Verifying the Magnitude Dependence in Earthquake Occurrence.

The existence of magnitude dependence in earthquake triggering has been reported. Such a correlation is linked to the issue of seismic predictability and it remains under intense debate whether it is physical or is caused by incomplete data due to the missing short-term aftershocks. Working firstly with a synthetic catalog generated by a numerical model that captures most statistical features of earthquakes and then with a high-resolution earthquake catalog for the Amatrice-Norcia (2016) sequence in Italy, where for the latter case we employ the stochastic declustering method to reconstruct the family tree among seismic events and limit our analysis to events above the magnitude of completeness, we found that the hypothesis of magnitude correlation can be rejected.

Sample-Based Neural Approximation Approach for Probabilistic Constrained Programs.

This article introduces a neural approximation-based method for solving continuous optimization problems with probabilistic constraints. After reformulating the probabilistic constraints as the quantile function, a sample-based neural network model is used to approximate the quantile function. The statistical guarantees of the neural approximation are discussed by showing the convergence and feasibility analysis. Then, by introducing the neural approximation, a simulated annealing-based algorithm is revised to solve the probabilistic constrained programs. An interval predictor model (IPM) of wind power is investigated to validate the proposed method.

The debate on the earthquake magnitude correlations: a meta-analysis.

Among the most important questions that await an answer in seismology, perhaps one is whether there is a correlation between the magnitudes of two successive seismic events. The answer to this question is considered of fundamental importance given the potential effect in forecasting models, such as Epidemic Type Aftershock Sequence models. After a meta-analysis of 29 papers, we speculate that given the lack of studies carried out with realistic physical models and given the possible bias due to the lack of events recorded in the experimental seismic catalogs, important improvements are necessary on both fronts to be sure to provide a statistically relevant answer.

Gravity Observations and Apparent Density Changes before the 2017 Jiuzhaigou Ms7.0 Earthquake and Their Precursory Significance.

An Ms7.0 earthquake struck Jiuzhaigou (China) on 8 August 2017. The epicenter was in the eastern margin of the Tibetan Plateau, an area covered by a dense time-varying gravity observation network. Data from seven repeated high-precision hybrid gravity surveys (2014-2017) allowed the microGal-level time-varying gravity signal to be obtained at a resolution better than 75 km using the modified Bayesian gravity adjustment method. The "equivalent source" model inversion method in spherical coordinates was adopted to obtain the near-crust apparent density variations before the earthquake. A major gravity change occurred from the southwest to the northeast of the eastern Tibetan Plateau approximately 2 years before the earthquake, and a substantial gravity gradient zone was consistent with the tectonic trend that gradually appeared within the focal area of the Jiuzhaigou earthquake during 2015-2016. Factors that might cause such regional gravitational changes (e.g., vertical crustal deformation and variations in near-surface water distributions) were studied. The results suggest that gravity effects contributed by these known factors were insufficient to produce gravity changes as big as those observed, which might be related to the process of fluid material redistribution in the crust. Regional change of the gravity field has precursory significance for high-risk earthquake areas and it could be used as a candidate precursor for annual medium-term earthquake prediction.

Synchronized and asynchronous modulation of seismicity by hydrological loading: A case study in Taiwan.

Delineation of physical factors that contribute to earthquake triggering is a challenging issue in seismology. We analyze hydrological modulation of seismicity in Taiwan using groundwater level data and GNSS time series. In western Taiwan, the seismicity rate reaches peak levels in February to April and drops to its lowest values in July to September, exhibiting a direct correlation with annual water unloading. The elastic hydrological load cycle may be the primary driving mechanism for the observed synchronized modulation of earthquakes, as also evidenced by deep earthquakes in eastern Taiwan. However, shallow earthquakes in eastern Taiwan (<18 km) are anticorrelated with water unloading, which is not well explained by either hydrological loading, fluid transport, or pore pressure changes and suggests other time-dependent processes. The moderate correlation between stacked monthly trends of large historic earthquakes and present-day seismicity implies a modestly higher seismic hazard during the time of low annual hydrological loading.

Assessing the Potential Earthquake Precursory Information in ULF Magnetic Data Recorded in Kanto, Japan during 2000-2010: Distance and Magnitude Dependences.

In order to clarify ultra-low-frequency (ULF) seismomagnetic phenomena, a sensitive geomagnetic network was installed in Kanto, Japan since 2000. In previous studies, we have verified the correlation between ULF magnetic anomalies and local sizeable earthquakes. In this study, we use Molchan's error diagram to evaluate the potential earthquake precursory information in the magnetic data recorded in Kanto, Japan during 2000-2010. We introduce the probability gain (PG') and the probability difference (D') to quantify the forecasting performance and to explore the optimal prediction parameters for a given ULF magnetic station. The results show that the earthquake predictions based on magnetic anomalies are significantly better than random guesses, indicating the magnetic data contain potential useful precursory information. Further investigations suggest that the prediction performance depends on the choices of the distance (R) and size of the target earthquake events (Es). Optimal R and Es are about (100 km, 108.75) and (180 km, 108.75) for Seikoshi (SKS) station in Izu and Kiyosumi (KYS) station in Boso, respectively.

Forecasting the magnitude of the largest expected earthquake.

The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.

Stability of earthquake clustering models: criticality and branching ratios.

We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.

Distribution of the largest event in the critical epidemic-type aftershock-sequence model.

This Brief Report corrects and extends the results of Zhuang and Ogata [Phys. Rev. E 73, 046134 (2006)] on the asymptotic behavior of the largest event in the epidemic-type aftershock-sequence model for earthquake occurrence. We show that, in the special case that the underlying branching process is critical, there exists a previously unnoticed mode of behavior, which occurs when the expected family size grows relatively slowly.

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks.

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata, Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method.