On the limits of linear moment tensor inversion of surface wave spectra

Some theoretical and practical limits to linear moment tensor inversion of surface waves are analyzed in detail, in particular when one or few stations are used for rapid determination of source parameters. The theory is briefly outlined and steps of preprocessing, especially corrections for source history and propagation, are discussed in order to guarantee the validity of the moment tensor inversion. The inverse problem is first studied from a theoretical point of view. Then the feasibility of the moment tensor inversion is tested from synthetic computations and the formalism is improved in order to obtain a better system conditioning. Finally, some cases of practical nonuniqueness of the solution are shown and possible restrictions to the applicability of the method are discussed. All steps are illustrated with the example of theM _s =6.9 Erzincan (Turkey) earthquake of March, 13, 1992.     

The inversion of anelastic coefficient,source parameters and site respond using genetic algorithm

It gradually becomes a common work using large seismic wave data to obtain source parameters, such as seismic moment, break radius, stress drop, with completingof digital seismic network in China (Hough, et al, 1999; Bindi, et al, 2001). These parameters are useful on earthquake prediction and seismic hazard analysis.Although the computation methods of source parameters are simple in principle and the many research works have been done, it is not easy to obtain the parameters accurately. There are two factors affecting the stability of computation results. The first one is the effect of spread path and site respond on signal. According to the research results, there are different geometrical spreading coefficients on different epicenter distance. The better method is to introduce trilinear geometrical spreading model (Atkinson, Mereu, 1992; Atkinson, Boore, 1995; WONG, et al, 2002). In addition, traditional site respond is estimated by comparing with rock station, such as linear inversion method (Andrews, 1982), but the comparative estimation will introduce some errors when selecting different stations. Some recent research results show that site respond is not flat for rock station (Moya, et al, 2000; ZHANG,. et al, 2001; JIN, et al, 2000; Dutta, et al, 2001). The second factor is to obtain low-frequency level and corner frequency fromdisplacement spectrum. Because the source spectrum model is nonlinear function,these values are obtained by eye. The subjectivity is strong. The small change of corner frequency will affect significantly the result of stress drop.     

应用近场速度记录快速估算川滇地区中强地震强度

采用Wu等(2004)提出的地震强度测定方法,应用近场速度波形记录,测定地震参数M_(ew),实现了川滇地区中强地震(M_W≥5.7)强度近实时快速测定。M_(ew)是一个与矩震级M_W对接的地震参数,与传统的应用振幅测定震级的方法相比,不会存在震级饱和问题,与全球矩心矩张量(GCMT)的矩震级M_W具有较好的一致性。该方法解决了应用近场波形资料和矩张量反演方法求取大地震矩震级比较困难的问题,可为区域中强地震速报提供近实时矩震级提供参考,从而提高地震速报的时效性和准确性,同时为强震加速度数据的应用奠定基础。     

Empirical models for estimating liquefaction-induced lateral spread displacement

Existing empirical models for estimating liquefaction-induced lateral spread displacement (D_LL) have been derived from a dataset poorly distributed with respect to earthquake magnitude and source distance, and also produced from different tectonic source types and faulting mechanisms. Both the poor distribution and mixed tectonic source types and faulting mechanisms of the data have an adverse impact on the reliability of the empirical models. To overcome these problems in the development of empirical models, we replace the direct use of magnitude and source distance with pseudo-displacement derived from spectral acceleration attenuation models that are well supported by earthquake data, and use a modification factor to account for effects of the non-linear soil response. Attenuation models derived from very large and reasonably well-balanced datasets have been selected, one being a Japanese attenuation model and other being a combination of the Sadigh et al. model and the Youngs et al. model. These models are capable of accounting for the effects of earthquake tectonic source type and faulting mechanism. We determined the model coefficients by selecting the pseudo-displacements calculated for a number of spectral periods to achieve an unbiased distribution of residuals with respect to earthquake magnitude and source distance. Sensitivity analyses have been carried out based on the new and existing models, and show that the new model is more robust than the existing models. Comparison with a limited number of data from the 1997 Kocaeli, Turkey earthquake suggests our model provides comparable liquefaction-induced lateral displacement D_LL estimates.     

