Simulation and characterization of multi-class spatial patterns from stochastic point processes of randomness,clustering and regularity

Spatial pattern analysis of data from multiple classes (i.e., multi-class data) has important implications. We investigate the resulting patterns when classes are generated from various spatial point processes. Our null pattern is that the nearest neighbor probabilities being proportional to class frequencies in the multi-class setting. In the two-class case, the deviations are mainly in two opposite directions, namely, segregation and association of the classes. But for three or more classes, the classes might exhibit mixed patterns, in which one pair exhibiting segregation, while another pair exhibiting association or complete spatial randomness independence. To detect deviations from the null case, we employ tests based on nearest neighbor contingency tables (NNCTs), as NNCT methods can provide an omnibus test and post-hoc tests after a significant omnibus test in a multi-class setting. In particular, for analyzing these multi-class patterns (mixed or not), we use an omnibus overall test based on NNCTs. After the overall test, the pairwise interactions are analyzed by the post-hoc cell-specific tests based on NNCTs. We propose various parameterizations of the segregation and association alternatives, list some appealing properties of these patterns, and propose three processes for the two-class association pattern. We also consider various clustering and regularity patterns to determine which one(s) cause segregation from or association with a class from a homogeneous Poisson process and from other processes as well. We perform an extensive Monte Carlo simulation study to investigate the newly proposed association patterns and to understand which stochastic processes might result in segregation or association. The methodology is illustrated on two real life data sets from plant ecology.     

地震平静特征与新疆的中强地震

系统分析了新疆地震活动的平静现象,认为新疆中强震前地震活动以平静为主要特征．并通过统计提取了新疆中强震前地震平静的预报指标．     

How Can One Test the Seismic Gap Hypothesis? The Case of Repeated Ruptures in the Aleutians

—The test that Kagan and Jackson (1991, 1995) applied to the seismic gap hypothesis did not bring us closer to understanding the generation of large earthquakes. On the contrary, it led some to the conclusion that the rebound theory of earthquake generation should be rejected. We disagree with this point of view and argue that a global test of the simplified gap hypothesis cannot be done because it cannot account for differences in the slip history of fault segments and tectonic differences between separate plate boundaries. Kagan and Jackson did show, however, that the original gap hypothesis was oversimplified and should be refined. We propose that consideration of all the facts, including slip history and seismicity patterns in the Andreanof Islands, show that the concept of seismic gaps and the elastic rebound theory are correct for that segment of the plate boundary. The coseismic slip in the M _w 8.7 earthquake that broke this plate boundary segment in 1957 was only 2 m, as published before the repeat earthquake of 1986 (M _w 8), and thus, using a plate convergence rate of 7.3 cm/year, the return time in this cycle was expected to be less than 30 years, unless substantial aseismic creep occurs. This supports the time predictable model of mainshock recurrence. In addition, Kisslinger et al. (1985) and Kisslinger (1986) noticed a seismic quiescence in the subsequent source volume before the 1986 earthquake and attempted to predict it. The specific parameters he estimated were not entirely correct although his interpretation of the observed quiescence as a precursor was. We conclude that the 1986, M _w 8, Andreanof earthquake was not an example that disproves the seismic gap hypothesis. On the contrary, it shows that the hypothesis that plate motions reload plate boundaries after most of the elastic energy is released in great ruptures was correct in this case. This suggests that great earthquakes occur preferably in mature gaps. We believe the testing of the seismic gap hypothesis by algorithm on a global scale is an example that illustrates that overly simplified tests can lead to erroneous conclusions. To make progress in the actual understanding of the physics of the process of great earthquake ruptures, one must consider all the facts known for case histories.     

Stress Shadows Determined from a Phase Dynamical Measure of Historic Seismicity

The Pattern Informatics (PI) technique (tiampo et al., 2002) is founded on the premise that changes in the seismicity rate are a proxy for changes in the underlying stress. These stress changes are correlated over large spatial regions, and can be quantified using a phase dynamical analysis of the changes in historic seismicity rates. This new approach to the study of seismicity quantifies its local and regional space-time patterns and identifies regions of local quiescence or activation. Here we study those local changes in an attempt to objectively quantify short-term stress shadow regions. We determine that, while persistent stress shadows are detectable with this method, they do not occur uniformly throughout the spatio-temporal region.     

