Stochastic Approximate Solutions of Stochastic Differential Equations with Random Jump Magnitudes and Non-Lipschitz Coefficients

A class of stochastic differential equations with random jump magnitudes( SDEwRJMs) is investigated. Under nonLipschitz conditions,the convergence of semi-implicit Euler method for SDEwRJMs is studied. The main purpose is to prove that the semi-implicit Euler solutions converge to the true solutions in the mean-square sense. An example is given for illustration.

Converting Tsunami Wave Heights to Earthquake Magnitudes

There is a fairly strict relation between maximum tsunami wave heights and causation earthquake magnitudes. This provides a new tool for estimating the magnitude of past earthquakes from the observed wave heights of related paleo-tsunami events. The method is subjected to a test versus two paleoseismic events with multiple independent estimates of corresponding earthquake magnitude. The agreement to the tsunami wave height conversion is good, confirming very high magnitudes of M 8.5 - 9.0 and M 8.4 - 8.5. Applying the same method to two Late Holocene events of methane venting tectonics indicates a ground shaking of forces equivalent to a M 8.0 earthquake, seriously changing previous long-term crustal hazard assessments.

A Bayesian Approach to Seismic Hazard Estmation: Maximum Values of Magnitudes and Peak Ground Accelerations

A rather simple straightforward procedure of estimating maximum values of the considered parameter (earthquake magnitude in a given region or seismic peak ground acceleration at the considered site) and quantiles of its probabilistic distribution in a future time interval of a given length is presented. To assess the peak ground acceleration using this method, the input information is the earthquake catalog and the regressive relation where the peak seismic acceleration at a given point bears the magnitude and epicentral distance of the site considered (seismic attenuation law). The method is based on the Bayesian approach, in which the influence of uncertainties of magnitudes and seismic acceleration values can be taken into account. The main assumptions for the method are the Poissonian character of the seismic event flow, a frequency-magnitude law of Gutenberg-Richter’s type with a cutoff maximum value for the estimated parameter, and an earthquake catalog that has a rather large number of events. The method has been applied to seismic hazard estimation in California, the Balkans, and Japan.

Last Deglacial Soft-Sediment Deformation at Shawan on the Eastern Tibetan Plateau and Implications for Deformation Processes and Seismic Magnitudes

The eastern margin of the Tibetan Plateau is characterized by frequent earthquakes; however, research of paleo-earthquakes in the area has been limited^ owing to the alpine topography and strong erosion. Detailed investigations of soft-sediment deformation(SSD) structures are valuable for understanding the trigger mechanisms, deformation processes, and the magnitudes of earthquakes that generate such structures, and help us to understand tectonic activity in the region. To assess tectonic activity during the late Quaternary, we studied a well-exposed sequence of Shawan lacustrine sediments, 7.0 m thick, near Lake Diexi in the upper reaches of the Minjiang River. Deformation is recorded by both ductile structures(load casts, flame structures,pseudonodules, ball-and-pillow structures, and liquefied convolute structures) and brittle structures(liquefied breccia, and microfaults). Taking into account the geodynamic setting of the area and its known tectonic activity, these SSD structures can be interpreted in terms of seismic shocks. The types and forms of the structures,the maximum liquefaction distances, and the thicknesses of the horizons with SSD structures in the Shawan section indicate that they record six strong earthquakes of magnitude 6-7 and one with magnitude >7. A recent study showed that the Songpinggou fault is the seismogenic structure of the 1933 Ms7.5 Diexi earthquake. The Shawan section is located close to the junction of the Songpinggou and Minjiang faults, and records seven earthquakes with magnitudes of ?7. We infer,therefore, that the SSD structures in the Shawan section document deglacial activity along the Songpinggou fault.

Determination of the local magnitudes of small earthquakes using a dense seismic array in the Changning-Zhaotong Shale Gas Field,Southern Sichuan Basin

