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This paper presents a new technical method for computing calendar time forecasts in a local area for large earthquakes of a target magnitude MT using a count small earthquakes MS < MT in the area, together with the Gutenberg-Richter (GR) magnitude-frequency relation. The GR relation states that for every large target earthquake of magnitude greater than MT , there are on average NGR small earthquakes of magnitude MT > M >= MS. The only assumption is that the GR statistics of the local area are the same as in the larger surrounding regions. This assumption is used to construct an ensemble of earthquakes in larger surrounding regions to be used in computing the forecast. The method has significant skill, as defined by the Receiver Operating Characteristic (ROC) test, which improves as time since the last major earthquake increases. The probability is conditioned on the number of small earthquakes n(t) that have occurred since the last large earthquake. There is no need to assume a probability model, as the probability is instead computed directly as the Positive Predictive Value (PPV) associated with the ROC curve. The method is validated by comparison to the UCERF3 forecast

We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as \~10^(Dm/2). The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future event as well as earthquake triggering. If earthquake magnitudes follow the Gutenberg-Richter law with b>D/2, small earthquakes collectively dominate stress transfer and earthquake triggering, because their greater frequency overcomes their smaller individual triggering potential. Using a Southern-California catalog, we observe that the rate of seismicity triggered by an earthquake of magnitude m increases with m as 10^(alpha m), where alpha=1.00+-0.05. We also find that the magnitude distribution of triggered earthquakes is independent of the triggering earthquake magnitude m. When alpha=b,

The Himalayan region, including Nepal, is prone to frequent and large earthquakes. Accurate forecasting of these earthquakes is crucial for minimizing loss of life and damage to infrastructure. In this study, we propose various time-scaled Epidemic Type Aftershock Sequence (ETAS) models to forecast earthquakes in Nepal. The ETAS model is a statistical model that describes the temporal and spatial patterns of aftershocks following a main shock. A dataset of earthquake occurrences in Nepal from 2000 to 2020 was collected, and this data was used to fit the models showcased in this article. Our results show that the time-scaled ETAS model is able to accurately forecast earthquake occurrences in Nepal, and could be a useful tool for earthquake early warning systems in the region.

This study presents a pilot investigation into a novel method for reconstructing real-time ground motion during small magnitude earthquakes (M < 4.5), removing the need for computationally expensive source characterization and simulation processes to assess ground shaking. Small magnitude earthquakes, which occur frequently and can be modeled as point sources, provide ideal conditions for evaluating real-time reconstruction methods. Utilizing sparse observation data, the method applies the Gappy Auto-Encoder (Gappy AE) algorithm for efficient field data reconstruction. This is the first study to apply the Gappy AE algorithm to earthquake ground motion reconstruction. Numerical experiments conducted with SW4 simulations demonstrate the method's accuracy and speed across varying seismic scenarios. The reconstruction performance is further validated using real seismic data from the Berkeley area in California, USA, demonstrating the potential for practical application of real-time earthquake data reconstruction using Gappy AE. As a pilot investigation, it lays the groundwork for future applications to larger and more complex seismic events.

Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock, previous studies have suggested that mainshocks can also trigger earthquakes in remote locations. Here we examine the earthquake rate in the days following mega-earthquakes (magnitude >= 7.5) and find that the rate is significantly lower beyond a certain distance from the epicenter compared to surrogate data. However, the remote earthquake rate after the strongest earthquakes (magnitude >= 8) can also be significantly higher than that of the rate based on surrogate data. Comparing our findings to the global ETAS model, we find that the model does not capture the earthquake rate found in the data, hinting at a potential missing mechanism. We suggest that the diminished earthquake rate is due the release of global energy/tension subsequent to substantial mainshock events. This conjecture holds the potential to enhance our comprehension of the intricacies governing post-seismic activity.