Seismic quiescence precursory to a past and a future Kurile island earthquake

A systematic search was made for seismicity rate changes in the segment of the Kurile island arc from 45°N to 53°N by studying the cumulative seismicity of shallow (h100 km) earthquakes within 11 overlapping volumes of radius 100 km for the time period 1960 through beginning of 1978. We found that in most parts of this island arc and most of the time the seismicity rate as obtained from the NOAA catalogue and not excluding any events is fairly constant except for increased seismicity in the mid 1960s in the southern portion due to the great 1963 mainshock there, and for seismicity quiescence during part of the time period studied within two well defined sections of the arc. The first of these is a volume of 100 km radius around a 1973 (M _s =7.3) mainshock within which the seismicity rate was demonstrated at the 99% confidence level to have been lower by 50% during 2100 days (5.75 years) before this mainshock. The second volume of seismic quiescence coincides with the 400 km long north Kuriles gap. In this gap the seismicity rate is shown (at the 99% confidence level) to be lower by 50% from 1967 to present (1978), in comparison with the rate within the gap befor 1967, as well as with the rate surrounding the gap. We propose that the anomalously low seismicity rate within the Kuriles gap is a precursor to a great earthquake, the occurrence time of which was estimated by the following preliminary relation between precursory quiescence time and source dimensionT=190L ^0.545. We predict that an earthquake with source length of 200–400 km (M>8) will occur along the north Kurile island arc between latitude 45.5°N and 49.2°N at a time between now and 1994.     

Precursory seismic quiescence along the Sumatra-Andaman subduction zone: past and present

In this study, the seismic quiescence prior to hazardous earthquakes was analyzed along the Sumatra-Andaman subduction zone (SASZ). The seismicity data were screened statistically with mainshock earthquakes of M _w?≥?4.4 reported during 1980–2015 being defined as the completeness database. In order to examine the possibility of using the seismic quiescence stage as a marker of subsequent earthquakes, the seismicity data reported prior to the eight major earthquakes along the SASZ were analyzed for changes in their seismicity rate using the statistical Z test. Iterative tests revealed that Z factors of N?=?50 events and T?=?2?years were optimal for detecting sudden rate changes such as quiescence and to map these spatially. The observed quiescence periods conformed to the subsequent major earthquake occurrences both spatially and temporally. Using suitable conditions obtained from successive retrospective tests, the seismicity rate changes were then mapped from the most up-to-date seismicity data available. This revealed three areas along the SASZ that might generate a major earthquake in the future: (i) Nicobar Islands (Z?=?6.7), (ii) the western offshore side of Sumatra Island (Z?=?7.1), and (iii) western Myanmar (Z?=?6.7). The performance of a stochastic test using a number of synthetic randomized catalogues indicated these levels of anomalous Z value showed the above anomaly is unlikely due to chance or random fluctuations of the earthquake. Thus, these three areas have a high possibility of generating a strong-to-major earthquake in the future.     

Statistical assessment of seismicity patterns in Italy: Are they precursors of subsequent events?

The variations of seismicity rate in Central Apenninesprior to the sequence started in September, 1997 (at00:33 UTC, M _L5.6) has been analysedby statistical methods, with the purpose of pointingup eventual periods of quiescence. The analysis wascarried out on the instrumental catalogue of theIstituto Nazionale di Geofisica (ING), covering theperiod from January 1975 to March 1998. In apreliminary phase, the catalogue was declustered usingthe Reasenberg algorithm. After that, eventualmagnitude shifts due to variations in the modalitiesof observation have been individuated and corrected.The subsequent analysis, carried out making use of theZmap software package, has put in evidence thatthe sequence of September 1997 was preceded bya 2.5 year period characterised by absence of eventsof magnitude larger than 3.2, in an area approximately20 × 40 km wide, including the epicentre of themain shock. The statistical methodology shows thatonly 1/10³ of the space-time volumes analysed inthis study, exhibited quiescence of the same level.The study of seismicity rate change correlated toprevious main shocks in a larger area of CentralApennines shows that none of them were preceded by aseismic quiescence, specially close to the epicentreof the main shock, and lasting until the time ofoccurrence of the main shock as in the 1997 case.Actually, we found other patterns of precursoryquiescence with different time or space distribution.We conclude that precursory quiescence is a realfeature of Central Apennines seismicity, but it isdifficult to define a simple hypothesis, which appliesto the generality of cases and can be tested beforeimplementation in a system of earthquake riskmitigation.     

