Applications of seismic moment tensor inversion in fast response to earthquakes

Using the technique of seismic moment tensor inversion, the source mechanisms of 10 earthquakes with Ms5.2that occurred in China from November 1996 to January 1998 were determined rapidly. The determined resultswere sent as 'Bulletins of Source Mechanism Parameters of Earthquakes' to the Seismic Regime Guards' Office,China Seismological Bureau, and the relevant provincial seismological bureaus. These bulletins have played rolein the fast response to large earthquakes.

Evaluation of the seismic moment of the April 20,2013 Lushan earthquake

The April 20, 2013 Lushan earthquake which occurred in Sichuan, China had only moderate thrust. However, the computed seismic moments （M0） for the Lushan earthquake calculated by several institutions differ significantly from 0.4 × 1019 to 1.69 ×019 Nm, up to four times difference. We evaluate ten computed Mos by using normal mode observations from superconducting gravimeters in China's Mainland. We compute synthetic normal modes on the basis of moment tensor solutions and fit them to the observed normal modes. Comparison of our results indicates that Mo is the main cause for some large differences between observations and synthetics. We sug- gest that a moment magnitude of Mw6.6, corresponding to a Mo of 0.97-1.08 × 1019 Nm, characterizes the size and strength of the seismic source of the Lushan earthquake.

Estimating seismic moments and Lg Q using Lg spectra

A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M0) and source corner frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG, MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M0 values obtained by Harvard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M0 values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained ap- parent Q0Lg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The Q0Lg values are 351±87, 349±86 and 300±27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are smaller than Q0Lg values for the paths to KUR, VOS, ZRN and CHK, which are 553±72, 569±58, 550±57 and 603±65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The Q0Lg value for the path to WMQ is 462±56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.

Control Parameters of Magnitude—Seismic Moment Correlation for the Crustal Earthquakes

In connection with conversion from energy class KR (KR = log10E R, where ER — seismic energy, J) to the universal magnitude estimation of the Tien Shan crustal earthquakes the development of the self-coordinated correlation of the magnitudes (mb , ML, Ms ) and KR with the seismic moment M0 as the base scale became necessary. To this purpose, the first attempt to develop functional correlations in the magnitude—seismic moment system subject to the previous studies has been done. It is assumed that in the expression M (mb , ML , Ms) = Ki + zi log10M0 , the coefficients ki? and zi? are controlled by the parameters of ratio?(where;f0 —corner frequency, Brune, 1970, 1971;M0, N×m). According to the new theoretical predictions common functional correlation of the advanced magnitudes Mm (mbm = mb , MLm = ML , MSm = MS ) from log10M0,? log10t0? and the elastic properties (Ci) can be presented as , where , and , for the averaged elastic properties of the Earth’s crust for thembmthe coefficients Ci= –11.30 and di = 1.0, for MLm: Ci = –14.12, di = 7/6;for MSm : Ci = –16.95 and di = 4/3. For theTien Shan earthquakes (1960-2012 years) it was obtained that , and on the basis of the above expressions we received that MSm = 1.59mbm – 3.06. According to the instrumental data the correlation Ms = 1.57mb – 3.05 was determined. Some other examples of comparison of the calculated and observed magnitude - seismic moment ratios for earthquakes of California, the Kuril Islands, Japan, Sumatra and South America are presented.

Seismic moment tensor representations and radiation patterns in unbounded media with elipsoidal cavities driven by low frequency pressure

Seismic waves generated in elastic media by ellipsoidal cavities driven by low frequency pressure can be solved by Eshelby′s method. In this paper we prove that this method, originally presented for elastostatic ellipsoidal inclusion problems, can also be applied to dynamic problems on the assumption that wavelengths are much longer than the dimensions of cavities. Comparison between the approximate solution for spherical cavities and its relevant precise solution shows that this method may be used for radii of cavities smaller than 100 m and for frequencies below 10 Hz. By this approach we show that, for low frequency seismic waves in the far field an explosive load on an ellipsoidal cavity can be equivalent to three dipoles oriented along the principal axes of that cavity. Seismic radiation patterns are given analytically and results thus obtained show that an explosion detonated in an ellipsoidal cavity may radiate significant S waves.

