Marked spatio-temporal point patterns, periodicity analysis and earthquakes: an analytical extension including hypocenter depth

Continuous technological growth and the corresponding environmental implications are triggering the enhancement of advanced environmental monitoring solutions, such as remote sensing. In this paper, we propose a new method for the spatial point patterns generation by classifying remote sensing images using convolutional neural network. To increase the accuracy, the training samples are extended by the suggested data augmentation scheme based on the similarities of images within the same part of the landscape for a limited observation time. The image patches are classified in accordance with the labels of previously classified images of the manually prepared training and test samples. This approach has improved the accuracy of image classification by 7% compared to current best practices of data augmentation. A set of image patch centers of a particular class is considered as a random point configuration, while the class labels are used as marks for every point. A marked point pattern is regarded as a combination of several subpoint patterns with the same qualitative marks. We analyze the bivariate point pattern to identify the relationships between points of different types using the features of a marked random point pattern.

Temporal clustering of tsunami sources is examined in terms of a branching process model. It previously was observed that there are more short interevent times between consecutive tsunami sources than expected from a stationary Poisson process. The epidemic‐type aftershock sequence (ETAS) branching process model is fitted to tsunami catalog events, using the earthquake magnitude of the causative event from the Centennial and Global Centroid Moment Tensor (CMT) catalogs and tsunami sizes above a completeness level as a mark to indicate that a tsunami was generated. The ETAS parameters are estimated using the maximum‐likelihood method. The interevent distribution associated with the ETAS model provides a better fit to the data than the Poisson model or other temporal clustering models. When tsunamigenic conditions (magnitude threshold, submarine location, dip‐slip mechanism) are applied to the Global CMT catalog, ETAS parameters are obtained that are consistent with those estimated from the tsunami catalog. In particular, the dip‐slip condition appears to result in a near zero magnitude effect for triggered tsunami sources. The overall consistency between results from the tsunami catalog and that from the earthquake catalog under tsunamigenic conditions indicates that ETAS models based on seismicity can provide the structure for understanding patterns of tsunami source occurrence. The fractional rate of triggered tsunami sources on a global basis is approximately 14%. Online Material: Figures of residual analysis for tsunami and earthquake catalogs.

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure. Many tests have been developed over recent years to test the similarity of certain types of spatial data, such as spatial point patterns, geostatistical data and images. This research proposes a generic spatial similarity test able to handle various types of spatial data, for example images (modelled spatially), point patterns, marked point patterns, geostatistical data and lattice patterns. A simulation study is done in order to test the method for each spatial data set. After the simulation study, it was concluded that the proposed spatial similarity test is not sensitive to the user-defined resolution of the pixel image representation. From the simulation study, the proposed spatial similarity test performs well on lattice data, some of the unmarked point patterns and the marked point patterns with discrete marks. We illustrate this test on property prices in the City of Cape Town and the City of Johannesburg, South Africa.

The main goal of this article is to decluster Iranian plateau seismic catalog by the epidemic-type aftershock sequence (ETAS) model and compare the results with some older methods. For this purpose, Iranian plateau bounded in 24°–42°N and 43°–66°E is subdivided into three major tectonic zones: (1) North of Iran (2) Zagros (3) East of Iran. The extracted earthquake catalog had a total of 6034 earthquakes (Mw > 4) in the time span 1983–2017. The ETAS model is an accepted stochastic approach for seismic evaluation and declustering earthquake catalogs. However, this model has not yet been used to decluster the seismic catalog of Iran. Until now, traditional methods like the Gardner and Knopoff space–time window method and the Reasenberg link-based method have been used in most studies for declustering Iran earthquake catalog. Finally, the results of declustering by the ETAS model are compared with result of Gardner and Knopoff (Bull Seismol Soc Am 64(5):1363–1367, 1974), Uhrhammer (Earthq Notes 57(1):21, 1986), Gruenthal (pers. comm.) and Reasenberg (Geophys Res 90:5479–5495, 1985) declustering methods. The overall conclusion is difficult, but the results confirm the high ability of the ETAS model for declustering Iranian earthquake catalog. Use of the ETAS model is still in its early steps in Iranian seismological researches, and more parametric studies are needed.

