Non-volcanic tremor was first recognized in Japan in 2002, and since then it has been detected in subduction zones and transform faults around the world, from Cascadia to Taiwan to the San Andreas Fault. Unlike a regular earthquake, which releases energy in a sudden rupture lasting seconds, tremor is an emergent signal of long duration and low amplitude, composed of swarms of tiny low-frequency earthquakes stacked on top of one another. It tends to occur on the plate interface near the edges of locked regions, and it is closely associated with slow slip events, the silent cousins of large earthquakes that can shift the ground by centimeters over days or weeks without producing any shaking people would notice. Fluids released by the dehydration of the sinking plate are widely implicated in generating tremor, and the phenomenon often appears in regions of high pore-fluid pressure where the fault is weakened and slipping is easier.

The Mexican subduction zone is an ideal natural laboratory for studying this behavior. There, the Cocos and Rivera plates dive beneath the North American plate at convergence rates ranging from about 2.0 to 6.8 centimeters per year, and the geometry of the subducted slab changes dramatically along strike, from steep subduction beneath Jalisco to an almost subhorizontal slab beneath Guerrero and Oaxaca. The region also contains the Guerrero seismic gap, a 200-kilometer-long segment that has not produced a significant earthquake since 1911 and is capable of generating an event of magnitude 8.1 to 8.4 if it ruptures in a single blow. Tremor in this zone has been documented in Guerrero, Jalisco-Colima, and Oaxaca, at depths ranging from about 10 to 50 kilometers, both near the trench and far down-dip of the locked interface.

Rodríguez-Pérez and his colleagues assembled catalogs of six tremor sequences recorded between 2005 and 2019, drawing on data from temporary seismic networks such as the Mesoamerican Subduction Experiment, the Mapping the Rivera Subduction Zone project, and the Guerrero Seismic Gap project, as well as ocean-bottom seismometers deployed more recently. The events ranged in magnitude from minus 0.8 to 3.65, far below anything a person could feel, and the team analyzed their sizes and the intervals between them using three complementary statistical frameworks: the classic Gutenberg-Richter relationship, non-extensive statistical mechanics, and multifractal detrended moving average analysis.

The Gutenberg-Richter analysis produced one of the study’s clearest findings. The b-value, which describes the ratio of small events to large ones, ranged from 1.25 to 2.42 across the sequences, and its distribution was not random. The highest values, between 2.22 and 2.42, occurred in the down-dip portion of the plate interface beneath Guerrero, while the lowest values, between 1.25 and 1.41, appeared in the interplate coupling region closer to the trench. High b-values indicate a fault zone dominated by small slips, which may reflect greater fracturing or different stress and fluid conditions at depth. In the coupling region, by contrast, the tremor b-values were not so different from those of ordinary tectonic earthquakes on the Cocos plate, which typically fall between 0.8 and 1.3.

The non-extensive statistical analysis told a complementary story. This framework, developed for complex systems far from equilibrium, uses a parameter called the q-value to quantify the length scale of spatial interactions and the degree of instability in the system. The researchers found q-values ranging from 1.39 to 1.65, and, crucially, the q-value behaved in exactly the opposite way to the b-value: it reached its highest values in the interplate coupling region near the coast and its lowest values down-dip. A Monte Carlo analysis confirmed a strong negative correlation between the two parameters, with a mean Pearson coefficient of minus 0.94. High q-values in the coupling zone suggest greater stress heterogeneity associated with plate locking and asperity distribution, while the lower values down-dip reflect different pressure, temperature, and rock structure conditions in that environment.

Perhaps the most technically ambitious part of the study was the multifractal analysis of both magnitude and interevent-time series. The team found that tremor sequences exhibit multifractal structures remarkably similar to those observed in ordinary tectonic earthquakes, meaning that their fluctuations display a spectrum of scaling behaviors rather than a single one. By shuffling the data and generating surrogate time series that destroy temporal correlations while preserving their statistical distributions, the researchers could distinguish between apparent multifractality, which arises simply from broad probability distributions, and intrinsic multifractality, which reflects genuine nonlinear dynamics. The answer was not uniform: only one sequence showed clear intrinsic multifractality, four displayed apparent multifractality, and five gave inconclusive results, indicating that no single mechanism dominates and that the origin of the complexity varies from place to place.