The November 2002 eruption at Piton de la Fournaise volcano,La Réunion Island: ground deformation,seismicity, and pit crater collapse

An eruption on the eastern flank of Piton de la Fournaise volcano started on 16 November, 2002 after 10 months of quiescence. After a relatively constant level of activity during the first 13 days of the eruption, lava discharge, volcanic tremor and seismicity increased from 29 November to 3 December. Lava effusion suddenly ceased on 3 December while shallow earthquakes beneath the Dolomieu summit crater were still recorded at a rate of about one per minute. This unusual activity continued and increased in intensity over the next three weeks, ending with the formation of a pit crater within Dolomieu. Based on ground deformation, measured by rapid-static and continuous GPS and an extensometer, seismic data, and lava effusion patterns, the eruptive period is divided into five stages: 1) slow summit inflation and sporadic seismicity; 2) rapid summit inflation and a short seismic crisis; 3) rapid flank inflation, onset of summit deflation, sporadic seismicity, accompanied by stable effusion; 4) flank inflation, coupled with summit deflation, intense seismicity, and increased lava effusion; and finally 5) little deflation, intense shallow seismicity, and the end of lava effusion. We propose a model in which the pre-intrusive inflation of Stage 1 in the months preceding the eruption was caused by a magma body located near sea level. The magma reservoir was the source of an intrusion rising under the summit during Stage 2. In Stage 3, the magma ponded at a shallow level in the edifice while the lateral injection of a radial dike reached the surface on the eastern flank of the basaltic volcano, causing lava effusion. Pressure decrease in the magmatic plumbing system followed, resulting in upward migration of a collapse front, forming a subterranean column of debris by faulting and stoping. This caused intense shallow seismicity, increase in discharge of lava and volcanic tremor at the lateral vent in Stage 4 and, eventually the formation of a pit crater in Stage 5.     

Global changes in the seismic regime and water surface level of the earth

Substantial changes in the seismic regime of the Earth during 1982–1993 are revealed on the basis of a new methodological approach to the study of the development of global seismogeodynamic processes. These changes are a more than threefold decrease in the recurrence rate of large earthquakes in the magnitude intervals M = 8.5 ± 0.2, M = 8.0 ± 0.2, M = 7.5 ± 0.2, and M = 7.0 ± 0.2 and a very intense activation of global seismicity after this relative seismic quiescence. Joint investigations of seismogeodynamic and hydrogeodynamic processes allowed us to reveal a certain synchronism between changes in the seismic regime of the Earth and the ocean water surface level. In this paper, we continue the search for a relation between changes in the regional seismicity and the level of closed water basins (with the Caspian Sea as an example), as well as investigations of the processes in individual seismic sources, in order to elaborate earthquake prediction methods. Hypotheses on the nature of the discovered phenomena are put forward, and structural phenomenological models are proposed. In particular, these correlated seismic and hydrologic phenomena are interpreted in terms of specific features of the seismogeodynamic regime in subduction zones on the periphery of the Pacific and Indian oceans.     

Self-organization of earthquake swarms

The temporal clustering of swarm activity differs significantly from characteristics of aftershock sequences accompanying mainshocks. This is often assumed to be caused by crustal structure complexities and fluid migration. However, the underlying mechanism is not yet fully understood, especially, the processes and conditions which lead to the apparent differences between the swarm patterns and typical mainshock–aftershock sequences. In previous works, we have shown that the most conspicuous characteristics of tectonic earthquakes can be reproduced by stick-slip block models incorporating visco-elastic interactions. Now, the same model is shown to reproduce an almost periodical occurrence of earthquake swarms in the case of an enlarged postseismic response. The simulated swarms respect not only the Gutenberg-Richter law for the event sizes, they also reproduce several observations regarding their spatio-temporal patterns. In particular, the comparison with the January 1997 and the year 2000 swarm in Vogtland/NW-Bohemia shows a good agreement in the interevent-time distributions and the spatio-temporal spreading of the swarm activity. The simulated seismicity patterns result from self-organization within the swarm due to local stress transfers and viscous coupling. Consequently, the agreement with the Vogtland swarm activity do not allow any decision about the preparatory process of the swarms; in particular, the question whether the swarms are initially triggered by fluid intrusion or tectonic motion cannot be answered. However, the model investigations suggest that the process of self-organization is very important for understanding the activity patterns of earthquake swarms.     

