Background Seismicity Highlights Tectonic Asperities

Abstract

The heterogeneity of a tectonic fault interface controls both the spatial features of seismicity and the locations of the foci of shallow earthquakes. Strong earthquakes are associated with ruptures of asperities. We present the Seismogenic Patches Detection (SPAD) algorithm to analyze background seismicity to reveal tectonic asperities. In the first stage, the algorithm detects background seismicity based on the nearest-neighbor method. In the second stage, fuzzy clustering of the background mode is performed. Dense clusters of background seismicity, called seismogenic patches, can be interpreted as tectonic asperities. The SPAD algorithm does not use a priori data about the localizations of strong earthquakes. Using SPAD, we analyzed the seismicity of the Kamchatka segment of the Kuril–Kamchatka subduction zone for the period from 1 January 1990 to 23 September 2025. The Kamchatka regional seismic catalog includes 39,104 events, and the magnitude of completeness Mc equals 3.0. We have identified seven seismogenic patches with a size of 170–270 km. Seismogenic patches correlate with the tectonic asperity determined by the maps of the slip distributions for the four largest earthquakes—Mw7.5 (8 June 1993), Mw7.8 (5 December 1997), Mw8.8 (30 July 2025), and Mw7.8 (13 September 2025).

1. Introduction

Spatiotemporal clustering of seismicity is the main feature of the seismic process that allows us to construct models for earthquake forecasting [1,2,3]. A statistical approach alone is not sufficient for improving earthquake forecasting [4]. A multilevel and multidisciplinary approach that considers the physical basis of the process is needed to expand our resources in the earthquake forecasting.

The most seismically active zones are subduction zones. Early investigations hypothesized that the maximum earthquake size is controlled by the fast convergence rate and the young buoyant lithosphere [5,6]. However, Bletery et al. [7] reported that two geological conditions (a fast convergence rate and young buoyant lithosphere) are not required to produce large earthquakes; large earthquakes preferentially rupture flat (low curvature) interfaces. Relatively high curvature can likely result in the absence of sources of major earthquakes at 600 km from the Kuril–Kamchatka subduction zone (KKSZ) to the south from N 49° (Figure 1). McCaffrey [8] suggested that any subduction zone can produce an earthquake with Mw ≥ 9. So, there is no full understanding of the nucleation and rupture of major earthquakes.

The asperity model is the predominant one for explaining the nature of earthquakes [9]. Tectonic asperities emerge at a fault interface because of the curvature of its sides. Curvature is an important structural feature of tectonic faults; the fault plane is characterized by different-scale roughness [10,11,12,13]. Originally, the asperity model was essentially a model of heterogeneous stress along a fault interface, and an asperity was assumed to have a high friction coefficient [14,15]. The size, configuration and distribution of asperities primarily determine the location of earthquakes.

The rheology of tectonic faults plays one of the most important roles in their slip behavior [16,17,18]. A modern model of asperity suggests that it shows not only high-friction but also velocity-weakening (VW) behavior. At the same time, relatively unloaded zones between asperities, as a rule, have low-friction and velocity-strengthening (VS) behavior [19]. The spatial heterogeneity of rheological properties can be traced at different scales [17,20]. An earthquake rupture is predetermined by the rheological and structural features of the fault interface [21,22,23,24,25]. Ordinary earthquakes usually nucleate in zones where VW prevails, whereas in zones where vs. prevails, slow-slip events and swarms of weak seismic events with low radiative efficiency usually occur [26,27,28]. The coseismic rupture starts at the boundary of asperity with VW behavior. The velocity of rupture decreases rapidly in the VS zones and increases again in the neighboring asperity. If the distance between asperities is large enough, the rupture stops [22,29,30,31].

