A new approach for separating mixed model parameters:application to simultaneous inversion of earthquake source parameters

A method for simultaneous determination of mixed model parameters,which have different physical dimensions or different responses to data,is presented.Mixed parameter estimation from observed data within a single model space shows instabilities and trade-offs of the solutions. We separate the model space into N-subspaces based on their physical properties or computational convenience and solve the N-subspaces systems by damped least-squares and singular-value decomposition. Since the condition number of each subsystem is smaller than that of the single global system,the approach can greatly increase the stability of the inversion. We also introduce different damping factors into the subsystems to reduce the tradeoffs between the different parameters. The damping factors depend on the conditioning of the subsystems and may be adequately chosen in a range from 0.1 % to 10 % of the largest singular value. We illustrate the method with an example of simultaneous determination of source history,source geometry,and hypocentral location from regional seismograms,although it is applicable to any geophysical inversion.     

球坐标系下多震相走时三参数同时反演成像

球坐标系下多震相走时三参数(速度、震源位置和反射界面)同时反演需要解决两个关键问题:(1)球坐标系下3D速度模型中多次透射、反射(折射)及转换波精确、快速的射线追踪;(2)同时反演时三种不同参数间的强耦合问题.为此,我们将直角坐标系下分区多步不规则最短路径算法推广至球坐标系中,进行区域或者全球尺度的多震相射线追踪.然后将其与适合多参数同时反演的子空间算法相结合,形成一种球坐标系下联合多震相走时三参数同时反演的方法技术.与双参数(速度和反射界面或速度和震源位置)同时反演的数值模拟对比分析显示:三参数与双参数的同时反演结果大体接近,并且它们对到时数据中可容许的随机噪声不太敏感.结果说明本文中的同时反演成像为一种提高成像分辨率,同时反演速度、震源位置和反射界面的有效方法.     

An Evaluation of Coulomb Stress Changes from Earthquake Productivity Variations in the Western Gulf of Corinth,Greece

Spatial and temporal evolution of the stress field in the seismically active and well-monitored area of the western Gulf of Corinth, Greece, is investigated. The highly accurate and vast regional catalogues were used for inverting seismicity rate changes into stress variation using a rate/state-dependent friction model. After explicitly determining the physical quantities incorporated in the model (characteristic relaxation time, fault constitutive parameters, and reference seismicity rates), we looked for stress changes across space and over time and their possible association with earthquake clustering and fault interactions. We focused our attention on the Efpalio doublet of January 2010 (M = 5.5 and M = 5.4), with a high aftershock productivity, and attempted to reproduce and interpret stress changes prior to and after the initiation of this seismicity burst. The spatial distribution of stress changes was evaluated after smoothing the seismological data by means of a probability density function (PDF). The inverted stress calculations were compared with the calculations derived from an independent approach (elastic dislocation model) and this comparison was quantified. The results of the two methods are in good agreement (up to 80 %) in the far field, with the inversion technique providing more robust results in the near field, where they are more sensitive to the uncertainties of coseismic slip distribution. It is worth mentioning that the stress inversion model proved to be a very sensitive stress meter, able to detect even small stress changes correlated with spatio–temporal earthquake clustering. Data analysis was attempted from 1975 onwards to simulate the stress changes associated with stronger earthquakes over a longer time span. This approach revealed that only M > 5.5 events induce considerable stress variations, although in some cases there was no evidence for such stress changes even after an M > 5.5 earthquake.     