With the development of unconventional shale gas in the southern Sichuan Basin,seismicity in the region has increased significantly in recent years.Though the existing sparse regional seismic stations can capture most earthquakes with ML≥2.5,a great number of smaller earthquakes are often omitted due to limited detection capacity.With the advent of portable seismic nodes,many dense arrays for monitoring seismicity in the unconventional oil and gas fields have been deployed,and the magnitudes of those earthquakes are key to understand the local fault reactivation and seismic potentials.However,the current national standard for determining the local magnitudes was not specifically designed for monitoring stations in close proximity,utilizing a calibration function with a minimal resolution of 5 km in the epicentral distance.That is,the current national standard tends to overestimate the local magnitudes for stations within short epicentral distances,and can result in discrepancies for dense arrays.In this study,we propose a new local magnitude formula which corrects the overestimated magnitudes for shorter distances,yielding accurate event magnitudes for small earthquakes in the Changning-Zhaotong shale gas field in the southern Sichuan Basin,monitored by dense seismic arrays in close proximity.The formula is used to determine the local magnitudes of 7,500 events monitored by a two-phased dense array with several hundred 5 Hz 3 C nodes deployed from the end of February 2019 to early May 2019 in the Changning-Zhaotong shale gas field.The magnitude of completeness(MC)using the dense array is-0.1,compared to MC 1.1 by the sparser Chinese Seismic Network(CSN).In addition,using a machine learning detection and picking procedure,we successfully identify and process some 14,000 earthquakes from the continuous waveforms,a ten-fold increase over the catalog recorded by CSN for the same period,and the MC is further reduced to-0.3 from-0.1 compared to the catalog obtained via manual processing using the same dense array.The proposed local magnitude formula can be adopted for calculating accurate local magnitudes of future earthquakes using dense arrays in the shale gas fields of the Sichuan Basin.This will help to better characterize the local seismic risks and potentials.

Moment magnitudes of two large Turkish earthquakes on February 6,2023 from long-period coda

Two large earthquakes(an earthquake doublet)occurred in south-central Turkey on February 6,2023,causing massive damages and casualties.The magnitudes and the relative sizes of the two mainshocks are essential information for scientific research and public awareness.There are obvious discrepancies among the results that have been reported so far,which may be revised and updated later.Here we applied a novel and reliable long-period coda moment magnitude method to the two large earthquakes.The moment magnitudes(with one standard error)are 7.95±0.013 and 7.86±0.012,respectively,which are larger than all the previous reports.The first mainshock,which matches the largest recorded earthquakes in the Turkish history,is slightly larger than the second one by 0.11±0.035 in magnitude or by 0.04 to 0.18 at 95%confidence level.

Differences between magnitudes of Taiwan earthquakes from catalogs of Taiwan and Beijing

Taiwan is a region with very high seismicity where hundreds of earthquakes with ms occurred per year and more than 40 with m≥7 since 1900 due to it is located at the boundary of collision between Eurasian and the Philippine Sea plates.The magnitudes for the same event from these two catalogs of Taiwan and Beijing are different due to diferent data sources selected and different magnitude scales used. To measure sizes of Taiwan events in uniform magnitude scale, the author adopted a catalog of earthquakes with uniform local magnitude scale (Shin, 1993)compiled by Cheng (1996) in compiling a new catalog of Chinese earthquakes. To measure sizes of Taiwan events,we adopted uniform local magnitude scale for events with 5≤M<6. For event with M≥6 we still adopted IASPEI surface wave magnitude scale. Thus the statistic difference between two magnitude values from Taiwan and Beijing in magnitude interval 5≤M<6 reflects difference between Taiwan uniform local magnitode scale and Beijing surface wave magnitude scale. The statistic difference in magnitude interval he6 reflects difference between IASPEI surface wave magnitude scale and Beijing surface wave magnitude scale. Three data sources from "Wang","Cheng" and "Chinese mainland" of Taiwan events with m≥7 are given in this paper, in order to obtain a complete catalog.The statistic result indicates that Taiwan magnitude is slightly larger than Beijing magnitude for 998 events with 5≤M<6. The mean difference is about 0.13 of magnitude unit with deviation 0.32. Similarly, the mean difference is about 0.09 of magnitude unit with deviation 0.23 for 298 eventS with m≥6. We also noted that the difference of magnitude values between Beijing and Taiwan surface wave magnitUdes changed in different time period.Before 1971, most Taiwan magnitude values of the events is larger than Beijing’s. In contrast, most Beijing magnitude values of the events are larger than Taiwan magnitUde values aller 1972. It is probably related to data sources. Three catalogs of events with m≥7 are given in this paper Wang’s catalog (1995) includes 44 events with M≥7, Cheng’s (1996) 39 events and Chinese catalog, before 1911 compiled by Min (1995), 1912-1990 compiled by Wang, et al (1997) and 1991-1998 compiled by Yang, includes 41 events. The variety of these data sources discussed in this paper can be a useful reference for seismologists who use catalog seismic data do their research.However the statistic results and empirical relations presented in this paper can not be used for converting between magnitude scales, since some of them are not the original observation values. In addition, three catalogs of events with M≥ 7 given in this paper can be used for seismicity research comprehensively.