大震前地震活动图像演变及中期向短期过渡的地震活动性标志

通过多震例分析，表明大震前地震活动图像具有类似的演变形式，即空段－背景空区－增强活动－条带－平静，地震平静可以看作是中期短期过渡的地震活动性标志，从图像演变角有助于识别异常平静，并有可能把震前平静的时间尺度缩短至几个月量级。     

Methods for Measuring Seismicity Rate Changes: A Review and a Study of How the M w 7.3 Landers Earthquake Affected the Aftershock Sequence of the M w 6.1 Joshua Tree Earthquake

The development of fault interaction models has triggered the need for an accurate estimation of seismicity rate changes following the occurrence of an earthquake. Several statistical methods have been developed in the past to serve this purpose, each relying on different assumptions (e.g., stationarity, gaussianity) pertaining to the seismicity process.In this paper we review these various approaches, discuss their limitations, and propose further improvements. The feasibility of mapping robust seismicity rate changes, and more particularly rate decreases (i.e., seismicity shadows), in the first few days of an aftershock sequence, is examined. To this aim, the hypothesis of large numbers of earthquakes, hence the use of Gaussian statistics, as is usually assumed, must be dropped.Finally, we analyse the modulation in seismicity rates following the 1992, June 28 M_w 7.3 Landers earthquake in the region of the 1992, April 22 M_w 6.1 Joshua Tree earthquake. Clear instances of early triggering (i.e., in the first few days) followed by a seismicity quiescence, are observed. This could indicate the existence of two distinct interaction regimes, a first one caused by the destabilisation of active faults by the travelling seismic waves, and a second one due to the remaining static stress perturbation.     

Precursory seismic quiescence: Past,present, and future

Precursory seismic quiescence has played a major role in most of the succesful earthquake predictions made to date. In addition to these successes, the number of detailed post-mainshock documentations of precursory quiescence is steadily growing. These facts suggest that precursory quiescence will play an important role in earthquake prediction programs of the future. For this reason it is important to critically evaluate the present state of knowledge concerning this phenomenon. The history of observations of precursory seismic quiescence includes work on seismic gaps and seismic preconditions as well as actual studies of temporal quiescence. These papers demonstrated the importance of quantitative evaluation of seismicity rates and the benefits of systematic analysis. During the early 1980's the impact of man-made effects on seismicity rates was demonstrated for the first time. Despite progress in catalog understanding, the identification and correction of man-made seismicity changes remains as the major barrier to earthquake prediction using these data. Effects of man-made changes are apparent in many past studies of seismicity patterns, making the results difficult to evaluate. Recent experience with real-time anomalies has demonstrated the necessity of determining the false alarm rates associated with quiescence precursors. Determination of false alarm rates depends on quantitative definitions of anomalies and statistical evaluations of their significance. A number of successful predictions, which have been made on the basis of seismic quiescence, provide important lessons for present and future work. There are many presently unanswered questions regarding seismic quiescence which must be answered before we can determine the reliability of this phenomena as a precursor.     

Seismicity simulation with a mass-spring model and a displacement hardening-softening friction law

Dieterich simulated aftershocks numerically, using a one-dimensional mass-spring model with a time-dependent friction law. But an important precursory phenomenon called quiescence cannot be produced by this model unless, as Mikumo and Miyatake showed with a three-dimensional continuum model, a somewhat arbitrary bimodal distribution of frictional strength is assumed. Here we used the friction law proposed by Stuart, which is a displacement hardening-softening model, and simulated the quiescence. By varying the parameters of the friction law in our mass-spring model, we found a variety of seismicity patterns. When we choose extremely large critical displacement we get a recurrent sequence of creep followed by mainshock without small earthquakes. But when we choose a critical displacement in the same order of magnitude as the slip-weakening critical displacement estimated by Papageorgiou and Aki from strong motion data, we get a normal seismicity pattern, including quiescence before large events. This simple model points to a promising approach for the interpretation of the rupture process during an earthquake by the same physical model.     