Site response and source spectra of S waves in the Zagros region, Iran

S wave amplitude spectra from shallow earthquakes with magnitudes ranging between 4.2 and 6.2 in the Zagros region of Iran that occurred between 1998 and 2008 are used to examine source parameters and site response of S waves. A generalized inversion scheme has been used to separate the source, propagation path, and local site effects from S wave spectra. For removing the trade-off between source and site terms and propagation effects (including geometric and anelastic attenuation), the spectral amplitudes of the records used were corrected for attenuation and geometrical spreading function using a path model proposed by Zafarani and Soghrat (Bull Seism Soc Am 102:2031–2045, 2012) for the region. We assume a Brune’s point source model to retrieve source parameters like corner frequency, moment magnitude, and high-frequency fall off coefficient, for each event. When the source spectra are interpreted in terms of Brune’s model, the average stress drops obtained are about 7.1 and 5.9 MPa (71 and 59 bars), respectively for the eastern and western Zagros regions. Stress drops range from 1.4 to 35.0 MPa (14 to 350 bars), with no clear dependence on magnitude. The results in terms of stress drop and S wave seismic energy indicate that the Zagros events are more similar to interplate earthquakes of western North America than to intraplate events of eastern North America. The method also provides us with site responses for all 40 stations individually and is an interesting alternative to other methods, such as the H/V method. A new empirical relationship between body-wave magnitudes and moment magnitude has been proposed for the Iranian plateau using derived seismic moment from the inversion.     

Nonlinear simultaneous inversion of pore structure and physical parameters based on elastic impedance

Carbonate reservoirs have complex pore structures, which not only significantly affect the elastic properties and seismic responses of the reservoirs but also affect the accuracy of the prediction of the physical parameters. The existing rockphysics inversion methods are mainly designed for clastic rocks, and the inversion objects are generally porosity and water saturation. The data used are primarily based on the elastic parameters, and the inversion methods are mainly linear approximations. To date, there has been a lack of a simultaneous pore structure and physical parameter inversion method for carbonate reservoirs. To solve these problems, a new Bayesian nonlinear simultaneous inversion method based on elastic impedance is proposed. This method integrates the differential effective medium model of multiple-porosity rocks, Gassmann equation,Amplitude Versus Offset(AVO) theory, Bayesian theory, and a nonlinear inversion algorithm to achieve the simultaneous quantitative prediction of the pore structure and physical parameters of complex porous reservoirs. The forward modeling indicates that the contribution of the pore structure, i.e., the pore aspect ratio, to the AVO response and elastic impedance is second only to that of porosity and is far greater than that of water saturation. The application to real data shows that the new inversion method for determining the pore structure and physical parameters directly from pre-stack data can accurately predict a reservoir's porosity and water saturation and can evaluate the pore structure of the effective reservoir.     

多震相走时联合三参数同时反演成像

采用新近研制的分区多步不规则最短路径多震相地震射线追踪正演技术,结合流行的子空间反演算法,提出了一种联合多震相走时资料进行地震三参数 （速度、反射界面和震源位置） 同时反演的方法技术.数值模拟反演实例、以及与双参数 （速度和反射界面或速度和震源位置） 同时反演的对比分析表明：三参数同时反演成像结果大体接近双参数同时反演成像的结果.另外,噪声敏感性试验表明：所提算法对到时数据中可容许的随机误差并不敏感,结果说明多震相走时的联合三参数同时反演成像方法技术不失为一种提高走时成像空间分辨率、进而降低重建模型参数失真度、行之有效的方法技术.     

Implications of 2007’s Earthquake Activity in Eğirdir Lake (SW Anatolia) Based on Moment Tensor Solutions and Inversion of Stress State

We analyzed the waveforms of the small- to moderate-sized earthquakes that took place in the northern part of the inner Isparta Angle (IA) to retrieve their source parameters and combine these results with the focal mechanism solutions of the larger events that occurred in 2007 in E?irdir Lake at the apex of IA. In total, source mechanisms of 20 earthquakes within the magnitude range 3.5 < M < 5.0 were calculated using a regional moment tensor inversion technique. The inversion of the focal mechanisms yields an extensional regime with a NNE–SSW (N38°E) trending σ ₃ axis. Inversion results are related to a mainly WNW–ESE oriented normal fault beneath E?irdir Lake. The R value of a NNE–SSW extensional regime is 0.562 showing a triaxial stress state in the region. The current stress regime results from complex subduction processes such as slab pull, slab break-off, roll-back and/or retreating mechanism along the Hellenic and Cyprus arcs and the southwestward extrusion of the Anatolian block since the early Pliocene.     