Comparison between different earthquake magnitudes determined by China Seismo-graph Network

By linear regression and orthogonal regression methods, comparisons are made between different magnitudes （local magnitude ML, surface wave magnitudes Ms and MsT, long-period body wave magnitude mB and short-period body wave magnitude mb） determined by Institute of Geophysics, China Earthquake Administration, on the basis of observation data collected by China Seismograph Network between 1983 and 2004. Empirical relations between different magnitudes have been obtained. The result shows that： ① As different magnitude scales reflect radiated energy by seismic waves within different periods, earthquake magnitudes can be described more objectively by using different scales for earthquakes of different magnitudes. When the epicentral distance is less than 1000 km, local magnitude ME can be a preferable scale; In case M〈4.5, there is little difference between the magnitude scales; In case 4.5〈M〈6.0, mB〉Ms, i.e., Ms underestimates magnitudes of such events, therefore, mB can be a better choice; In case M〉6.0, Ms〉mB〉mb, both mB and mb underestimate the magnitudes, so Ms is a preferable scale for determining magnitudes of such events （6.0〈M〈8.5）; In case M〉8.5, a saturation phenomenon appears in Ms, which cannot give an accurate reflection of the magnitudes of such large events; ② In China, when the epicentral distance is less than 1 000 km, there is almost no difference between ME and Ms, and thus there is no need to convert between the two magnitudes in practice; ③ Although Ms and Ms7 are both surface wave magnitudes, Ms is in general greater than Ms7 by 0.2～0.3 magnitude, because different instruments and calculation formulae are used; ④ mB is almost equal to mb for earthquakes around mB4.0, but mB is larger than mb for those of mB〉4.5, because the periods of seismic waves used for measuring mB and mb are different though the calculation formulae are the same.

Comparison between earthquake magnitudes determined by China seismograph network and US seismograph networks (I): Body wave magnitude

By using orthogonal regression method, a systematic comparison is made between body wave magnitudes determined by Institute of Geophysics of China Earthquake Administration (IGCEA) and National Earthquake Information Center of US Geological Survey (USGS/NEIC) on the basis of observation data from China and US seismograph networks between 1983 and 2004. The result of orthogonal regression shows no systematic error between body wave magnitude mb determined by IGCEA and mb (NEIC). Provided that mb (NEIC) is taken as the benchmark, body wave magnitude determined by IGCEA is greater by 0.2-0.1 than the magnitude determined by NEIC for M=3.5-4.5 earthquakes; for M=5.0-5.5 earthquakes, there is no difference; and for M greater than or equal 6.0 earthquakes, it is smaller by no more than 0.2. This is consistent with the result of comparison by IDC (International Data Center).

Calculation of Calibration Functions and Explosive Aftershock Magnitudes in the Near Field

The current calibration function used in calculating the magnitude of natural earthquakes within 5km is a constant; a fact that causes several serious difficulties for the calculation of the magnitude of small and shallow-focus earthquakes. According to the attenuation law of explosions and the propagation theory of elastic waves, the calibration function is calculated for near field quakes from 0km to 5km. Magnitudes of two aftershock sequences are calculated. The magnitudes of most explosion earthquakes are small, ranging mainly from magnitude -0.5 to 1.0. The M-t chart of the explosive aftershocks is completely different from that of strong earthquake aftershocks. It not only shows positive columnar lines indicating large magnitudes but also short negative columnar lines indicating small magnitudes.

Seismic Risk Assessment and Maximum Magnitudes of Potential Earthquakes on Active Faults near Lanzhou City

The Zhuanglang river and Baiyin Baiyangshu river faults are late Quaternary faults near Lanzhou city, which pose a threat to the safety of the city. However, the cause of medium- strong earthquakes along the fault is rather complicated and even uncertain. It is important for us how to assess the magnitudes of maximum potential earthquakes and the seismic risk of the faults. The authors make reference to the method that Wen Xueze, et ai. （2007） developed to assess the magnitudes of maximum potential earthquakes in sub-areas of moderately and weakly active faults in the eastern Chinese Mainland, and brought forward an empirical relationship between the maximum magnitudes Mmax and the at/b values of the sub-areas＇ frequency- magnitude relationships in the Lanzhou area. By using this empirical relationship, the authors have estimated the upper-limits Mu of the Zhuanglang river and Baiyin Baiyangshu river active faults near Lanzhou city as Ms6.9 and 6.3, respectively. In addition, they have assessed the average interval recurrence time and the probabilities of destructive earthquakes on the faults.