RESEARCH ON THE DEFORMATIONS IN QINGHAI_TIBET PLATEAU AND ITS MARGINS BY INVERTING SEISMIC MOMENT TENSORS AND GPS VELOCITIES

We have determined approximate average rates of deformation in the Qinghai_Tibet plateau and its margins from the GPS data for last 10 years and the moment tensors from earthquakes between 1900 and 1999.We also determined the strain rate (seismic strain rate) associated with the seismic deformation using 254 M w ≥5.0 earthquakes,and estimated the shortening and extension rates for every block in the area as well.We also estimated the strain rate (geodetic strain rate)by 80 GPS sites’ velocity vectors and analyzed characteristic of kinematics by two kinds of strain rates and discussed earthquake potential in the area.As a result,the deformation rates from seismic moment tensors and from GPS velocities are basically agreed with each other.It is feasible to analyze seismic risk by comparing geodetic strain rate with seismic strain rate based on the opinion that strain energy will be released through earthquake.It is concluded that there is no strong earthquake potential (>M7) in the Qinghai_Tibet plateau and its margins,but there is earthquake potential (>M5) in middle Tibet in a few years.

Effectiveness of two conventional methods for seismic retrofit of steel and RC moment resisting frames based on damage control criteria

This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation methods, concentric chevron bracing（CCB） and cylindrical friction damper（CFD） were selected. The performance assessment procedure of the frames is divided into two distinct phases. First, the limit state probabilities of the structures before and after rehabilitation are investigated. In the second phase, the seismic risk of structures in terms of life safety and financial losses（decision variables） using the recently published FEMA P58 methodology is evaluated. The results show that the proposed retrofitting methods improve the serviceability and life safety performance levels of steel and RC structures at different rates when subjected to earthquake loads. Moreover, these procedures reveal that financial losses are greatly decreased, and were more tangible by the application of CFD rather than using CCB. Although using both retrofitting methods reduced damage state probabilities, incorporation of a site-specific seismic hazard curve to evaluate mean annual occurrence frequency at the collapse prevention limit state caused unexpected results to be obtained. Contrary to CFD, the collapse probability of the structures retrofitted with CCB increased when compared with the primary structures.

Optimal seismic retrofit model for steel moment resisting frames with brittle connections

Based on performance-based seismic engineering, this paper proposes an optimal seismic retrofit model for steel moment resisting frames（SMRFs） to generate a retrofit scheme at minimal cost. To satisfy the acceptance criteria for the Basic Safety Objective（BSO） specified in FEMA 356, the minimum number of upgraded connections and their locations in an SMRF with brittle connections are determined by evolutionary computation. The performance of the proposed optimal retrofitting model is evaluated on the basis of the energy dissipation capacities, peak roof drift ratios, and maximum interstory drift ratios of structures before and after retrofitting. In addition, a retrofit efficiency index, which is defined as the ratio of the increment in seismic performance to the required retrofitting cost, is proposed to examine the efficiencies of the retrofit schemes derived from the model. The optimal seismic retrofit model is applied to the SAC benchmark examples for threestory and nine-story SMRFs with brittle connections. Using the retrofit efficiency index proposed in this study, the optimal retrofit schemes obtained from the model are found to be efficient for both examples in terms of energy dissipation capacity, roof drift ratio, and maximum inter-story drift ratio.

A new methodology for energy-based seismic design of steel moment frames

A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom （SDOF） systems are applied to multi-degree-of-freedom （MDOF） steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault- normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design （EBSD） procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.

Seismic design factors for RC special moment resisting frames in Dubai,UAE

This study investigates the seismic design factors for three reinforced concrete （RC） framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code （IBC＇09）. Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years （10/50 and 2/50, respectively） are used. The nonlinear dynamic resPonses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor （R）, deflection amplification factor （Cd）, system overstrength factor （Ωo）, and response modification factor for ductility （Rd） in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion （10/50 versus 2/50）. Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the D~ factor, which shows a mere 30% increase. Based on the observed trends, perioddependent R and Cd factors are recommended if consistent collapse probability （or collapse prevention performance） in moment frames with varying heights is to be expected.

A Catalogue of Earthquakes With Moment Magnitude of the Center-Southern Asia Test Area of the Global Seismic Hazard Assessment Program

We compile a regional catalogue of earthquakes with moment magnitude of the Center-Southern Asia test area(20°-35°N,85°-105°E)for the Global Seismic Hazard Assessment Program(GSHAP).There are significant inhomogeneous and uncompleted data,and n uniformity of earthquake magnitudes in this test area because this region is situated on the boundaries of many countries,such as China,India,Nepal,Vietnam,etc.We establish a relationship between Gutenberg surface-wave magnitude and IASPEI surface-wave magnitude,which can be used for conversion of different magnitude scales into moment magnitude for this catalogue.A catalogue of events with Mw≥6.0 of this test area is given at the end of this paper.