To test whether geophysical anomalies contribute to earthquake forecasts beyond the inherent clustering effects in seismicity, we develop a self and external excitation point‐process model by incorporating anomalies into the temporal Epidemic‐Type Aftershock Sequence (ETAS) model. The model is applied to earthquakes that occurred between 2001 and 2010 around the Kakioka (KAK) station in Japan, with two types of anomalies, ultralow frequency (ULF) magnetic anomalies and carbon monoxide (CO) anomalies, as external excitations. Results indicate that 14.33% of the earthquakes can be interpreted by the external excitation of anomalies. Proposed ETAS + ULF + CO model achieves an overall probability gain of 1,013.55 in forecasting 218 earthquakes compared to the purely temporal ETAS model. Statistical significance is assessed by fitting the same model to the same earthquake catalog but with randomized anomaly occurrence times, confirming that the performance improvement is not due to overfitting. These findings highlight the potential for enhancing short‐term earthquake forecasts using non‐seismic precursors, particularly when multiple precursors are combined.

The depth of seismicity preceding the 2010 Fimmvörðuháls and Eyjafjallajökull eruptions in South Iceland has implications for the interpretation of the magma plumbing system that was active prior to those eruptions. Significant discrepancies exist in the hypocentral depths reported by different studies of the same earthquakes beneath Eyjafjallajökull in early-mid March 2010. Reported depths range from 3 km to 12 km. We use both real earthquake data and synthetic tests to show that the dominant factor controlling the best-fit hypocentral depths beneath the Eyjafjallajökull glacier is the network configuration. Hypocentral depths of 6–12 km are obtained when only data from permanent seismometer stations operated by the Icelandic Meteorological Office are used, the closest of which is located 13 km from the epicentral zone. Inclusion of data from six temporary seismometer stations deployed around Eyjafjallajökull, all within 4–15 km of the epicentral zone, constrains earthquake depths to be shallower than ∼6 km. A lack of proximal stations on top of the glacier limits resolution of earthquake sources that are shallower than ∼4 km, even when data from the six temporary stations are included. The choice of two plausible distinct velocity models has only a second-order effect on inferred hypocentral depths. We suggest that the true depth of seismicity is ∼2–6 km, which coincides with the depth of inflating magmatic intrusions inferred from surface deformation at that time.

Geophysical monitoring of the geodynamic regime of the territory of Armenia is carried out including observations of the chemical composition of groundwater, changes in the stress-strained state of the earth’s crust and current seismicity. Hydrogeochemical effects of changing the stress-strained state of the medium as indicators of modern geodynamic processes have been revealed. Based on published data, the authors suggest that the nature of the manifestation of geochemical anomalies depends on the parameters of the forthcoming seismic event – magnitude (M) and epicentral distance (Δ). A map of the spatial-temporal distribution of deformations of the earth’s crust because of earthquakes over the past three years in the region has been compiled. The main components of ionic (Cl–, HCO3, SO4, Mg2 +, total mineralization) and gas (CO2) composition of mineral waters in comparison with seismicity in the earth’s crust are studied. A map of the distribution of earthquake epicenters in space and in time has been compiled. The obtained graph shows the hypocenters dependence of magnitude of earthquakes that occurred during the investigated period on the depth of hypocenters. Earthquake catalogue is using to plot earthquake recurrence. Statistical analysis of observational data showed that the most informative predictive characteristic is the dispersion of carbon dioxide content in water. According to the time series of concentrations of chemical indicators, the effects associated with the geodynamic regime of the earth’s crust of Central Armenia were determined. A map of the distribution of deformations in the earth’s crust of central Armenia was compiling taking into account the depths of the hypocenters of earthquakes.

The Epidemic Type Aftershock‐Sequences (ETAS) model is a point process representing the temporal activity of earthquakes in a certain geophysical region. A method for fast and accurate computation of the likelihood is suggested for the ETAS model. Double sums of variables in the logarithm of the likelihood function with respect to the earthquake occurrence data is reduce to a single sum by using the recursive relation of the integrands in the Gamma transformation of the modified Omori functions. Then the integral is computed in unusually high accuracy by using the Double Exponential transformation followed by an application of the trapezoidal rule with an equal mesh size. The computing run time is greatly improved to be proportional to the number of recorded earthquakesNcompared to the order ofN² for the naive computation method. The present numerical procedures put the parameter estimation of the ETAS model to practical use in large number of occurrence records.