Transfrontier macroseismic observations of the Ml = 5.4 earthquake of February 22, 2003 at Rambervillers,France

The 2003 Ml = 5.4 Rambervillers earthquake, north-east of France, is the largest seismic event recorded north of the Alps since the 1992 Ms = 5.3, I₀ = VII, Roermond earthquake, Netherlands. With a maximum macroseismic intensity of VI-VII EMS-98, the 2003 event was broadly felt to a distance of 300 km from the epicentre. It provides a unique opportunity to test and compare the different procedures used in France, Germany and Switzerland when evaluating macroseismic intensities. The main purpose of this paper is to present a common transfrontier macroseismic map based on the EMS-98 intensity scale. Maximum horizontal accelerations recorded in the area are compared to the intensity values, and we propose to use a differential technique to re-estimate the magnitude of the 1682 Remiremont, I₀ = VIII, earthquake, which occurred 40 km south of Rambervillers.     

Validation of a kinematic and parametric approach to calculating intensity scenarios

We employ our semi-empirical kinematic model for shear body waves (KF) [Sirovich L. A simple algorithm for tracing out synthetic isoseismals. Bull Seism Soc Am 1996;86(4):1019–27; Sirovich L. Synthetic isoseismals of three earthquakes in California-Nevada. Soil Dyn Earthquake Eng 1997;16:353–62] to back-predict and then validate the regional intensity scenario of a destructive earthquake (Loma Prieta, California, M_s 7.1, October 17, 1989). Only the pre-1988 geological and seismotectonic knowledge was used to set the 11 source parameters of KF (in this sense, our procedure was deterministic). Then, the ranges of the pre-1988 uncertainties were explored by grid search and the parametric combination produced 59,049 sources. The quality of our prediction was measured using the field intensities of 1989 by the US Geological Survey (in the MMI scale). The squared scenario residuals are: 73 for the mean KF scenario and 123 for the best available empirical attenuation of MMI intensity. We stress that, before using KF in the forward mode, its automatic inverse application has already been validated by refinding a series of earthquake sources [Gentile F, Pettenati F, Sirovich L. Validation of the automatic nonlinear source inversion of the US geological survey intensities of the Whittier Narrows, 1987 Earthquake. Bull Seism Soc Am 2004;94(5):1737–47; Pettenati F, Sirovich L. Intensity-based source inversion of three destructive California earthquakes. Bull Seism Soc Am 2007;97(5):1587–606; Sirovich L, Pettenati F. Source inversion of intensity patterns of earthquakes: a destructive shock in 1936 in northeast Italy. J Geophys Res 2004;109:B10309, doi:10.1029/2003JB002919:1–16]. If our technique had been available at the time, the 1989 pattern of damage south of San Francisco would have been conservatively foreseen even from 1983 on.     

Near-realtime source analysis of the 20 March 2012 Ometepec-Pinotepa Nacional,Mexico earthquake

We apply a single-step, finite-fault analysis procedure to derive a coseismic slip model for the large M_W 7.4 Ometepec-Pinotepa Nacional, Mexico earthquake of 20 March 2012, using teleseismic P waveforms recorded by the Global Seismographic Network. The inversion is conducted in near-realtime using source parameters available from the USGS/NEIC and the Global Centroid Moment Tensor (gCMT) project. The fault orientation and slip angle are obtained from the gCMT mechanism assuming that the fault coincides with the shallow-dipping nodal plane. The fault dimensions and maximum rise time are based on the magnitude reported for the event. Teleseismic data from the USGS/NEIC Continuous Waveform Buffer database are used in the inversion with record start times set to the P-wave arrivals used to compute the earthquake hypocenter. The inversion is stabilized by requiring a smooth transition of slip across the fault while minimizing the seismic moment. These constraints are applied using a smoothing weight that is estimated from the inverse problem, allowing the recovery of the least-complicated rupture history in a single step. Inversion of the deconvolved, ground-displacement waveforms reveals a simple, circular rupture similar in extent to the source identified by the USGS/NEIC using body-and surface-wave data, indicating that the teleseismic P waves can provide a first-order source model for the event in near-realtime. Additional inversions conducted using velocity records identify a more-detailed rupture model characterized by an elliptical 2500 km² source region extending updip and downdip from the hypocenter. This elliptical source preserves the orientation and overall dimensions of a dual-source slip model obtained recently by other investigators using local strong motions and global seismic waveforms. The results indicate that velocity waveforms could provide additional details of the earthquake rupture in near-realtime, finite-fault inversions using teleseismic P waves.     