Seismic Evaluation of Steel Moment Resisting Frames (MRFs)—Supported by Loose Granular Soil

Soil underneath a structure might affect the behavior and the overall response of the structure in seismic events. The role of loose soil conditions and the inclusion of soil-structure interaction (SSI) in the analysis are important issues that need to be addressed. Since steel structures are light, two configurations designed as spatial and perimeter are considered to study the effect of soil on the steel structural frames for the same building. The paper provides a parametric analysis on the influence of SSI on the overall performance of MRFs (Moment Resisting Frames) according to the provisions of Saudi Building Code (SBC) [1]. A case study has been developed in which spatial and perimeter moment resisting frames of 12, 6 and 3 stories residential buildings are designed using Saudi Building Code (SBC) prescriptions. A modal response spectrum analysis has been carried out to see the influence of SSI on the fundamental period of vibration, top story displacement and inter-story drift limitations. Moreover, a static non-linear analysis has been performed to investigate the performance of frames, thus allowing to identify the influence of SSI on the structural design of steel MRFs.

Relationships between moment magnitude and fault parameters:theoretical and semi-empirical relationships

Fault parameters are important in earthquake hazard analysis.In this paper,theoretical relationships between moment magnitude and fault parameters including subsurface rupture length,downdip rupture width,rupture area,and average slip over the fault surface are deduced based on seismological theory.These theoretical relationships are further simplified by applying similarity conditions and an unique form is established.Then,combining the simplified theoretical relationships between moment magnitude and fault parameters with seismic source data selected in this study,a practical semi-empirical relationship is established.The seismic source data selected is also to used to derive empirical relationships between moment magnitude and fault parameters by the ordinary least square regression method.Comparisons between semi-empirical relationships and empirical relationships show that the former depict distribution trends of data better than the latter.It is also observed that downdip rupture widths of strike slip faults are saturated when moment magnitude is more than 7.0,but downdip rupture widths of dip slip faults are not saturated in the molnent magnitude rangcs of this study.

Evaluation of the seismic hazard for 20 cities in Romania using Monte Carlo based simulations

This work focuses on the evaluation of the seismic hazard for Romania using earthquake catalogues generated by a Monte Carlo approach. The seismicity of Romania can be attributed to the Vrancea intermediate-depth seismic source and to 13 other crustal seismic sources. The recurrence times of large magnitude seismic events（both crustal and subcrustal）, as well as the moment release rates are computed using simulated earthquake catalogues. The results show that the largest contribution to the overall moment release for the crustal seismic sources is from the seismic regions in Bulgaria, while the seismic regions in Romania contribute less than 5% of the overall moment release. In addition, the computations show that the moment release rate for the Vrancea subcrustal seismic source is about ten times larger than that of all the crustal seismic sources. Finally, the Monte Carlo approach is used to evaluate the seismic hazard for 20 cities in Romania with populations larger than 100,000 inhabitants. The results show some differences between the seismic hazard values obtained through Monte-Carlo simulation and those in the Romanian seismic design code P100-1/2013, notably for cities situated in the western part of Romania that are influenced by local crustal seismic sources.

On temporal and spatial distribution of seismic apparent stresses in Yunnan area

The method of radiation energy （ER） of the earthquake wave measured by the peak velocity （r·v） of the ground motion is applied to a detailed study on the temporal and spatial distribution of the seismic apparent stresses （σa） for the moderate and small earthquakes and two aftershock sequences in Yunnan area. The results show that there exists an obvious non-homogeneity for the seismic apparent stresses in the spatial distribution. The concentrated regions of the high apparent stresses are related to the active places of the moderate and small earthquakes. Before the Dayao M=6.2 earthquake, there was a period in which the apparent stresses were high and the value was 5 times of the average value, 0.25 MPa. The relatively high values of apparent stresses distribute around the epicentral area of the major shock and nearby. It indicates that the variation characteristics of the apparent stresses can be taken as a new kind of criterion for the earthquake-risk forecast. Usually the ratio of the apparent stresses of the aftershock sequence σaA to the ones σaM of main shock is less than 1.0.

Global shear stress pattern in main seismic active belts

Based on the relationship between body wave magnitued m b and seismic moment M 0 presented by PEI SHAN CHEN (1981), by using the moment tensor and focal mechanism solution in the earthquake reports of EDR, a global shear stress pattern including shear stress values and directions of P and T principal axis was obatained. The distribution of ambient shear stress values in the globe is: the highest in intraplate followed by subduction zone, and the lowest in oceanic ridge. The horizontal directions of the maximum principal stresses we got are coincident very well with the result of Zoback (1989). The detail analysis of the stress state in Tonga region shows that: The subduction slab bends down in shallow by press and bends up in deep because of the resistance from deeper part. Between them, the slab is in an equilibrum state. After analysizing the global stress distribution, we got the result that: the plate is driven by a drag force from under its bottom, the plate motion results in its extensional state in oceanic ridge and compressive state in subduction zone.