The Hurst exponent, a measure of long-term memory in a time series, ranged from 0.65 to 1.06, with most sequences showing strong persistence above 0.95. Values above unity suggest a transition toward non-stationary behavior and should be interpreted with caution, but the overall picture is one of strong temporal correlations, meaning that tremor activity in the present is statistically linked to tremor activity far into the future. The authors suggest, cautiously, that these high correlations may reflect localized regions perturbed by fluids, though they emphasize that this interpretation remains speculative. Notably, the measured Hurst exponents are statistically comparable to those reported for regional seismicity and aftershock sequences in southern Italy, Taiwan, Greece, and the San Andreas Fault, hinting that ordinary earthquakes and tremor share a deep common structure in how their timing is organized.

When the team examined the intervals between tremor events, they found that most sequences were best described by a Lognormal distribution, with a Gamma distribution fitting better for two sequences in the coupling region. The Exponential distribution, which would imply purely random timing, fit worst in every case. The authors interpret this mixture as evidence of complex, mixed statistical characteristics, though they caution that a lognormal fit alone does not prove mixed tectonic and volcanic behavior, since it also occurs in purely tectonic settings. Meanwhile, the relationship between tremor duration and magnitude proved disappointingly weak, with coefficients of determination ranging from only 0.03 to 0.34. Unlike regular earthquakes, where duration scales robustly with size, tremor duration appears to be governed by partially independent processes, a finding that may reflect both the complex generation mechanism of tremor and the difficulty of measuring signals that lack clear phase arrivals.

For a region that sits atop one of the world’s most significant seismic gaps, these results carry real weight. Tremor marks the transition between creeping and locked segments of the plate interface, and understanding its statistical fingerprints helps clarify how strain energy accumulates and is released in the quiet intervals between great earthquakes. The work also demonstrates that the tools of modern statistical physics, from non-extensive entropy to multifractal analysis, can extract meaningful structure from signals that are barely above the noise floor. As ocean-bottom seismometers and denser networks continue to expand the tremor record along the Mexican coast, the statistical portrait drawn by this study offers a baseline against which future changes, and perhaps precursors to the next great rupture, may one day be recognized.

Subject of Research: Statistical properties of non-volcanic tremor sequences in the Mexican subduction zone

Article Title: Statistical characteristics of non-volcanic tremor distributions along the Mexican Subduction Zone

Article References: Statistical characteristics of non-volcanic tremor distributions along the Mexican Subduction Zone. (n.d.). https://doi.org/10.5194/se-17-803-2026

Image Credits: AI Generated

DOI: 10.5194/se-17-803-2026

Keywords: non-volcanic tremor, Mexican subduction zone, Guerrero seismic gap, b-value, Gutenberg-Richter law, non-extensive statistics, multifractal analysis, Hurst exponent, slow slip events, plate interface, seismic hazard, Cocos plate

The heart of the framework is the remote sensing ecological index, or RSEI, a composite measure first formulated in 2013 that blends four fundamental dimensions of ecosystem condition: greenness, captured by the normalized difference vegetation index; wetness, derived from the tasseled-cap wetness component; dryness, represented by the normalized difference built-up and soil index; and heat, measured as daytime land surface temperature. Rather than assigning arbitrary weights to these ingredients, the method uses principal component analysis to let the data itself determine how the indicators combine. The first principal component is mathematically re-oriented so that higher values always correspond to better ecological quality, then rescaled to a range from zero to one. In this study, that first component explained between roughly 72 and 90 percent of the variance in any given year, a remarkably strong signal for a single statistical axis.

What distinguishes the new work is not the index itself but the assembly line built around it. Annual satellite composites were generated in Google Earth Engine from MODIS surface reflectance and land surface temperature products, with pixels contaminated by cloud, cirrus, snow, ice or adjacent-cloud effects systematically excluded using the sensors’ native quality layers, a critical step in a high-altitude region where cloud and snow routinely obscure the surface. A hierarchical window-selection strategy, tuned to phenology and vegetation conditions, then produced clean annual mosaics at 500 metres for reflectance and 1 kilometre for temperature. From there, a chain of Python and ArcPy scripts runs the entire analysis: index construction, spatial statistics, trend testing, persistence diagnostics, trajectory modelling and driver analysis, all with publicly released source code and archived statistics so that any reader can reproduce the results by changing only file paths.

The analytical philosophy is deliberately layered, because each statistical tool answers a different question and none answers them all. Sen’s slope estimator measures the direction and magnitude of monotonic change, while the Mann-Kendall test determines whether that trend is statistically significant. But a time series can rise gradually, accelerate, or jump abruptly, so the framework adds trajectory modelling that fits linear, quadratic and step-change models to every pixel and selects the best form using the Akaike information criterion. The Hurst exponent then asks whether the observed tendency is historically persistent, self-reversing, or essentially random, with values above 0.5 indicating persistence and values below 0.5 suggesting a tendency toward reversal. Finally, Global and Local Moran’s I statistics map whether ecological quality is spatially clustered, and GeoDetector quantifies how much of the spatial variation is statistically associated with sixteen environmental and human-pressure variables.