Crustal velocity structure of central Gansu Province from regional seismic waveform inversion using firework algorithm

The firework algorithm (FWA) is a novel swarm intelligence-based method recently proposed for the optimization of multi-parameter, nonlinear functions. Numerical waveform inversion experiments using a synthetic model show that the FWA performs well in both solution quality and efficiency. We apply the FWA in this study to crustal velocity structure inversion using regional seismic waveform data of central Gansu on the northeastern margin of the Qinghai-Tibet plateau. Seismograms recorded from the moment magnitude (M _W) 5.4 Minxian earthquake enable obtaining an average crustal velocity model for this region. We initially carried out a series of FWA robustness tests in regional waveform inversion at the same earthquake and station positions across the study region, inverting two velocity structure models, with and without a low-velocity crustal layer; the accuracy of our average inversion results and their standard deviations reveal the advantages of the FWA for the inversion of regional seismic waveforms. We applied the FWA across our study area using three component waveform data recorded by nine broadband permanent seismic stations with epicentral distances ranging between 146 and 437 km. These inversion results show that the average thickness of the crust in this region is 46.75 km, while thicknesses of the sedimentary layer, and the upper, middle, and lower crust are 3.15, 15.69, 13.08, and 14.83 km, respectively. Results also show that the P-wave velocities of these layers and the upper mantle are 4.47, 6.07, 6.12, 6.87, and 8.18 km/s, respectively.     

用应变地震观测求解震源矩张量的基本原理

震源机制解,即对地震矩张量的推断,对于地震研究具有至关重要的意义.应变地震观测是张量观测,与摆式地震仪的位移矢量观测不同,可以为地震研究提供新的数据源.本文讨论用应变地震观测求解震源矩张量的基本原理.在距离震源足够远的地方,地震波可以看成平面波,其性质决定于震源矩张量.假设平面地震波的应变张量可以由震源矩张量通过坐标变换计算得到,就可以通过观测应变地震波求解震源机制.这个假设至少对于双力偶震源机制是成立的.由此可以证明,在理想的无限介质中,只要有两个以上不同地点的应变地震波观测,就可以解出震源矩张量.这为解决震源机制问题提供了新的方法.目前的地震矩张量求解方法需要两方面的条件:或者需要很多观测点(例如体波反演),或者需要长周期地震波资料(例如面波反演).这些方法只适用于分析比较大的地震.对于小震,因为通常其震中周围不会有足够多的摆式地震仪观测点观测到其地震波,而地震波周期又短,难以利用传统方法给出可靠的震源机制解,所以只需少数观测点就能求解震源矩张量的新方法特别有意义.用应变地震观测求解震源机制,可以给出更为精确的结果.     

Inversion of potential field data using the structural index as weighting function rate decay

Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.     

Tectonic and Kinematic Regime along the Northern Caribbean Plate Boundary: New Insights from Broad-band Modeling of the May 25, 1992, Ms = 6.9 Cabo Cruz, Cuba, Earthquake

—On May 25th, 1992, an M _s = 6.9 earthquake occurred off the southwestern tip of Cuba, along the boundary between the Caribbean and North American plates. This earthquake was the largest to strike southern Cuba since 1917 and the largest ever recorded in that region by global seismic networks. It is therefore a key element for our understanding of the tectonic and kinematic regime along the northern Caribbean plate boundary. In order to test the previously proposed source parameters of the Cabo Cruz earthquake and to better constrain its focal mechanism, we derived a new set of source parameters from unfiltered broad-band teleseismic records. We used a hybrid ray tracing method that allows us to take into account propagation effects of seismic waves in a realistic crustal model around the source. Our solution is consistent with the long-period focal mechanism solution of Virieux et al. (1992). Our solution also models the higher frequency crustal and water layer phases. The primarily strike-slip focal mechanism has a small thrust component. Its shows an east-west trending nodal plane dipping 55° to the north that we interpret as the rupture plane since it corresponds to the geometry of the major active fault in that area. The displacement on this plane is a left-lateral strike-slip combined with a small amount of southward thrust. The result is in good agreement with the active tectonic structures observed along the Oriente fault south of Cuba. The small thrust component demonstrates that, contrary to prior belief, the transpressive regime extends along this whole segment of the Caribbean/North American plate boundary. Together with historical seismicity, it suggests that most of the stress accumulated by the Caribbean/North American plate motion is released seismically along the southern Cuban margin during relatively few but large earthquakes.     