The recent exploitation of natural resources and associated waste water injection in the subsurface have induced many small and moderate earthquakes in the tectonically quiet Central United States. This increase in seismic activity has produced an exponential growth of seismic data recording, which brings the necessity for efficient algorithms to reliably detect earthquakes among this large amount of noisy data. Most current earthquake detection methods are designed for moderate and large events and, consequently, they tend to miss many of the low-magnitude earthquake that are masked by the seismic noise. Perol et. al (2018) has focused on the problem of earthquake detection by using a deep-learning approach: the authors proposed a convolutional neural network (ConvNetQuake) to detect and locate earthquake events from seismic records. This reports aims at reproducing part of the methodology proposed by the author, which is the implementation of a convolutional neural network for classification of events (i.e., earthquake vs. noise) from seismic records.

The exact mechanisms leading to an earthquake are not fully understood and the space-time structural features are non-trivial. Previous studies suggest the seismicity of very low intensity earthquakes, known as micro-earthquakes, may contain information about the source process before major earthquakes, as they can quantify modifications to stress or strain across time that finally lead to a major earthquake. This work uses the history of seismic activity of micro-earthquakes to analyze the spatio-temporal statistical independence among the monitoring stations of a seismic network. Using point process distance measures applied to the micro-earthquakes' spike trains recorded in these stations, a pre-earthquake state is defined statistically with the aim of finding a relation between the level of dissimilarity among stations' readings and the future occurrence of larger earthquakes in the region. This paper also addresses the compatibility of this statistical approach with the Burridge-Knopoff spring-block physical model for earthquakes. Based on the results, there is evidence for an earthquake precursory state associated with an increase in spike train dissimilarity as evaluated by

Unfortunately, working scientists sometimes reflexively continue to use "buzz phrases" grounded in once prevalent paradigms that have been subsequently refuted. This can impede both earthquake research and hazard mitigation. Well-worn seismological buzz phrases include "earthquake cycle," "seismic cycle," "seismic gap," and "characteristic earthquake." They all assume that there are sequences of earthquakes that are nearly identical except for the times of their occurrence. If so, the complex process of earthquake occurrence could be reduced to a description of one "characteristic" earthquake plus the times of the others in the sequence. A common additional assumption is that characteristic earthquakes dominate the displacement on fault or plate boundary "segments." The "seismic gap" (or the effectively equivalent "seismic cycle") model depends entirely on the "characteristic" assumption, with the added assumption that characteristic earthquakes are quasi-periodic. However, since the 1990s numerous statistical tests have failed to support characteristic earthquake and seismic gap models, and the 2004 Sumatra earthquake and 2011 Tohoku earthquake both ripped through several supposed

Physical phenomena observed before strong earthquake have been reported over centuries. Radon anomalies, electrical signals, water level changes, earthquake lights near the epicenter are recognized as pre-earthquake signals to approach earthquake prediction. Anomalous negative signals observed by ground-based atmospheric electric field instrument under fair weather open up a new way to earthquake prediction. Abnormal heat radiation before the earthquake bring fair weather around the epicenter in theory. In order to figure out the weather conditions around the epicenter before earthquakes, 213 global earthquake events with magnitude of 6 or above from 2013 to 2020 were collected. Based on our definition of fair weather, in 96.7% of the events in the statistics, the weather before the earthquake is fair. Besides, the fair state before the earthquake lasted more than 7 hours, leaving us with enough early warming time.

We introduce a cluster algebraic generalization of Thurston's earthquake map for the cluster algebras of finite type, which we call the \emph{cluster earthquake map}. It is defined by gluing exponential maps, which is modeled after the earthquakes along ideal arcs. We prove an analogue of the earthquake theorem, which states that the cluster earthquake map gives a homeomorphism between the spaces of $\mathbb{R}^\mathrm{trop}$- and $\mathbb{R}_{>0}$-valued points of the cluster $\mathcal{X}$-variety. For those of type $A_n$ and $D_n$, the cluster earthquake map indeed recovers the earthquake maps for marked disks and once-punctured marked disks, respectively. Moreover, we investigate certain asymptotic behaviors of the cluster earthquake map, which give rise to "continuous deformations" of the Fock--Goncharov fan.