Tectonic asperities concentrate a slip deficit that slowly increases during interseismic periods and is ultimately released through large earthquakes. Interseismic coupling, which represents the percentage of slip deficit with respect to the long-term tectonic loading of a fault, can be calculated from GPS data [32,33,34]. Near an asperity, which is a locked segment of a fault in the interseismic period, the seismic coupling is close to 1. In aseismic creeping segments, the coupling is small [35]. Unfortunately, no threshold coupling value is suggested to correspond to the spatial extent of tectonic asperity and, consequently, earthquake rupture. The geometrical complexity of fault rupture can be captured by an inversion of strong motion data [36,37] or the joint inversion of seismic and geodetic data [38,39]. The areas of maximum displacement are the tectonic asperities in the maps of coseismic displacement. As a rule, an earthquake source embraces an area of one asperity, but cases in which a rupture, starting at an asperity, can spread to neighboring areas, are known [40]. The sources of the strongest mega-earthquakes can embrace three or even more tectonic asperities [41,42,43].

Analyzing weak seismicity allows an improved understanding of the physics of the processes that take place in zones of strong earthquake nucleation and reveals the structures of fault interfaces [44,45,46,47,48]. Seismic data should be considered based on the current understanding of fault structure and mechanical processes that take place in fault zones [18,49]. We developed and tested the SPAD algorithm for the analysis of background seismicity to determine the long-term structure of the subduction boundary. By using the example of seismicity in the Kuril–Kamchatka subduction zone (KKSZ), we showed that the SPAD algorithm allows us to reveal the zones of tectonic asperity localization well in advance, not after a strong earthquake.

2. Geological Frameworks

A vast majority of global seismicity is located inside the circum-Pacific subduction zone. Earthquakes with magnitudes exceeding 8.5 have been registered in the Chile subduction zone (1960, Mw9.5), Japan (2011, Mw9.1) and Alaska (1964, Mw9.3) [50,51,52]. There is some information about the great historical earthquakes in Kamchatka (1952, Mw9.0) and Ecuador (1906, M8.6) [50,53]. The shallow megathrusts of subduction zones host the largest earthquakes. These faults are the only faults capable of Mw ≥ 9 ruptures.

In Kamchatka, all attributes of active subduction are clearly exhibited, including a well-established ocean trench, deep seismicity in the Benioff zone, and a continuous arc characterized by a chain of Holocene volcanoes [54]. KKSZ extends for approximately 2100 km from Hokkaido Island in Japan, along the Kuril Islands and the Pacific coast of the Kamchatka Peninsula, until it intersects the Aleutian arc near the Commander Islands (Figure 1) [55]. The Pacific oceanic plate subducts beneath the Okhotsk continental plate, and along the Kamchatka segment, the subduction angle remains nearly constant—approximately 55° between N50° and N55° [56]. Farther north, the angle decreases to approximately 35° [57]. Plate convergence occurs almost perpendicularly to the strike of the Kamchatka trench, resulting in minor active deformation inside the arc [58]. Nevertheless, the velocity of the downgoing Pacific plate varies from about 77 mm/yr at N55° to 83 mm/yr at N47° [59,60]. The age of subduction for the KKSZ increases from north to south in the range of the northern latitudes of N50°–N56° from 77 to 104.5 million years [57]. The seismicity of the KKSZ has been investigated for more than a hundred years. Fedotov [61] sets a 17-year effective period of repetition of the strongest earthquakes and their harmonics. Based on instrumental and historical data, the average duration of the seismic cycle between two consequent earthquakes with magnitudes of M ≥ 7.7 at a particular location is about 140 ± 60 years or 120 ± 50 years [62]. In the range of northern latitudes from N50° to N56°, the maximum depth of earthquakes decreases from 500 km to 100 km [57]. The Kamchatka segment ruptured during seven earthquakes with M > 7.5 in the 20th–21st centuries, and the largest earthquake was the Mw9.0 earthquake in 1952 [63,64].