Estimation of maximum mass velocities in the focal zones of strong earthquakes based on measured displacements of rock blocks: A case study of Kyrgyzstan

An important task in seismic hazard assessment is estimation of the intensity and frequency of extremely strong earthquake effects, in particular, peak ground velocities (PGV). Earlier, a method was proposed to evaluate PGV values based on the magnitude of displacements of rock blocks (Rodkin et al., 2012). In this study, this method is used to analyze field data on the source zones of the August 19, 1992, M_S = 7.3 Susamyr earthquake and the January 3, 1911, M_w = 7.9 Kemin earthquake, and estimate maximum ground shaking at the upper construction site of the Upper Naryn series of hydropower plants, Kyrgyz Republic. It is shown that the resulting estimates are consistent with data obtained through other techniques. Therefore, the new approach can be recommended to estimate earthquake effects.     

中国东南地区塑性流动波与地震迁移(Ⅰ)

根据岩石圈塑性流动网络与塑性流动波 (网络波 )的观点 ,在采用和改进以往对于亚洲中东部其它地区网络波研究方法的基础上 ,通过地震活动沿塑性流动网带的迁移、速度场及边界起波期等研究 ,绘制了中国东南地区网络波走时等值线图和波峰带分布图 ,初步展示了网络波控制下的地震能量背景 ,为进一步的研究及该地区地震能量背景的物理预测提供了依据     

3D crustal structure and long-period ground motions from a M9.0 megathrust earthquake in the Pacific Northwest region

We have developed a community velocity model for the Pacific Northwest region from northern California to southern Canada and carried out the first 3D simulation of a M_w 9.0 megathrust earthquake rupturing along the Cascadia subduction zone using a parallel supercomputer. A long-period (<0.5 Hz) source model was designed by mapping the inversion results for the December 26, 2004 Sumatra–Andaman earthquake (Han et al., Science 313(5787):658–662, 2006) onto the Cascadia subduction zone. Representative peak ground velocities for the metropolitan centers of the region include 42 cm/s in the Seattle area and 8–20 cm/s in the Tacoma, Olympia, Vancouver, and Portland areas. Combined with an extended duration of the shaking up to 5 min, these long-period ground motions may inflict significant damage on the built environment, in particular on the highrises in downtown Seattle.     

A compact representation of spatio-temporal slip distribution on a rupturing fault

We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379–27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (M _W6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed. Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained by conventional kinematic source inversions.     

The 1991 Racha earthquake, Caucasus: Multiple source model with compensative type of motion

The source of the 1991 Racha earthquake in the Greater Caucasus generally corresponds to thrusting, which is characteristic of the predominant regional compression stress field. A more adequate view of the rupture process is provided by a complex source model composed of three subsources. This model is reconstructed by the body-wave inversion and consistent with the spatial distribution of the aftershocks. In terms of the suggested model, at the last stage of the rupture process, the opposite slip type (normal faulting) is observed in the source, which seems to be objective. It compensates the rapid (probably short) local redistribution of stresses caused by the thrusts in the first two subsources. The surface deformations observed in the epicentral zones of strong earthquakes are probably the analogs of such a compensative mechanism. For example, in the rear parts of the thrusts associated with the surface ruptures, normal faults trending parallel to the strike of the thrust line occur. Another analog of the compensative motion is probably the peculiarities of the aftershock sources. It has long since been noted (Kuznetsova et al., 1976) that some fault plane solutions in the aftershock sequences of strong earthquakes are close to the main shock solution, while others are different. The explanation of this phenomenon is suggested in (Kuznetsova et al., 1976; Kostrov and Das, 1988). In (Kuznetsova et al., 1976), these events are referred to as the aftershocks due to the fracture growth and aftershocks of relaxation, respectively.     