Micro-macro evolution of mechanical behaviors of thermally damaged rock:A state-of-the-art review

The influence of thermal damage on macroscopic and microscopic characteristics of different rocks has received much attention in the field of rock engineering.When the rocks are subjected to thermal treatment,the change of macroscopic characteristics and evolution of micro-structure would be induced,ultimately resulting in different degrees of thermal damage in rocks.To better understand the thermal damage mechanism of different rocks and its effect on the rock performance,this study reviews a large number of test results of rock specimens experiencing heating and cooling treatment in the laboratory.Firstly,the variations of macroscopic behaviors,including physical parameters,mechanical parameters,thermal conductivity and permeability,are examined.The variations of mechanical parameters with thermal treatment variables(i.e.temperature or the number of thermal cycles)are divided into four types.Secondly,several measuring methods for microstructure,such as polarizing microscopy,fluorescent method,scanning electron microscopy(SEM),X-ray computerized tomography(CT),acoustic emission(AE)and ultrasonic technique,are introduced.Furthermore,the effect of thermal damage on the mechanical parameters of rocks in response to different thermal treatments,involving temperature magnitude,cooling method and thermal cycle,are discussed.Finally,the limitations and prospects for the research of rock thermal damage are proposed.

Rydberg-Atom Terahertz Heterodyne Receiver with Ultrahigh Spectral Resolution

Terahertz heterodyne receivers with high sensitivity and spectral resolution are crucial for various applications.Here,we present a room-temperature atomic terahertz heterodyne receiver that achieves ultrahigh sensitivity and frequency resolution.At a signal frequency of 338.7 GHz,we obtain a sensitivity of 2.88±0.09V·cm^(−1)·Hz^(−1/2) for electric field measurements.The calibrated linear dynamical range spans approximately 89 dB,ranging from−110 dBV/cm to−21 dBV/cm.We demodulate a 400 symbol stream encoded in 4-state phase-shift keying,demonstrating excellent phase detection capability.By scanning the frequency of the local oscillator,we realize a terahertz spectrometer with Hz level frequency resolution.This resolution is more than two orders of magnitude higher than that of existing terahertz spectrometers.The demonstrated terahertz heterodyne receiver holds promising potential for working across the entire terahertz spectrum,significantly advancing its practical applications.

The Collaboratory for the Study of Earthquake Predictability in China:Experiment Design and Preliminary Results of CSEP2.0

Since the inaugural international collaboration under the framework of the Collaboratory for the Study of Earthquake Predictability(CSEP)in 2007,numerous forecast models have been developed and operated for earthquake forecasting experiments across CSEP testing centers(Schorlemmer et al.,2018).Over more than a decade,efforts to compare forecasts with observed earthquakes using numerous statistical test methods and insights into earthquake predictability,which have become a highlight of the CSEP platform.

Software Cost Estimation Using Social Group Optimization

This paper introduces the integration of the Social Group Optimization(SGO)algorithm to enhance the accuracy of software cost estimation using the Constructive Cost Model(COCOMO).COCOMO’s fixed coefficients often limit its adaptability,as they don’t account for variations across organizations.By fine-tuning these parameters with SGO,we aim to improve estimation accuracy.We train and validate our SGO-enhanced model using historical project data,evaluating its performance with metrics like the mean magnitude of relative error(MMRE)and Manhattan distance(MD).Experimental results show that SGO optimization significantly improves the predictive accuracy of software cost models,offering valuable insights for project managers and practitioners in the field.However,the approach’s effectiveness may vary depending on the quality and quantity of available historical data,and its scalability across diverse project types and sizes remains a key consideration for future research.

Towards fast focal mechanism inversion of shallow crustal earthquakes in the Chinese mainland

We have developed an automatic regional focal mechanism inversion system based on the Earthquake Rapid Report(ERR) system and the real-time three-component seismic waveform stream of 1 000 broadband seismic stations provided by the China Earthquake Networks Center(CENC). The system can rapidly provide a double couple solution and centroid depth within 5–15 min after receiving earthquake information from the ERR system.The data processing is triggered by earthquake information obtained from the ERR system. The system is capable of determining the focal mechanism of all shallow-depth earthquakes in the Chinese mainland with a magnitude of 5.5–6.5. It utilizes waveform data recorded by seismic stations located within 500 km from the epicenter,enabling the reporting of a focal mechanism solution within 5–15 min of an earthquake occurrence. Additionally,the system can assign a corresponding grade(A B C) to the focal mechanism solution. We processed a total of 301earthquakes that occurred from 2021 to June 2022, and after the quality control, 166 of them were selected.These selected solutions were manually checked, and 160 of them were compiled in a focal mechanism catalog.This catalog can be conveniently downloaded online via the Internet. The automatic focal mechanism solution of earthquakes in eastern China exhibits a good agreement with that provided by the Global Centroid Moment Tensor(GCMT), when available. The average Kagan angle between this catalog and GCMT is 22°, and the average difference in MWis 0.17. Furthermore, compared with GCMT, the minimum magnitude of our catalog has been reduced from approximately 5.0 to 4.0. The correlation between the centroid depth and crustal thickness in the Chinese mainland confirms the distribution of the centroid depth.

