns of NVT sequences and differences in clustering across regions. The relationship between tremor duration and magnitude, however, shows substantial scatter, resulting in weak scaling with low coefficients of determination. While positive scaling coefficients are consistently observed, their magnitudes remain poor predictors of tremor duration. Part of this variability may reflect observational uncertainties, as tremor signals lack clear phase arrivals and their parameters are difficult to constrain. Nevertheless, the persistence of this behavior across all sequences, despite similar tectonic settings and depths, suggests that first-order structural differences do not primarily control it. Rather, the weak correlation likely reflects the complex, heterogeneous nature of tremor generation, in which partially independent or multiscale processes may govern duration and magnitude.