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions. We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.     

2013年四川芦山MS7.0地震 强地面运动模拟

运用经验格林函数法模拟2013年4月20日芦山M_S7.0地震的近场强地面运动. 在拟合过程中, 首先参考前人远场反演结果给出的滑动量分布特征和主震波形的包络线特征, 确定强震动生成区的大致范围和数量; 然后利用Somerville等提出的地震矩与凹凸体面积的经验关系式确定强震动生成区细小划分的初值, 继而利用遗传优化算法确定以上二者的最优值及其它震源参数. 将数值模拟波形与实际地震观测记录在时间域和频率域分别进行比较, 结果显示, 在所选取的30个观测台站中, 多数台站的数值模拟结果与实际观测结果符合得很好, 特别是大于1 Hz的高频部分. 断层面上有两个强震动生成区, 其位置与前人反演的滑动量集中分布区相一致, 而且强震动生成区规模比Somerville等获得的标度率估计值要小.      

地震自相似现象初探

依据破裂过程和震源物理参数相似性,给出了自相似震源椭球体三轴之比约为a:b:c=1:0.2:0.2。基于分维理论和方法,讨论了自相似的地震时空分布的分维和强震前的降维现象。由前兆展布范围,大震前区域地震活动特征以及地震空区等可导出近源前兆(红肿)区线性尺度约为震源区的5倍。     

Focal Mechanism Solutions of the 2008 Wenchuan earthquake sequence from P-wave polarities and SH/P amplitude ratios: new results and implications

The 2008 Wenchuan earthquake, a major intraplate earthquake with M _w 7.9, occurred on the slowly deforming Longmenshan fault. To better understand the causes of this devastating earthquake, we need knowledge of the regional stress field and the underlying geodynamic processes. Here, we determine focal mechanism solutions (FMSs) of the 2008 Wenchuan earthquake sequence (WES) using both P-wave first-motion polarity data and SH/P amplitude ratio (AR) data. As P-wave polarities are more reliable information, they are given priority over SH/P AR, the latter of which are used only when the former has loose constraint on the FMSs. We collect data from three categories: (1) permanent stations deployed by the China Earthquake Administration (CEA); (2) the Western Sichuan Passive Seismic Array (WSPSA) deployed by Institute of Geology, CEA; (3) global stations from Incorporated Research Institutions for Seismology. Finally, 129 events with magnitude over M _s 4.0 in the 2008 WES are identified to have well-constrained FMSs. Among them, 83 are well constrained by P-wave polarities only as shown by Cai et al. (Earthq Sci 24(1):115–125, 2011), and the rest of which are newly constrained by incorporating SH/P AR. Based on the spatial distribution and FMSs of the WES, we draw following conclusions: (1) the principle compressional directions of most FMSs of the WES are subhorizontal, generally in agreement with the conclusion given by Cai et al. (2011) but with a few modifications that the compressional directions are WNW–ESE around Wenchuan and ENE–WSW around Qingchuan, respectively. The subhorizontal compressional direction along the Longmenshan fault from SW to NE seems to have a left-lateral rotation, which agrees well with regional stress field inverted by former researchers (e.g., Xu et al., Acta Seismol Sin 30(5), 1987; Acta Geophys Sin 32(6), 1989; Cui et al., Seismol Geol 27(2):234–242, 2005); (2) the FMSs of the events not only reflected the regional stress state of the Longmenshan region, but also were obviously controlled by the faults to some extent, which was pointed out by Cai et al. (2011) and Yi et al. (Chin J Geophys 55(4):1213–1227, 2012); (3) while the 2008 Wenchuan earthquake and some of its strong aftershocks released most of the elastic energy accumulated on the Longmenshan fault, some other aftershocks seem to occur just for releasing the elastic energy promptly created by the 2008 Wenchuan earthquake and some of its strong aftershocks. (4) Our results further suggest that the Longmenshan fault from Wenchuan to Beichuan was nearly fully destroyed by the 2008 Wenchuan earthquake and accordingly propose that there is less probability for great earthquakes in the middle part of the Longmenshan fault in the near future, although there might be a barrier to the southwest of Wenchuan and it is needed to pay some attention on it in the near future.