A Markov regenerative process with recurrence time and its application

This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times, in particular, forward and backward recurrence processes. We obtain the transient solution of the process in the form of a generalized Markov renewal equation. A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model. To model the credit rating dynamics to demonstrate its applicability, we apply the proposed stochastic process to Standard and Poor’s rating agency’s data. Further, statistical tests confirm that the proposed model captures the rating dynamics better than the existing models, and the inclusion of recurrence times significantly impacts the transition probabilities.

Statistical behaviours of earthquake occurrences in the Central Anatolian Region of Turkey: region-time-magnitude analyses

The main objective of this work is to make detailed region-time-magnitude analyses by describing the statistical behaviours of earthquakes in the Central Anatolian Region of Turkey. In this scope, several seismic and tectonic parameters such as Mcomp, b-value, Dc-value, Z-value, recurrence times and annual probabilities were evaluated. For the analyses, a homogeneous catalogue including 10,146 earthquakes with 1.0 ≤ Md ≤ 5.7 between 30 July 1975 and 29 December 2018 was used and spatio-temporal changes of earthquake behaviours were mapped for the beginning of 2019. Earthquake magnitudes varied from 1.9 to 3.0 on average, and hence Mcomp was considered to be 2.6. The b-value was calculated as 1.26 ± 0.07, and this relatively large value indicates that small-magnitude events are dominant. The Dc-value was computed as 1.31 ± 0.03. This small value means that distances between epicentres approach the diameter of the cluster, and seismic activity is more clustered at smaller scales or in larger regions. The spatio-temporal analyses of recurrence times suggest that the Central Anatolian Region has an intermediate/long-term earthquake hazard in comparison to occurrences of strong earthquakes in the short term. Several anomaly regions of a small b-value and a large Z-value were found in and around the Tuzgölü Fault Zone, Central Anatolian Fault Zone, Salanda fault and Niğde fault at the beginning of 2019. Thus, a combination of the regions with a lower b-value, a higher Z-value and also moderate recurrence times may give significant clues for the future possible earthquakes, and detected regions may be thought to be the most likely areas for strong/large events in the Central Anatolian Region.

Slab Avalanche Release: Data and Field Experiments

Starting zone sizes are shown to obey statistical laws, named “power laws”, stating that the recurrence time of an event of a given size increases in a precise proportion with its size. Extrapolation of such laws fitted on small-sized events allows a determination of recurrence times for big and uncommon events. The key role of the weak layer (WL) failure is illustrated by “Propagation Saw Tests” (PST), showing that the collapse of a WL zone of a few decimeters may act as a switch, triggering a very large scale spontaneous WL failure. However, the consequences of such a collapse may be damped down by sintering of broken WL grains. We analyze bridging indexes, often used to estimate WL resistance to collapse under loading. We define a new bridging index, extending the usual one to the case of elastic bending, and we discuss the validity domains of both of them.

Magma chamber evolution during the 1650 AD Kolumbo eruption provides clues about past and future volcanic activity

Kolumbo submarine volcano lies 7 km NE of Santorini caldera and its last eruption which occurred in 1650 AD, caused damage and casualties to the nearby islands. Here a simple model of a chamber, containing silicic magma underlain by a smaller quantity of mafic magma, is utilised in order to understand the chamber behaviour during the 1650 AD eruption. Results show that in order to reproduce the duration (83–281 days) and the dense rock equivalent volume ($${\sim }\,2\, \hbox {km}^3$$ ∼ 2 km 3 ) of the eruption, initial overpressure in the chamber should be around 10 MPa and the mafic magma should occupy up to 5% of the chamber volume. It is found that the time needed to inject mafic magma equal to 1–15% of the chamber volume varies between 1.4–13.7 ka, if the radius of the chamber is about 1500 m as inferred from tomographic images. These long recurrence times agree well with the small number of eruptions ($$N = 5$$ N = 5 ) within a period of > 70 ka and suggest that an eruption in the near future is unlikely. Volcanic activity at Kolumbo is probably triggered by a combination of exsolved volatiles and a small but steady influx of mafic melt in the chamber.

X-ray quasi-periodic eruptions from the galactic nucleus of RX J1301.9+2747

Following the recent discovery of X-ray quasi-periodic eruptions (QPEs) coming from the nucleus of the galaxy GSN 069, here we report on the detection of QPEs in the active galaxy named RX J1301.9+2747. QPEs are rapid and recurrent increases of the X-ray count-rate by more than one order of magnitude with respect to a stable quiescent level. During a XMM-Newton observation lasting 48 ks that was performed on 30 and 31 May 2019, three strong QPEs lasting about half an hour each were detected in the light curves of RX J1301.9+2747. The first two QPEs are separated by a longer recurrence time (about 20 ks) compared to the second and third (about 13 ks). This pattern is consistent with the alternating long-short recurrence times of the GSN 069 QPEs, although the difference between the consecutive recurrence times is significantly smaller in GSN 069. Longer X-ray observations will better clarify the temporal pattern of the QPEs in RX J1301.9+2747 and will allow a detailed comparison with GSN 069 to be performed. The X-ray spectral properties of QPEs in the two sources are remarkably similar, with QPEs representing fast transitions from a relatively cold and likely disk-dominated state to a state that is characterized by a warmer emission similar to the so-called soft X-ray excess, a component that is almost ubiquitously seen in the X-ray spectra of unobscured, radiatively efficient active galaxies. Previous X-ray observations of RX J1301.9+2747 in 2000 and 2009 strongly suggest that QPEs have been present for at least the past 18.5 yr. The detection of QPEs from a second galactic nucleus after GSN 069 rules out contamination by a Galactic source in both cases, such that QPEs ought to be considered a novel extragalactic phenomenon associated with accreting supermassive black holes.