Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a one-dimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%.
Pattern informatics (PI) technique can be used to detect precursory seismic activation or quiescence and make earthquake forecast. Here we apply the PI method for optimal forecasting of large earthquakes in Japan, using the data catalogue maintained by the Japan Meteorological Agency. The PI method is tested to forecast large (magnitude m >= 5) earthquakes for the time period 1995-2004 in the Kobe region. Visual inspection and statistical testing show that the optimized PI method has forecasting skill, relative to the seismic intensity data often used as a standard null hypothesis. Moreover, w…
A prominent feature of earthquakes is their empirical laws including memory (clustering) in time and space. Several earthquake forecasting models, like the EpidemicType Aftershock Sequence (ETAS) model, were developed based on earthquake empirical laws. Yet, a recent study showed that the ETAS model fails in reproducing significant long-term memory characteristics found in real earthquake catalogs. Here we modify and generalize the ETAS model to include short- and long-term triggering mechanisms, to account for the short- and long-time memory (exponents) recently discovered in the data. Our ge…
We present an axiomatic approach to earthquake forecasting in terms of multi-component random fields on a lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of strong earthquakes under conditions on the levels of precursors. Also, it provides an approach for setting multilevel alarm system and hypothesis testing for binary alarms. We use a method of comparison for different earthquake forecasts in terms of the increase of Shannon information. 'Forecasting' and 'prediction' of earthquakes are equivalent in this approa…
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.…
Earthquake Aftershock Forecasting using Conditional Generative Models
Department of Earth and Planetary Science, University of California, Berkeley（加州大学伯克利分校地球与行星科学系）；Berkeley Seismological Laboratory, University of California, Berkeley（加州大学伯克利分校伯克利地震实验室）
Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we present a class of smoothed seismicity models (SSMs) based on the principles of the Epidemic Type Aftershock Sequence (ETAS) model, which forecast the location, time and magnitude of all future earthquakes using the estimates of the background seismicity rate and the rates of future aftershocks of all generations. Using the Californian earthquake catalog, we f…
Following N.Kozyrev's idea about the influence of the gravitational fields of the Sun and the Moon on the Earth's crust, we consider a low-frequency resonance of the Earth's crust blocks is happening before the occurrence of the earthquake. The resonance affects several geophysical parameters and is associated with many short-term precursory phenomena; the most notable are the release of underground gases (radon), the air temperature rises, change of thermal radiation in the troposphere, and an increase in the electron density in the ionosphere. During the final stage of the earthquake genesis…
One of the main interests in seismology is the formulation of models able to describe the clustering in time occurrence of earthquakes. Analysis of the Southern California Catalog shows magnitude clustering in correspondence to temporal clustering. Here we propose a dynamical scaling hypothesis in which time is rescaled in terms of magnitude. This hypothesis is introduced in the context of a generalized trigger model and gives account for clustering in time and magnitude for earthquake occurrence. The model is able to generate a synthetic catalog reproducing magnitude and inter-even time distr…
Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to…
In this study, we propose an analysis of the earthquake clusters that occurred in North-Eastern Italy and western Slovenia from 1977 to today. Given a mainshock generating alarm in the population, we are interested in forecasting if a similar magnitude earthquake will follow. We classify the earthquake clusters associated with mainshocks of magnitude Mm into two classes: if the strongest aftershock has a magnitude >=Mm-1 (swarms or large aftershock seismic sequences) as type A, otherwise (smaller aftershocks seismic sequences) as type B. A large aftershock following a main shock can cause sign…
How to quantify earthquake predictability? Advances in earthquake forecasting and predictability limits
The Institute of Statistical Mathematics（统计数学研究所）；the Graduate University for Adavanced Studies (SOKENDai)（advanced studies 研究生院（SOKENDai））；Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology（南方科技大学风险分析、预测与管理研究院）
We propose two methods to calibrate the parameters of the epidemic-type aftershock sequence (ETAS) model based on expectation maximization (EM) while accounting for temporal variation of catalog completeness. The first method allows for model calibration on long-term earthquake catalogs with temporal variation of the completeness magnitude, $m_c$. This calibration technique is beneficial for long-term probabilistic seismic hazard assessment (PSHA), which is often based on a mixture of instrumental and historical catalogs. The second method generalizes the concept of $m_c$, considering rate- an…