3. Seismic Data

In this work, we use the regional seismic catalog of the Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences, which contains information about 39,104 seismic events for the period of instrumental seismic observations from 1990 to 2025 (available online https://sdis.emsd.ru/info/earthquakes/catalogue.php (accessed on 8 January 2026)). Most of the stations of the network are installed in the Kamchatka Peninsula. The hypocenter locations for earthquakes in the shallow part of the Benioff zone are subject to significant trade-offs between the lateral position and depth, with errors in the latter reaching a few tens of kilometers [65]. The completeness Mc of the seismic catalog was calculated according to the method of maximum likelihood and equaled 3.0 [66]. The magnitude-frequency distribution is as follows [67]:

$$\log N\left[{year}^{-1}\right]=7.25-0.93·M.$$

(1)

Figure 2 shows a map of the seismicity of the Kamchatka region. The earthquake distribution clearly traces the architecture of the subduction interface. The distribution of seismicity is essentially heterogeneous in space. One can see that both areas have concentrated epicenters and areas with a set of diffuse points. Seven earthquakes with magnitudes Mw > 7 occurred during the period from January 1990 to July 2025 in the zone under consideration (above N48°). They all localized along the entire length of the Kamchatka trench. In the region of the Kamchatka Peninsula and the Kuril Islands, at depths of 1–70 km, thrust and oblique-thrust fault slips are predominantly observed in earthquake foci. For these events, the azimuths of the compression axes (P)—indicating the direction of maximum stress—range from 90° to 150°, with the axes dipping to the south-east relative to the Earth’s surface. This orientation is consistent with the azimuthal direction of the displacement of the Pacific Plate [68].

In the following study, we analyze earthquakes localized within a slab with M ≥ Mc. We used the subduction zone geometry model Slab2 [69], and all the hypocenters confined to the slab were projected to its upper boundary. In total, 22,011 events from the original 39,104 seismic events were included.

4. SPAD Algorithm

The SPAD algorithm rests on the following physical concepts. Any fractured rock mass showing VW emits seismic vibrations during structural changes, and the scale of the process governs the magnitudes of seismic events [70,71]. The evolution of the stress state of an asperity continues in time, so the structural features of the interface should appear in the seismicity.

Fault interface heterogeneity can be traced at different scale levels [17,20,72,73], and some events can be triggered in the areas between asperities. The grouping of events should be observed regardless of the time of observation (timeless feature), since it is determined precisely by the localization of asperities. Since an asperity is assumed to have a fractal (self-similar) structure, dense sets of earthquakes are formed in the vicinity of asperity [74,75]. To analyze the structural timeless features of the fault interface, it is necessary to exclude events caused by foreshock and aftershock activities, as well as seismic swarms.

The SPAD algorithm includes three stages, which rest on the available ideas about the physical and geometrical peculiarities of the fault interface:

• Declustering of the seismic catalog and detection of background seismicity.
• Fuzzy clustering of background seismicity.
• Mapping seismogenic patches.

4.1. Background Seismicity

The declustering of the catalog was performed via the calculation of the nearest-neighbor distance in the time–space–magnitude domain. For any two earthquakes i and j, we define the proximity function [76]:

$${\eta }_{ij}=\left\{\begin{array}{c}{t_{ij}\left(r_{ij}\right)}^{d_f}{10}^{-{bM}_i},t_{ij}>0\\ +\infty , t_{ij}\le 0\end{array} \right.,$$

(2)

where $t_{ij}$ and $r_{ij}$ are the earthquake intercurrence time and the distance between earthquakes, respectively; M_i is the magnitude of event i; b is the scale parameter of the magnitude-frequency distribution (Equation (1)); and d_f is the fractal dimension of the earthquake spatial distribution. The nearest neighbor η* for a given event j is ${\eta }^{*}=\mathit{min}({\eta }_{ij},\hspace{0.33em}i<j)$. Additionally, for excluding aftershocks, we deselect earthquakes with magnitudes smaller than M, which are within a 0.02 × 10^0.5M km radius circle during the first 0.04 × 10^0.55M days after a magnitude M event [77].