Pattern Dynamics and Forecast Methods in Seismically Active Regions

—Large, extended fault systems such as those in California demonstrate complex space-time seismicity patterns, which include repetitive events, precursory activity and quiescence, and aftershock sequences. Although the characteristics of these patterns can be qualitatively described, a systematic quantitative analysis remains elusive. Our research suggests that a new pattern dynamics methodology can be used to define a unique, finite set of seismicity patterns for a given fault system. In addition, while a long-sought goal of earthquake research has been the reliable forecasting of these events, very little progress has been made in developing a successful, consistent methodology. In this report, we document the discovery of systematic space-time variations in seismicity from southern California using a new technique. Here we present examples of this analysis technique on data obtained prior to events in seismically active areas that show coherent regions associated with the future occurrence of major earthquakes in the same areas. These results strongly support the hypothesis that seismic activity is highly correlated across many space and time scales within large volumes of the earth's crust.     

On applicability of the RTL prognostic algorithms and energy estimation to Sakhalin seismicity

Premonitory phases (seismic quiescence and foreshock activity) have been retrospectively identified before the Neftegorsk and Uglegorsk earthquakes using the RTL technique. The probabilities that these phases were accidental are less than 1 and 2%, respectively. This allows an optimistic assessment of the possibility of applying this technique to seismicity at Sakhalin. The estimates of the time and energy class for the two earthquakes, using a model of self-organized seismic criticality, proved to be unconvincing because obvious acceleration of the seismic process prior to these seismic events did not occur. The applicability of this approach to the seismicity at Sakhalin should be tested for future large earthquakes. The regional Sakhalin catalog for 1980–2000, with a lowest completely reported energy class of K = 8 (lent by the Geophysical Service, Russian Academy of Sciences) was used as the database for this study.     

Preliminary report on an approach to testing for normality

The report is the introductory step to our investigation on joint probability distributions of crustal movements and geological parameters (basement depth, heat flow, seismicity and gravity anomalies) which will be carried out in the near future.Because of the remarkable role of the normal distribution, the working out of procedures testing for normality has been a continuing research subject of statisticians. Recently, Shapiro and Wilk (1965) and Shapiro et al. (1968) proposed a new test statistic and carried out a Monte Carlo comparative study with the known test statistics, and the result indicates superiority of their procedure from the test power point of view. The present report considers an approach to testing for normality which is related to the Shapiro-Wilk procedure. Also, the closed form of the test statistic is given. A brief historical outline of both the normal distribution theory and testing procedures is presented, making it of more methodological value, since the normal distribution is often involved in geodesy.     

Magma intrusion as a driving mechanism for the seismic clustering following the 9 May 1989 earthquake swarms at the Canary Islands

On 9 May 1989 a M _L = 5.2 earthquake struck a region between the islands of Tenerife and Gran Canaria. We investigated the time-spatial evolution of seismic patterns affecting the Canary Islands region during 1989–1995, using a quantitative spatial fractal analysis method. This method allows quantitative investigation of subtle trends in seismicity distribution through time. The fractal analysis indicates that epicenters clustered around a large zone during the May 1989 sequence affected narrow zones during 1991–1993, but then larger zones during 1993–1995 with an overall trend to shallower focal depths. The spatial localisation of seismic data and its time evolution appear to be related to magmatic rather than tectonic activity. Spatial clustering properties of seismicity are consistent with a major intrusive episode in 1989, followed by a period of quiescence and renewed deep intrusive activity from 1993 onwards. This interpretation suggests an increasing probability of future volcanic hazard in the region investigated.     

A diffusion approach to the statistical analysis of Kamchatka Seismicity

A diffusion approach was used to develop a statistical model of seismicity and to analyze Kamchatka earthquakes in order to detect features in the changes that are typical of random walk processes. We proposed a hypothesis of relationships among events and used an energy criterion to decompose the earth-quake catalog into a set of sequences, with each being a Brownian process with definite spatial, temporal, and energy scales. We constructed statistical distributions for these sequences over the number of their terms and total energies, as well as distributions of the sequences over distance, time, and flight times between events. We discuss non-local properties and memory effects in the random walk under different conditions.