This research presents one possible way for imminent prediction of earthquake magnitude, depth and epicenter coordinates by solving the inverse problem using a data acquisition network system for monitoring, archiving and complex analysis of geophysical variables precursors. Among many possible precursors the most reliable are the geoelectromagnetic field, the boreholes water level, the radon surface concentration, the local heat flow, the ionosphere variables, the low frequency atmosphere and Earth core waves. In this study only geomagnetic data are used. Within the framework of geomagnetic q…
In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts, than can be achieved by ignoring data uncertainties. Earthquake forecasting, too, suffers from measurement errors and partial model information and may thus gain significantly from data assimilation. We present perhaps the first fully implementable data assimilation method for earthquake forecasts generated by a point-process model of seismicity. We test the …
No proven method is currently available for the reliable short time prediction of earthquakes (minutes to months). However, it is possible to make probabilistic hazard assessments for earthquake risk. These are primarily based on the association of small earthquakes with future large earthquakes. In this paper we discuss a new approach to earthquake forecasting. This approach is based on a pattern informatics (PI) method which quantifies temporal variations in seismicity. The output is a map of areas in a seismogenic region (``hotspots'') where earthquakes are forecast to occur in a future 10-…
Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquake…
Università La Sapienza（罗马第一大学）；The Pennsylvania State University（宾夕法尼亚州立大学）
Earthquake forecasting and prediction have long and in some cases sordid histories but recent work has rekindled interest based on advances in early warning, hazard assessment for induced seismicity and successful prediction of laboratory earthquakes. In the lab, frictional stick-slip events provide an analog for earthquakes and the seismic cycle. Labquakes are ideal targets for machine learning (ML) because they can be produced in long sequences under controlled conditions. Recent works show that ML can predict several aspects of labquakes using fault zone acoustic emissions. Here, we general…
Earthquakes are one of the most devastating natural disasters that plague society. A skilled, reliable earthquake forecasting remains the ultimate goal for seismologists. Using the detrended fluctuation analysis (DFA) and conditional probability (CP) methods we find that memory exists not only in inter-occurrence seismic records, but also in released energy as well as in the series of the number of events per unit time. Analysis of the conventional earthquake model (Epidemic Type Aftershock Sequences, ETAS) indicates that earthquake memory can be reproduced only for a narrow range of model's p…
Over the past decades much effort has been devoted towards understanding and forecasting natural hazards. However, earthquake forecasting skill is still very limited and remains a great scientific challenge. The limited earthquake predictability is partly due to the erratic nature of earthquakes and partly to the lack of understanding the underlying mechanisms of earthquakes. To improve our understanding and potential forecasting, here we study the spatial and temporal long-term memory of interevent earthquakes above a certain magnitude using lagged conditional probabilities. We find, in real …
Recent studies in the literature have introduced a new approach to earthquake forecasting based on representing the space-time patterns of localized seismicity by a time-dependent system state vector in a real-valued Hilbert space and deducing information about future space-time fluctuations from the phase angle of the state vector. While the success rate of this Pattern Informatics (PI) method has been encouraging, the method is still in its infancy. Procedural analysis, statistical testing, parameter sensitivity investigation and optimization all still need to be performed. In this paper, we…
Integrating Artificial Intelligence and Geophysical Insights for Earthquake Forecasting: A Cross-Disciplinary Review
University of Science and Technology Beijing（北京科技大学）；Beijing Engineering Research Center of Industrial Spectrum Imaging（北京市工业光谱成像工程研究中心）；New York University Abu Dhabi（纽约大学阿布扎比分校）；Southern University of Science and Technology（南方科技大学）；China University of Geosciences (Beijing)（中国地质大学（北京））
Institute of Earthquake Forecasting, China Earthquake Administration（中国地震局地震预测研究所）；National Institute of Natural Hazards, Ministry of Emergency Management of China（中国应急管理部国家自然灾害防治研究院）；University of Leicester（莱斯特大学）；Nanyang Technological University（南洋理工大学）；University of Trento（特伦托大学）；National Institute for Nuclear Physics, the Trento Institute for Fundamental Physics and Applications（意大利国家核物理研究院特伦托基础物理与应用研究所）；Chapman University（查普曼大学）；Queen's University Belfast（贝尔法斯特女王大学）；Nantong University（南通大学）