Applied to Qinghai, the framework reveals a story told in four acts. From 2000 to 2005, ecological quality held in a period of stable adjustment. Between 2005 and 2010 came sustained improvement, followed by a phase of fluctuating degradation from 2010 to 2015, and then a strong recovery enhancement from 2015 through 2024. Across the full period, poor and fair conditions contracted while moderate-to-excellent conditions expanded, shifting the province’s ecological structure upward even though the broad spatial template stayed fixed. That template is striking: a persistent northwest-to-southeast gradient runs through every annual map, with the poorest conditions concentrated in the arid northwestern basins and the best conditions in the wetter southeast and its favourable mountain-valley systems.

The spatial statistics confirm that this organization is deeply structured. Global Moran’s I remained consistently high throughout the 25 years, indicating strong positive spatial autocorrelation, with clustering strengthening early in the record and weakening modestly toward the end. Local indicators of spatial association pin down the geography: Low-Low clusters of poor ecological quality persist in the northwest, High-High clusters of good quality anchor the southeast, and mixed High-Low and Low-High outliers mark ecological transition zones where conditions change sharply over short distances. Perhaps the most striking quantitative result comes from the trajectory analysis: 94.91 percent of the province followed positive trajectories over the 25 years, with abrupt, step-like improvements more common than smooth linear ones, while negative and neutral trajectories covered just 4.12 and 0.97 percent respectively.

The driver analysis adds crucial nuance. In areas of ecological improvement, precipitation was the dominant associated factor, with a GeoDetector q statistic of 0.764, followed by soil pH, potential evapotranspiration, temperature and elevation. In degraded areas, precipitation again led at 0.625, but the profile shifted toward climatic stress and human pressure, with potential evapotranspiration, temperature, road density and human footprint ranking prominently. The interaction detector showed that two-factor combinations always explained more variation than single factors alone, with precipitation paired with evapotranspiration, elevation or soil pH dominating in improving areas, and precipitation combined with road density standing out in degrading ones. The authors are careful to stress that these are statistical associations, not demonstrated causal effects, since the q statistic measures spatial correspondence rather than response direction.

The team is equally candid about the framework’s limits, and this transparency is part of its scientific value. RSEI inherits the sensitivities of its components: vegetation indices saturate in dense canopies and respond to short-term rainfall pulses, the wetness component is a spectral proxy rather than a direct water measurement, and built-up indices can confuse bare soil with construction. An alpine desert with naturally sparse vegetation will score low regardless of its ecological integrity. The 500-metre MODIS resolution, ideal for provincial time series, blends wetlands, rivers, mines and restoration patches into mixed pixels that dampen local extremes, which may partly explain why this study’s improvement figures diverge from finer-scale assessments in Sanjiangyuan National Park and the Qinghai Lake Basin. Annual min-max normalization also creates a moving reference frame, meaning year-to-year comparisons reflect a consistent procedure rather than a fixed absolute scale.

For land managers, the practical message is that surface condition, trajectory stability and intervention priority are separate questions. A high or rising RSEI identifies candidate areas for consolidation but does not guarantee resilience, while curved, reversing or locally degrading trajectories, particularly in alpine wetlands, arid margins and riparian corridors, deserve priority for high-resolution imagery and field verification. The fluctuating degradation of 2010 to 2015 is best read as a period of heightened ecological sensitivity, compatible with early-warning behaviour documented in drylands and alpine grasslands worldwide, though the study cannot determine whether any threshold was approached. Because the entire workflow is modular and open, with Google Earth Engine preprocessing scripts, Python pipelines and example data released through a public repository, the authors argue it can be transferred to other mountain, arid and semi-arid regions simply by redefining the study area, provided indicators and validation are recalibrated locally.

Ultimately, the study offers both a finding and a tool. The finding is that one of the world’s most ecologically fragile and strategically important regions, the water tower of Asia, has undergone a broad, nonlinear, spatially structured recovery over 25 years, driven in large part by hydrothermal conditions and supported after 2015 by a warmer, wetter climate and sustained conservation programmes. The tool is a template for monitoring such change honestly, separating what satellites can measure from what they can only suggest. Rising greenness on a plateau is not proof of restored function, and the authors themselves note that independent validation with biomass, soil, biodiversity and restoration-monitoring data remains the essential next step. Used as a screening and hypothesis-generating instrument rather than a verdict, this framework points toward a future where ecological recovery across vast, remote landscapes can be tracked continuously, transparently and reproducibly, one annual satellite composite at a time.