Some Statistical Aspects for Algerian Earthquake Catalogue

The scope of this study is to analyze some aspects of the Algerian earthquake catalogue between 1980 and 2009.Seismicity analysis is based on reliable compilation of earthquake catalogs obtained from different agencies.All intensities and magnitudes were converted to Ms magnitude using appropriate relationships.Dependent events were removed using adapted time and space windows.In addition,the completeness of the catalogue as a function of magnitude was determined from the standard deviation of occurrence rate plots,using the Stepp’s methodology.The remaining 2,016 independent earthquakes with Ms 2.2 were used to obtain various parameters(b-value,z-value)to characterize the temporal and spatial seismic activity for the entire northern part of Algeria.Finally,the obtained results are discussed to explain parameters variability.

Fault detection based on microseismic events

In unconventional reservoirs, small faults allow the flow ofoil and gas as well as act as obstacles to exploration; for, （1） fracturing facilitates fluid migration, （2） reservoir flooding, and （3） triggering of small earthquakes. These small faults are not generally detected because of the low seismic resolution. However, such small faults are very active and release sufficient energy to initiate a large number of microseismic events （MEs） during hydraulic fracturing. In this study, we identified microfractures （MF） from hydraulic fracturing and natural small faults based on microseismicity characteristics, such as the time-space distribution, source mechanism, magnitude, amplitude, and frequency. First, I identified the mechanism of small faults and MF by reservoir stress analysis and calibrated the ME based on the microseismic magnitude. The dynamic characteristics （frequency and amplitude） of MEs triggered by natural faults and MF were analyzed; moreover, the geometry and activity types of natural fault and MF were grouped according to the source mechanism. Finally, the differences among time-space distribution, magnitude, source mechanism, amplitude, and frequency were used to differentiate natural faults and manmade fractures.

Stripe of normal mechanisms for crustal earthquakes with M ≤ 3.5 flanking the western side of the thrust front zone in the Andes backarc

Earthquakes with magnitudes M ≤ 3.5 were registered in the Andes backarc between ~32.5°S 33.75°S within a temporary experiment from November 2002 to March 2003. Data were collected from 15 seismological broad band stations, deployed above flat subduction section and also above the transitional to normal section of the Nazca plate. Seismic events were located mostly in part of the Southern Precordillera and Cerrilladas Pedemontanas of Mendoza Province. Focal mechanism solutions were obtained, for selected data between15 kmand35 kmdepths, from P wave first motion using FOCMEC software. A band trending NW-NNW of normal focal mechanism earthquakes is located just by the thrust front towards West, and covers the Southern tip of the Southern Precordillera and the Western side of the Cerrilladas Pedemontanas, Mendoza Province, Argentina. Thrust focal mechanism solutions obtained in the present work for events with magnitude less than or equal to 3.5 also show that the thrust front South of ~33.1°S is located in the same place as Mw ≥ 3.6 earthquakes. The most significant findings in this work are these signals of extensional regimen which appear in a compressional subduction tectonic regimen. Nevertheless the short temporal experiment precludes firm interpretations about this particular phenomenon. Probably it is related to a temporary stress relaxation. The normal earthquakes are likely associated to normal faults, and/or to their subsidiaries, that were inverted by contraction and now re-inverted at least transitorily as normal. These faults, which are near and to the East of the suture between Chilenia and Cuyania Paleozoic terranes, were originally involved in the Cuyo Triassic basin formation.

The Distance Modulus in Dark Energy and Cardassian Cosmologies via the Hypergeometric Function

The presence of the dark energy allows both the acceleration and the expansion of the universe. In the case of a constant equation of state for dark energy we derived an analytical solution for the Hubble radius in terms of the hypergeometric function. An approximate Taylor expansion of order seven is derived for both the constant and the variable equation of state for dark energy. In the case of the Cardassian cosmology, we also derived an analytical solution for the Hubble radius in terms of the hypergeometric function. The astronomical samples of the distance modulus for Supernova (SN) of type Ia allows the derivation of the involved cosmological in the case of constant equation of state, variable equation of state and Cardassian cosmology.