线性矩法在分布未知条件下的随机结构抗震可靠度分析

在工程结构领域,由于数据不足,结构参数的分布通常未知,这成为结构可靠性分析中常见而复杂的挑战。在结构参数分布未知的情况下,本文提出了随机结构抗震可靠度分析的线性矩法。构造了仅由两个基本随机变量描述的随机动力系统:(1)基于结构随机参数的前四阶线性矩,借助标准正态分布随机变量的随机函数表达,将结构参数的随机变量表示为仅有一个基本随机变量的一元三次多项式;(2)利用一个基本随机变量的随机函数‐谱表示模型描述非平稳地震动过程。在此基础上,根据数论方法确定两个基本随机变量的代表点集,进行时程分析并计算结构响应极值,进而计算确定界限下功能函数的样本及其线性矩;利用功能函数的前四阶线性矩求解三次多项式转换系数;并根据一元三次方程根的求解,建立基于线性矩的结构抗震可靠指标表达式。以结构参数分布未知的非线性单自由度为例说明了本文方法的应用,同时与Monte Carlo模拟结果对比,验证了本文方法的精确性。

Estimation of seismic stress drop from the peak velocity of ground motion

According to the source dislocation model suggested by Brune(1970), the authors have calculated the displacement spectra of S wave and source parameters of the Heqing M S 5 3 earthquake sequence, using the digital data of this sequence obtained in the Western Yunnan Earthquake Prediction Experimental Field (WYEPEF). Based on this calculation we have studied the dependence of the peak velocity ( rv ) of ground motion on the seismic stress drop Δ σ . From the seismic scaling law we obtained ( rv )∝Δ σ 2/3 , thus the three formulae of calculating seismic stress drop Δ σ using the peak velocity parameters can be derived: lg( rv)=d 1+13lg M 0+23lgΔ σ ; lg( rv) =d 2+13 M L+23lgΔ σ ; lgΔ σ =-1 0+1 5lg( rv ) Assuming that the average stress drop Δ σ =3.0×10 6 Pa for great and small earthquakes, then the constants d 1=-3 88 and d 2=-0 38 are determined by the observational data of the Heqing M S5 3 sequence. Results of the source parameters for this sequence show that the seismic moment M 0 is between 10 11 N·m and 10 15 N·m, the rupture radius a of the source is between 200 m and 600 m, the stress drop Δ σ is between 0 1 MPa and 10 MPa and the average stress drop Δ σ =3 7 MPa calculated from the peak velocity parameter of the ground motion. Δσ values measured from these scaling relations are basically in agreement with the results given by Brune′s method( 1970). Results of this study show that the dependence of the ground motion peak velocity parameter (rv) on the stress drop Δσ is even stronger than that on the seismic moment M 0 .

Studies on seismic source

During the period of 1999~2002, the Chinese seismologists made a serious of developments in the study on seismic sources including observations, experiments and theory. In the field of observation, the methods of the accuracy location of earthquake sources, the inversion of seismic moment tensor and the mechanism of earthquake source are improved and developed. A lot of important earthquake events are studied by using these methods. The rupture processes of these events are inverted and investigated combined with the local stress fields and the tectonic moment by using the measurements of surface deformation. In the fields of experiments and theory, many developments are obtained in cause of seismic formation, condition of stress and tectonics, dynamics of earthquake rupture, rock fracture and nucleation of strong earthquakes.

Moment tensor inversion of near-source broadband data

Moment tensor inversion was carried out for small and moderate earthquakes with near-source broadband data recorded by a temporal small-aperture network consisting of three component accelerographs. Accelerograms were integrated twice to produce displacement seismograms and filtered by a Butterworth band-pass filter. Green's functions were calculated for a homogeneous semi-infinite elastic medium in the inversion. Direct P,S and converted SP phases were identified for the inversion with reference to the synthetic seismograms. Through the moment tensor inversion it is demonstrated that with very simple structure model and selected phases, one is able to retrieve the source mechanism and the seismic moment for small events, andthe source mechanism for moderate events. It is also demonstrated that the technique described in this studyis convenient for the determination of source mechanismal and stress state in dealing with numbers of small andmoderate earthquakes without detailed knowledge about the structure. As an application of the present technique, moment tensors of 15 aftershocks of the Ms 6. 1 earthquake occurred on April 18, 1985 in Luquan,Yunnan Province, China were retrieved. The inversion results show that these events can be reasonably modeled by a predominant double couple. It can be found from the distribution of principal stress axes and the average moment tensor that the pressure axis in this area lies horizontally in the NNW direction, which is consistent with the results obtained from previous studies. It implies that the occurrence of the Luquan earthquake sequence is tectonically related to the relative collision motion between the Indian and Eurasian Plates.