Subject of Research: Automated RSEI-based spatiotemporal assessment of ecological quality in Qinghai Province, China

Article Title: An automated framework for RSEI-based spatiotemporal assessment of ecological quality: a case study in Qinghai Province, China

Article References: Wanghe, K., Zhao, Z., Suo, N., Hu, F., Tong, C., Ahmad, S., Bosso, L., Dai, Y., Yao, D., Zhang, D., He, N., & Guo, X. (2026). An automated framework for RSEI-based spatiotemporal assessment of ecological quality: a case study in Qinghai Province, China. Environmental and Sustainability Indicators, 32, Article 101549. https://doi.org/10.1016/j.indic.2026.101549

Image Credits: AI Generated

DOI: 10.1016/j.indic.2026.101549

Keywords: remote sensing ecological index, Qinghai Province, Tibetan Plateau, Google Earth Engine, ecological quality monitoring, principal component analysis, Sen's slope, Mann-Kendall test, Hurst exponent, GeoDetector, spatial autocorrelation, ecological restoration

The study, conducted by Amaury de Souza of the Federal University of Mato Grosso do Sul and José Francisco de Oliveira Junior of Fluminense Federal University and the Federal University of Alagoas, focused on the capital cities of Midwest Brazil: Brasília, Goiânia, Cuiabá, and Campo Grande. The team drew on the TerraClimate dataset, a high-resolution global climate product with roughly four-kilometer spatial resolution, to extract monthly precipitation and actual evapotranspiration from 1958 to 2024. Crucially, the dataset contained no missing values, eliminating the need for gap-filling procedures that can introduce artificial structure into a time series. From these two variables, the researchers constructed what they call the Hydroclimatic Balance Index, or HBI — the difference between precipitation and actual evapotranspiration, accumulated over twelve months and standardized as a z-score.

The choice of actual evapotranspiration rather than potential evapotranspiration is what sets the HBI apart from its better-known cousin, the Standardized Precipitation Evapotranspiration Index, or SPEI. Potential evapotranspiration measures how much water the atmosphere would demand if supply were unlimited; actual evapotranspiration measures how much water is genuinely exchanged between the land surface and the atmosphere, constrained by soil moisture, vegetation dynamics, and land-surface feedbacks. In tropical continental environments where evapotranspiration is a major component of the hydrological cycle, that distinction matters. The authors stress that the HBI is not intended to replace established drought indices, but to complement them by capturing realized hydroclimatic conditions rather than atmospheric demand alone. As a benchmark, the team also computed the classic Standardized Precipitation Index at the twelve-month scale, SPI-12, which relies exclusively on rainfall.

Before turning to fractal analysis, the researchers established a rigorous statistical baseline. Linear regression of annual precipitation, evapotranspiration, and HBI series revealed only weak slopes with p-values all exceeding the five percent significance level and coefficients of determination that were vanishingly small. The non-parametric Mann-Kendall test, which operates on data ranks and is robust to the outliers that plague hydroclimatic records, told the same story: Kendall’s tau coefficients hovered near zero, confirming the absence of significant monotonic trends. The Pettitt change-point test, designed to detect abrupt structural shifts without assumptions of normality, found significant breakpoints only in the evapotranspiration series of Goiânia in 2001 and Cuiabá in 2009. By every conventional measure, the region’s climate looked stable — which is precisely what made the next set of results so striking.

That next step was Multifractal Detrended Fluctuation Analysis, or MFDFA, a technique developed by Kantelhardt and colleagues in 2002 that extends earlier methods for detecting long-range correlations in nonstationary signals. The procedure integrates the original series, divides it into segments of varying lengths, removes local polynomial trends from each segment, and then examines how fluctuation magnitudes scale with segment size. For a monofractal process, the generalized Hurst exponent h(q) remains constant regardless of the moment order q. For a multifractal process, h(q) varies systematically with q, revealing that small and large fluctuations obey different scaling rules — a hallmark of complex, intermittently organized systems. Rainfall, temperature, wind, and river flow have all been shown to behave this way, but multifractal assessments of drought indices in tropical continental settings have remained scarce.