Amongst the available technologies for earthquake research, remote sensing has been commonly used due to its unique features such as fast imaging and wide image-acquisition range. Nevertheless, early studies on pre-earthquake and remote-sensing anomalies are mostly oriented towards anomaly identification and analysis of a single physical parameter. Many analyses are based on singular events, which provide a lack of understanding of this complex natural phenomenon because usually, the earthquake signals are hidden in the environmental noise. The universality of such analysis still is not being …
Forecasting fault failure is a fundamental but elusive goal in earthquake science. Here we show that by listening to the acoustic signal emitted by a laboratory fault, machine learning can predict the time remaining before it fails with great accuracy. These predictions are based solely on the instantaneous physical characteristics of the acoustical signal, and do not make use of its history. Surprisingly, machine learning identifies a signal emitted from the fault zone previously thought to be low-amplitude noise that enables failure forecasting throughout the laboratory quake cycle. We hypot…
In this paper we present an approach for forecasting the imminent regional seismic activity by using geomagnetic data and Earth tide data. The time periods of seismic activity are the time periods around the Sun-Moon extreme of the diurnal average value of the tide vector module. For analyzing the geomagnetic data behaviour we use diurnal standard deviation of geomagnetic vector components F for calculating the time variance Geomag Signal. The Sun storm influence is avoided by using data for daily A-indexes (published by NOAA). The precursor signal for forecasting the incoming regional seismic…
Design and Implementation of a 25-Yr Pseudoprospective Earthquake Forecasting Experiment in China (AoyuX)
School of Systems Science, Beijing Normal University（北京师范大学系统科学学院）；International Academic Center of Complex Systems, Beijing Normal University（北京师范大学复杂系统国际学术中心）；Department of Systems Science, Faculty of Arts and Sciences, Beijing Normal University（北京师范大学文理学院系统科学系）
ANADEF: A Nested-Permutation Alarm for Dual-Parameter Earthquake Forecasting
University of Beira Interior（比拉伊内里乌大学）；Atmosphere and Ocean Research Institute (AORI), the University of Tokyo（东京大学大气海洋研究所）；Farhangian University（法尔坎吉安大学）
Scaling-law-informed neural point processes for earthquake sequence forecasting
Yunnan Key Laboratory of Complex Systems and Brain-Inspired Intelligence（云南省复杂系统与类脑智能重点实验室）；Kunming University of Science and Technology（昆明理工大学）；Faculty of Science, Kunming University of Science and Technology（昆明理工大学理学院）；Environmental Physics, Ben-Gurion University of the Negev（内盖夫本古里安大学环境物理系）；Ben-Gurion University of the Negev（内盖夫本古里安大学）
Modern, powerful techniques for the residual analysis of spatial-temporal point process models are reviewed and compared. These methods are applied to California earthquake forecast models used in the Collaboratory for the Study of Earthquake Predictability (CSEP). Assessments of these earthquake forecasting models have previously been performed using simple, low-power means such as the L-test and N-test. We instead propose residual methods based on rescaling, thinning, superposition, weighted K-functions and deviance residuals. Rescaled residuals can be useful for assessing the overall fit of…
We present a method of constructing low-dimensional nonlinear models describing the main dynamical features of a discrete 2D cellular fault zone, with many degrees of freedom, embedded in a 3D elastic solid. A given fault system is characterized by a set of parameters that describe the dynamics, rheology, property disorder, and fault geometry. Depending on the location in the system parameter space we show that the coarse dynamics of the fault can be confined to an attractor whose dimension is significantly smaller than the space in which the dynamics takes place. Our strategy of system reduct…
The aims of the project 2011-2014) are in the project title- Complex Research of Earthquakes Forecasting Possibilities, Seismic and Climate Change Correlations- to create a team for researching the above mentioned problem. In the Project participated 76 scientists from 16 Institutes and 8 countries- Armenia, Bulgaria, Georgia, Greece, Macedonia, Slovenia, Turkey and Ukraine. The main results are shortly listed in the next. Creating a group which is able to fulfill a Complex Research of Earthquakes Forecasting Possibilities; The main result is statistical prove of imminent forecasting possibili…
Time Series Foundation Models and Deep Learning Architectures for Earthquake Temporal and Spatial Nowcasting
University of Virginia（弗吉尼亚大学）；University of California, Davis（加州大学戴维斯分校）；Santa Fe Institute（圣达菲研究所）；Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；University of California, Irvine（加州大学欧文分校）
Uncovering the distribution of magnitudes and arrival times of aftershocks is a key to comprehend the characteristics of the sequence of earthquakes, which enables us to predict seismic activities and hazard assessments. However, identifying the number of aftershocks immediately after the main shock is practically difficult due to contaminations of arriving seismic waves. To overcome the difficulty, we construct a likelihood based on the detected data incorporating a detection function to which the Gaussian process regression (GPR) is applied. The GPR is capable of estimating not only the para…
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statisti…