The distributions of the nearest-neighbor distance ${\eta }_{ij}^{*}=T_{ij}{R}_{ij}$ and its components ($T_{ij}={\tau }_{ij}10^{-b{M}_i/2}$, $R_{ij}={r_{ij}}^{d_f}10^{-b{M}_i/2}$) are shown in Figure 3. The distributions are prominently bimodal, revealing the existence of two statistically distinct earthquake populations. The 2D distributions of the spatial and temporal components of ${\eta }_{ij}^{*}$ clearly separate the two modes. The distribution of the nearest-neighbor proximity function may be considered a Gaussian mixture model with two modes, and the best boundary between modes is η₀ = −1.72 [78]. The bimodality of the distribution of the nearest-neighbor proximity function allows us to formally attribute each event to either the background (${\eta }_{ij}> {\eta }_0$) or cluster (${\eta }_{ij}< {\eta }_0$) modes (Figure 3a).

The spatial localization of background seismicity shows severe inhomogeneity (Figure 4). At the same time, the populations of background and clustered modes localize in the same areas, and the distributions of the pairwise distances between events of two modes are similar. The characteristic values of the distribution peaks are 85–100 km (Figure 4c).

Localization of background seismicity is timeless and highlights structural features of the fault interface. According to geological studies, large-slip surfaces are smooth, elongated, and quasielliptical bumps, and the geometry of the fault surface predetermines the tectonic asperity configuration [9,10,79]. As clustered seismicity is localized in the vicinity of tectonic asperities, the characteristic peak in the distribution of pairwise distances of both clustered and background seismicity should correspond to the wavelength of bumps and the characteristic distance between tectonic asperities.

4.2. Fuzzy Clustering

Any fault surface is rough at wavelengths up to tens of kilometers [12], and earthquake locations may be used to probe fault surface roughness [80]. The fractal character of fault roughness must determine that background seismicity forms dense clusters of events. To reveal spatially dense clusters, we applied a Discrete Perfect Sets (DPS) algorithm related to fuzzy clustering [81]. The algorithm filters the original space by singling out its densest subset against a general background. The algorithm is described in detail in the work of [82]. The DPS algorithm considers the nonhomogeneity of the event distribution and was used to analyze seismicity [83,84].

The DSP has two free parameters: the index q < 0 to calculate the radius of localization and the parameter $\beta \in \left[-1, 1\right]$, which represents the maximum level of the required density of detected DPS clusters. For a set of recognition objects (epicenters of background seismicity) W, the radius of localization is determined as

$$r_q\left(W\right)={\left({\displaystyle \frac{\sum _{d\in D\left(W\right)}{d}^q}{\left|D\left(W\right)\right|}}\right)}^{1/q}$$

(3)

where d is the Euclidean distance, and $\left|D\left(W\right)\right|$ is the number of nontrivial pairwise distances in the set of recognition objects D(W):

$$D\left(W\right)=\left\{d\left(w_1,w_2\right):w_1,w_2\in W,d\left(w_1,w_2\right)\ne 0\right\},$$

(4)

where w is a point in W. For a specified radius of location r, the density of an arbitrary subset A ⊆ W at point w ∈ W is defined as the sum of the weights of the points localized in the r-neighborhood $B_A\left(w,r\right)$:

$$P_A\left(w\right)={\sum }_{\xi \in B_A\left(w,r\right)}\left(1-{\displaystyle \frac{d\left(w,\xi \right)}{r}}\right).$$

(5)

The determination of the density level rests on a fuzzy comparison. The measure of comparison of the densities $P_W\left(W\right)$ of the set W at all its points w ∈ W with values of the density level α is defined as follows [82]:

$$n\left(P_W\left(W\right),\alpha \right)=〈{\displaystyle \frac{P_W\left(W\right)-\alpha }{\max \left(P_W\left(W\right),\alpha \right)}}〉.$$

(6)

The parameter β defines the maximality level of density P against the background of W. The maximality level β uniquely determines the level of density α:

$$n\left(P_W\left(W\right),\alpha \right)=\beta$$

(7)

If two parameters q and β are defined, then the DPS algorithm allocates clusters as its own subsets to the set of recognition objects W and builds a set $\left\{B_1,...,B_n\right\}$, whose density is not less than α at its points:

$$DPS\left(q,\beta \right):W\left(\alpha \right)\to \left(B_1,...,B_n\right)$$

(8)