We consider two issues related to the 2011 Tohoku mega-earthquake: (1) what is the repeat time for the largest earthquakes in this area, and (2) what are the possibilities of numerical short-term forecasts during the 2011 earthquake sequence in the Tohoku area. Starting in 1999 we have carried out long- and short-term forecasts for Japan and the surrounding areas using the GCMT catalog. The forecasts predict the earthquake rate per area, time, magnitude unit and earthquake focal mechanisms. Long-term forecasts indicate that the repeat time for the m9 earthquake in the Tohoku area is of the order of 350 years. We have archived several forecasts made before and after the Tohoku earthquake. The long-term rate estimates indicate that, as expected, the forecasted rate changed only by a few percent after the Tohoku earthquake, whereas due to the foreshocks, the short-term rate increased by a factor of more than 100 before the mainshock event as compared to the long-term rate. After the Tohoku mega-earthquake the rate increased by a factor of more than 1000. These results suggest that an operational earthquake forecasting strategy needs to be developed to take the increase of the short-te

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic (ROC) methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using statistical simulations of earthquake catalogs computed using Epidemic Type Aftershock Sequence (ETAS) simulations. ETAS earthquake simulations are currently in widespread use for a variety of tasks, in modeling, analysis and forecasting. After examining several of the standard ETAS models, we propose a version of the ETAS model that conforms to the standard ETAS statistical relations of magnitude-frequency scaling, aftershock scaling, Bath's law, and the productivity relation, but with an additional property. We modify the model to introduce variable non-Poisson aftershock

Computational earthquake sequence models provide generative estimates of the time, location, and size of synthetic seismic events that can be compared with observed earthquake histories and assessed as rupture forecasts. Here we describe a three-dimensional probabilistic earthquake sequence model that produces slip event time series constrained across geometrically complex non-planar fault systems. This model is kinematic in nature, integrating the time evolution of geometric moment accumulation and release with empirical earthquake scaling laws. The temporal probability of event occurrence is determined from the time history of geometric moment integrated with short-term Omori-style rate decay following each earthquake achieving long-term time-averaged moment balance. Similarly, the net geometric moment monotonically controls the probability of event localization, and seismic events release geometric moment with spatially heterogenous slip on three-dimensional non-planar fault surfaces. We use this model to generate a synthetic earthquake sequence on the Nankai subduction zone over a 1,250-year-long interval, including 700+ $\MW{=}5.5{-}8.5$ coseismic events, with decadal-to-cente

Probabilistic seismic hazard and risk models are essential to improving our awareness of seismic risk, to its management, and to increasing our resilience against earthquake disasters. These models consist of a series of components, which may be tested and validated individually, however testing and validating these types of models as a whole is challenging due to the lack of recognised procedures. Estimations made with other models, as well as observations of ground shaking and damages in past earthquakes lend themselves to testing the components for ground motion modelling and for the severity of damage to buildings. Here, we are using observations of damages caused by the Le Teil 2019 earthquake, third-party estimations of macroseismic intensity for this seismic event, and ShakeMap analyses in order to make comparisons with estimations made with scenario simulations using model components developed in the context of the 2020 Euro-Mediterranean Seismic Hazard Model and the European Seismic Risk Model. The comparisons concern the estimated ground motion intensity measures, the macroseismic intensity, the number of damaged buildings, and the probabilities of the damage grade. The d

This study utilizes a hybrid Finite Element Method (FEM) and Material Point Method (MPM) to investigate the runout of liquefaction-induced flow slide failures. The key inputs to this analysis are the earthquake ground motion, which induces liquefaction, and the post-liquefaction residual strength. The influence of these factors on runout is evaluated by subjecting a model of a tailings dam to thirty different earthquake motions and by assigning different values of post-liquefaction residual strength. Ground motions with larger peak ground accelerations (PGA) generate liquefaction to larger depths, thus mobilizing a greater mass of material and resulting in a flow slide with greater runout. However, different ground motions with the same PGA yield significant variations in the depth of liquefaction, indicating that other ground motion characteristics (e.g., frequency content) also exert significant influence over the initiation of liquefaction. Ground motion characteristics of peak ground velocity (PGV) and Modified Acceleration Spectrum Intensity (MASI) show a strong correlation to the induced depth of liquefaction because they capture both the intensity and frequency content of th