Analysis of massive marked point patterns with stochastic partial differential equations

We applied the epidemic type aftershock sequence (ETAS) model, the two-stage ETAS model and the non-stationary ETAS model to investigate the detailed features of the series of earthquake occurrences before and after the M6.7 Hokkaido Eastern Iburi earthquake on 6 September 2018, based on earthquake data from October 1997. First, after the 2003 M8.0 Tokachi-Oki earthquake, seismic activity in the Eastern Iburi region reduced relative to the ETAS model. During this period, the depth ranges of the seismicity were migrating towards shallow depths, where a swarm cluster, including a M5.1 earthquake, finally occurred in the deepest part of the range. This swarm activity was well described by the non-stationary ETAS model until the M6.7 main shock. The aftershocks of the M6.7 earthquake obeyed the ETAS model until the M5.8 largest aftershock, except for a period of several days when small, swarm-like activity was found at the southern end of the aftershock region. However, when we focus on the medium and larger aftershocks, we observed quiescence relative to the ETAS model from 8.6 days after the main shock until the M5.8 largest aftershock. For micro-earthquakes, we further studied the separated aftershock sequences in the naturally divided aftershock volumes. We found that the temporal changes in the background rate and triggering coefficient (aftershock productivity) in respective sub-volumes were in contrast with each other. In particular, relative quiescence was seen in the northern deep zones that includes the M5.8 largest aftershock. Furthermore, changes in the b-values of the whole aftershock activity showed an increasing trend with respect to the logarithm of elapsed time during the entire aftershock period, which is ultimately explained by the spatially different characteristics of the aftershocks.

The Epidemic Type Aftershock Sequence (ETAS) model is a self-exciting point process which is used to model and forecast the occurrence of earthquakes in a geographical region. The ETAS model assumes that the occurrence of mainshock earthquakes follows an inhomogeneous spatial point process, with their aftershock earthquakes modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters, due to the complexity of the likelihood function and the difficulty in estimating an appropriate spatial mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model, which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process, and show how efficient parameter inference can be carried out using auxiliary latent variables. We demonstrate how our model can be used for medium-term earthquake forecasts in a number of geographical regions.

Understanding the conditions and mechanisms that produce earthquakes is of high scientific relevance. The central Southern Alps/Kā Tiritiri o te Moana of New Zealand is an active orogen that offers a unique opportunity to study the processes that drive seismogenesis. A new high‐quality, matched‐filter‐based microseismicity catalog has been constructed by following a fully automated detection and location process. The catalog spans from 2009 to 2020 with local magnitudes between −1.81 and 3.42. Our results indicate a seasonal pattern in earthquake occurrence, with a notable correlation between shallow‐depth earthquakes (6 km hypocentral depths) and large, mostly summer, rainfall events beneath three separate glaciers. We hypothesize that a combination of seasonal snowmelt and heavy rainfall events raises the water table during spring and summer, changing pore‐fluid pressure in the upper crust and triggering earthquakes. Our findings highlight the role of extreme rainfall and glacier dynamics in triggering shallow earthquakes, which can improve hazard assessment in the central Southern Alps/Kā Tiritiri o te Moana and similar alpine regions worldwide.

This paper investigates the shallow seismicity occurring in the Taiwan region during the 20th century using a stochastic declustering method that has been developed on the basis of the theory of the epidemic‐type aftershock sequence model. It provides a probability based tool to objectively separate the space‐time occurrences of earthquakes into a background and a clustering component. On the basis of the background and clustering seismicity rates, we discuss the correlation between the distribution of the cluster ratio and the regional seismotectonic structures. Specifically, we find that the areas of the highest clustering ratio correspond to the major strike‐slip fault traces in and around Taiwan. Additionally, in the Taiwan inland region, during the period 1960–1990, the outputs for the stochastically declustered catalogue show a clear quiescence in background seismicity preceding the recovery of activation and the occurrences of the 1999 Chi‐Chi earthquake of ML7.3, while the other active regions show stationary background activity. This could be interpreted as an effect of the aseismic slip in the Chi‐Chi rupture fault, whereby the inland region around the Chi‐Chi source becomes a stress shadow.

Numerous Tibetan lower-crustal and upper-mantle earthquakes, detected by Sn/Lg ratios, suggest crustal delamination or drip tectonics

Statistical analysis of seismicity in a wide region around the 1998 Mw 8.1 Balleny Islands earthquake in the Antarctic Plate