Applying the DPS algorithm to analyze seismicity implies expert assignment of parameters q and β. Considering the physical aspects of seismicity localization on the fault interface, we can avoid ambiguity in defining the spatial location and number of dense sets. Two physically based conditions must be applied to find a unique solution:

• Since earthquake localization is predetermined by asperities with fractal roughness at the km scale, one should select a configuration, out of all the possible configurations, for which the number of clusters and the number of events in these clusters are maximized. This configuration of dense sets best represents the current state.
• If there are several configurations with identical numbers of dense clusters and events in the clusters, the optimal configuration is determined via the analysis of pairwise distances between events in dense clusters. Dense clusters localize in zones of tectonic asperity localization; hence, the characteristic distance between events, which form dense sets, should correspond to the maximum distribution of distance between all the background events (Figure 4c).

Based on the analysis of the full seismic catalog (up to January 2025), 2233 local dense sets were detected in the Kamchatka segment; these sets represent 44% of the background mode (Figure 5a).

4.3. Mapping Seismogenic Patches

Dense sets should be spatially grouped to determine large-scale structural objects—seismogenic patches—which are areas of background seismicity concentration (Figure 5). We used a clustering algorithm based on the construction of the minimal spanning tree in the Euclid metrics [85]. The level of the dendrogram, at which the dense sets are divided into separate space clusters, corresponds to the peak of the distribution of earthquake pairwise distances (Figure 4c). The area where all the dense sets of separate clusters are localized is the seismogenic patch.The contours of the patch are defined as the least convex polygons that embrace all epicenters of the clusters [86].

The configuration of the seismogenic patches becomes apparent at time intervals beginning at 5 years. In short time intervals, the configuration and size of seismogenic patches change significantly; however, the localization of the patches remains unchanged. At time intervals of 15 years or longer, the relative change in the area of seismogenic patches does not exceed 10% of the asperity area. The localization and configuration of seismogenic patches are preserved, i.e., the seismogenic patches are timeless features of background seismicity. Seven seismogenic patches are detected along the Kamchatka segment of the KKSZ. Their characteristic sizes, L, vary from 170 km to 270 km. These sizes correspond to earthquake sources with magnitudes ranging from 7.8 to 8.2 [87].

5. Localization of the Strongest Earthquakes

An analysis of the seismicity along the Kamchatka segment of the KKSZ shows that epicenters of strong earthquakes are distributed along the entire Kamchatka segment. A total of 13 out of 16 strong earthquakes before 1990 and 7 out of 8 after 1990 were localized within the patches (Figure 6). Notably, these events were not considered when detecting seismogenic patches because they were removed during declustering via the nearest-neighbor method. It is worth mentioning that the maximum magnitude of background mode is 6.3.

The foci of strong earthquakes are large, and hypocenters point to only the starting point of tectonic asperity rupture. The configuration of tectonic asperities is revealed retrospectively by the inversion of seismic and/or geodetic data. At the same time, the configuration of tectonic asperities controls earthquake nucleation and failure processes. Scenarios of earthquake rupture evolution suggest the rupture of both a single asperity and several neighboring asperities synchronously [9,89,90].

Since seismogenic patches are a timeless feature of the fault interface, we assume that seismogenic patches are, in fact, seismic sketches of tectonic asperities. To support this supposition, we compared a map of seismogenic patches with the slip inversion models of the strongest earthquakes (Figure 7).

There are four earthquakes in the Kamchatka segment of the KKSZ, for which maps of the slip inversion models are available (

Table 1. List of the earthquakes Mw ≥ 7.5 of the Kamchatka segment with available slip distribution on the fault plane.