Earthquake early warning systems are required to report earthquake locations and magnitudes as quickly as possible before the damaging S wave arrival to mitigate seismic hazards. Deep learning techniques provide potential for extracting earthquake source information from full seismic waveforms instead of seismic phase picks. We developed a novel deep learning earthquake early warning system that utilizes fully convolutional networks to simultaneously detect earthquakes and estimate their source parameters from continuous seismic waveform streams. The system determines earthquake location and magnitude as soon as one station receives earthquake signals and evolutionarily improves the solutions by receiving continuous data. We apply the system to the 2016 Mw 6.0 earthquake in Central Apennines, Italy and its subsequent sequence. Earthquake locations and magnitudes can be reliably determined as early as four seconds after the earliest P phase, with mean error ranges of 6.8-3.7 km and 0.31-0.23, respectively.

Earthquake phase association algorithms aggregate picked seismic phases from a network of seismometers into individual earthquakes and play an important role in earthquake monitoring. Dense seismic networks and improved phase picking methods produce massive earthquake phase data sets, particularly for earthquake swarms and aftershocks occurring closely in time and space, making phase association a challenging problem. We present a new association method, the Gaussian Mixture Model Association (GaMMA), that combines the Gaussian mixture model for phase measurements (both time and amplitude), with earthquake location, origin time, and magnitude estimation. We treat earthquake phase association as an unsupervised clustering problem in a probabilistic framework, where each earthquake corresponds to a cluster of P and S phases with hyperbolic moveout of arrival times and a decay of amplitude with distance. We use a multivariate Gaussian distribution to model the collection of phase picks for an event, the mean of which is given by the predicted arrival time and amplitude from the causative event. We carry out the pick assignment for each earthquake and determine earthquake parameters (i

Forecasting the full distribution of the number of earthquakes is revealed to be inherently superior to forecasting their mean. Forecasting the full distribution of earthquake numbers is also shown to yield robust projections in the presence of "surprise" large earthquakes, which in the past have strongly deteriorated the scores of existing models. We show this with pseudo-prospective experiments on synthetic as well as real data from the Advanced National Seismic System (ANSS) database for California, with earthquakes with magnitude larger than 2.95 that occurred between the period 1971-2016. Our results call in question the testing methodology of the Collaboratory for the study of earthquake predictability (CSEP), which amounts to assuming a Poisson distribution of earthquake numbers, which is known to be a poor representation of the heavy-tailed distribution of earthquake numbers. Using a spatially varying ETAS model, we demonstrate a remarkable stability of the forecasting performance, when using the full distribution of earthquake numbers for the forecasts, even in the presence of large earthquakes such as Mw 7.1 Hector Mine, Mw 7.2 El Mayor-Cucapah, Mw 6.6 Sam Simeon earthqua

It has been observed that the earthquake events possess short-term memory, i.e. that events occurring in a particular location are dependent on the short history of that location. We conduct an analysis to see whether real-time earthquake data also possess long-term memory and, if so, whether such autocorrelations depend on the size of earthquakes within close spatiotemporal proximity. We analyze the seismic waveform database recorded by 64 stations in Japan, including the 2011 "Great East Japan Earthquake", one of the five most powerful earthquakes ever recorded which resulted in a tsunami and devastating nuclear accidents. We explore the question of seismic memory through use of mean conditional intervals and detrended fluctuation analysis (DFA). We find that the waveform sign series show long-range power-law anticorrelations while the interval series show long-range power-law correlations. We find size-dependence in earthquake auto-correlations---as earthquake size increases, both of these correlation behaviors strengthen. We also find that the DFA scaling exponent $α$ has no dependence on earthquake hypocenter depth or epicentral distance.