The results were unambiguous. Across all four capitals, the generalized Hurst exponent declined systematically with increasing moment order, confirming genuine multifractal scaling in both SPI-12 and HBI-12 series. The Hurst exponent at q equals two ranged from approximately 0.87 to 1.11, values that indicate strong long-range dependence — a form of hydroclimatic memory in which wet and dry conditions cluster together rather than arriving randomly. Persistent systems of this kind are prone to drought clustering and prolonged anomalies, a property with direct implications for agriculture and hydropower in a region that anchors Brazil’s agricultural production and generates a substantial share of its electricity. The width of the singularity spectrum, denoted delta-alpha, served as the study’s measure of multifractal strength: values below 0.5 indicate weak multifractality, values between 0.5 and 1.0 moderate, and values above 1.0 strong.

The spatial patterns proved revealing. Brasília exhibited the weakest multifractality, with SPI-12 producing a narrow spectrum of just 0.194, though even there the HBI-12 spectrum widened to 0.517 when evapotranspiration entered the calculation. Goiânia showed strong multifractality for both indices, at 1.333 and 1.382 respectively, suggesting that rainfall variability alone already accounts for much of its complexity. The most dramatic contrasts emerged in Cuiabá and Campo Grande. Cuiabá jumped from weak multifractality under SPI-12 at 0.254 to strong multifractality under HBI-12 at 1.008, while Campo Grande surged from a moderate 0.755 to 1.488 — the strongest multifractal signature of any capital. In these locations, evapotranspiration processes, vegetation dynamics, soil moisture availability, and land-surface feedbacks amplify nonlinear fluctuations far beyond what precipitation alone can explain.

Perhaps the most consequential finding came from splitting the record into two sub-periods, 1958 to 1990 and 1991 to 2024. The recent period showed broader singularity spectra in several capitals, with Campo Grande reaching a delta-alpha of 1.938 and Cuiabá 1.341, indicating intensified intermittency and hydroclimatic heterogeneity in recent decades. Brasília, by contrast, showed a modest reduction, underscoring the spatially uneven character of the change. Spectral asymmetry values predominantly exceeded one, meaning that large-magnitude fluctuations — the extreme wet and dry events — contribute disproportionately to the multifractal organization. Yet throughout, generalized Hurst exponents remained above unity, confirming persistent long-range dependence across all cities and both periods. The intensification of variability, in other words, is happening within a persistently memory-laden system, a combination that favors clustering of extremes.

The contrast between the classical and fractal diagnoses carries a pointed message for drought monitoring. Linear regression, Mann-Kendall tests, and Pettitt analysis detected almost nothing, yet the multifractal framework revealed substantial structural variability, growing intermittency, and shifts in scaling behavior that no trend statistic could capture. The authors argue that hydroclimatic change in Central Brazil should not be judged solely by the presence or absence of monotonic trends; increasing persistence, enhanced intermittency, and greater scaling heterogeneity may be equally important indicators of environmental change. This resonates with a broader body of climate-complexity research showing that scaling diagnostics can expose structural variability invisible to conventional methods, particularly in regions governed by monsoon dynamics and land-atmosphere interactions.

The study’s implications extend beyond Brazil. The measured spectrum widths, ranging from roughly 0.19 to 1.94, are comparable to or exceed those reported for Mediterranean rainfall systems, Indian monsoon basins, African semi-arid regions, and East Asian monsoon domains — but the gap between precipitation-only and water-balance multifractality appears unusually large in Central Brazil, underscoring the outsized role of evapotranspiration in tropical continental hydroclimates. The authors acknowledge limitations: the analysis rests entirely on gridded TerraClimate data, which may smooth local extremes; only the twelve-month accumulation scale was evaluated; and causal attribution to land-use change, though plausible given the Cerrado’s rapid agricultural transformation, would require integration with remote sensing and land-cover datasets. Still, the core conclusion stands. Drought monitoring frameworks built on precipitation alone may systematically underestimate hydroclimatic complexity in monsoon-influenced tropical regions, and as warming and land-use change continue, complexity-based diagnostics may become essential tools for anticipating when quiet variability turns into visible crisis.

Subject of Research: Multifractal assessment of hydroclimatic variability and drought indices in Midwest Brazil

Article Title: Multifractal assessment of hydroclimatic variability in Midwest Brazil using the hydroclimatic balance index (HBI): a comparison with the standardized precipitation index (SPI)

Article References: de Souza, A., & de Oliveira Junior, J. F. (2026). Multifractal assessment of hydroclimatic variability in Midwest Brazil using the hydroclimatic balance index (HBI): a comparison with the standardized precipitation index (SPI). Theoretical and Applied Climatology, 157(10), Article 682. https://doi.org/10.1007/s00704-026-06467-6

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06467-6

Keywords: multifractal analysis, MFDFA, drought, hydroclimatic variability, Brazil, Cerrado, evapotranspiration, Standardized Precipitation Index, Hurst exponent, TerraClimate, South American Monsoon, water balance