No.	Data	Magnitude, Mw	Source
1	8 July 1993	7.5	https://earthquake.usgs.gov/earthquakes/eventpage/usp0005u7b/finite-fault (accessed on 8 January 2026)
2	5 December 1997	7.8	https://earthquake.usgs.gov/earthquakes/eventpage/usp0008btk/finite-fault (accessed on 8 January 2026)
3	29 July 2025	8.8	[91]
4	13 September 2025	7.5	https://earthquake.usgs.gov/earthquakes/eventpage/us7000qx2g/finite-fault (accessed on 8 January 2026)

). Earthquakes have a complex source structure, and several maxima in the slip distribution can be detected. The maxima of slip distribution for earthquakes 1 and 4 (Table 1) are localized in different sections of KKSZ within the separate patches. The 1997 Kronotsky earthquake is characterized by two distribution maxima, which are localized on neighboring patches. For the 2025 megaearthquake, there are three maxima that are localized within three different patches near their contours to the south of 52° N.

6. Discussion

When the physics of a process is uncertain, machine-learning algorithms demonstrate high efficiency [92,93]. The developed SPAD algorithm aimed at studying features of seismicity allows us to better define the geometry and heterogeneity of the subduction interface and to unambiguously contour the tectonic asperity of major earthquakes. The SPAD algorithm is based on unsupervised learning and does not use a priori data about the localization of strong earthquakes. To avoid ambiguity in detecting seismogenic patches, we introduce two criteria, which account for the physics of the process and the geological structure of the tectonic fault. It is thought that changes in the stress-strain state of tectonic asperity take place without the emission of seismic vibrations, which formally results in the occurrence of seismic gaps [94,95]. This statement was true when seismic arrays could not register earthquakes with magnitudes less than 4, but from the point of view of rock friction, it is false. When the background seismicity is reliably recorded (the magnitude of background seismicity is essentially lower than the magnitude of the main event), the seismic gap should be interpreted as a lack of strong earthquakes but not as a complete absence of seismicity. The main part of seismic events is concentrated in the zones of asperities. The background seismicity shows the timeless structural features of a tectonic fault and reflects the different-scale roughness of tectonic faults. The structure of asperities has been preserved for tens of years. We showed that large-scale roughness controls asperity spacing (Figure 7). At small scales, it manifests via the fractality and self-similarity of asperities [11,12,75]. An analysis of waveforms of seismic events confined to the Japan Trench in the Naka district revealed that all earthquakes with magnitudes ranging from 2 to 5, whose hypocenters are in a small neighborhood, were characterized by identical wave onset times, while the time interval between events was approximately 15 years [96].

Algorithms for detecting earthquake-prone areas are aimed at identifying zones where strong earthquakes can occur [97,98]. As a rule, algorithms are based on supervised learning, which means that they use information about previous strong earthquakes. A distinctive feature of the SPAD algorithm is the construction of a map of tectonic asperities, which can define the configuration of the earthquake source and the dynamics of fault rupture [99]. We have shown that zones where strong earthquakes nucleate can be detected via an analysis of background seismicity when there is no prior information about the localization of strong earthquakes. Seismogenic patches are sketchy displays of tectonic asperities. For the Kamchatka subduction zone, we can unambiguously say that we realize the configuration and sizes of tectonic asperities.

Revealing the map of tectonic asperities based on the physical aspects of fault evolution improves our understanding of earthquake nucleation and failure processes. The SPAD method can be used to prognosticate possible earthquake scenarios. In the future, if the accuracy of the location remains high enough, it is reasonable to perform estimations of the interface roughness [80], which controls the earthquake size and the stress drop on a tectonic asperity [13]. The Kamchatka earthquakes have shown that each tectonic asperity may independently rupture many times before it can rupture with neighboring asperities [33,100]. The synchronization of a rupture of two or more asperities is a challenge for assessing the geodynamic hazard, and thus far, it is uncertain.

7. Conclusions

We present a new technique, SPAD, to infer tectonic asperities at the subduction interface. SPAD does not use any information about strong earthquakes or any expertly specified parameters, and the identified seismogenic patches should be associated with tectonic asperities. The physical parameterization of subduction interface can be used to prognosticate earthquake scenarios.