Source and high-frequency decay parameters for the Azores region for stochastic finite-fault ground motion simulations

Strong ground motion prediction based on finite-fault simulation requires the identification of the fault (strike, dip, length and width), source kinematics parameters (stress drop, rupture velocity and slip distribution), regional crustal properties (geometrical spreading, anelastic structure, and upper crustal amplification and attenuation parameters) and the determination of amplification effects due to the local site geology. The general purpose of this study is to understand source and attenuation properties in the Azores, by the determination of stress drop, quality factor and kappa, through records obtained by the Portuguese digital seismic and accelerometer network. Source Spectra were obtained, for each record, after correcting observed spectra from geometrical spreading and anelastic attenuation effect: quality factor was estimated based on coda decay in the time domain and the kappa parameter was estimated by fitting the high-frequency decay of the acceleration spectrum with a straight line in a log-linear scale. Mean stress drop value was obtained considering that ω-squared model for the source spectra prevails. Parameters kappa, k, and quality factor, Q, have been estimated to be k = (0.075 ± 0.02)s and \(Q(f) = (76 \pm 11)f^{0.69 \pm 0.09}\), respectively. A mean value of stress drop was estimated to be around 90–130 bars for the earthquakes in analysis. The knowledge of source and path parameters, in association with other ground motion parameters, allows improving ground-motion estimates for the Azores and, consequently, will lead to more accurate seismic hazard assessment for the Azores and better characterization of seismic scenarios.     

The Beni Haoua,Algeria, Mw 4.9 earthquake: source parameters,engineering, and seismotectonic implications

A moderate Mw 4.9 earthquake struck the Beni Haoua (Algeria) coastal area on April 25, 2012. The mainshock was largely recorded by the accelerograph network of the Centre National de Recherche Appliquée en Génie Parasismique (CGS). The same day the earthquake occurred, eight mobile short period stations were deployed through the epicentral area. In this study, we use accelerogram and seismogram data recorded by these two networks. We combined the focal mechanism built from the first motion of P waves and from waveform inversion, and the distribution of aftershocks to well constrain the source parameters. The mainshock is located with a shallow focal depth, ～9 km, and the focal mechanism shows a nearly pure left lateral strike slip motion, with total seismic moment of 2.8?×?10¹⁶ N.m (M_w?=?4.9). The aftershocks mainly cluster on a narrow NS strip, starting at the coast up to 3–4 km inland. This cluster, almost vertical, is concentrated between 6 and 10 km depth. The second part of this work concerns the damage distribution and estimated intensity in the epicentral area. The damage distribution is discussed in connection with the observed maximum strong motion. The acceleration response spectrum with 5 % damping of the mainshock and aftershocks give the maximum amplitude in high frequency which directly affects the performance of the high-frequency structures. Finally, we tie this earthquake with the seismotectonic of the region, leading to conclude that it occurred on a N–S transform zone between two major compressional fault zones oriented NE–SW.     

The 15 August 2007 Peru Earthquake and Tsunami: Influence of the Source Characteristics on the Tsunami Heights

The tsunami caused by the 2007 Peru earthquake (M_w 8.0) provoked less damage than by the seismic shaking itself (numerous casualties due to the earthquake in the vicinity of Pisco). However, it propagated across the Pacific Ocean and small waves were observed on one tide gauge in Taiohae Bay (Nuku Hiva, Marquesas, French Polynesia). We invert seismological data to recover the rupture pattern in two steps. The first step uses surface waves to find a solution for the moment tensor, and the second step uses body waves to compute the slip distribution in the source area. We find the slip distribution to consist of two main slip patches in the source area. The inversion of surface waves yields a scalar moment of 8.9 10²⁰ Nm, and body-wave inversion gives 1.4 10²¹ Nm. The inversion of tsunami data recorded on a single deep ocean sensor also can be used to compute a fault slip pattern (yielding a scalar moment of 1.1 10²¹ Nm). We then use these different sources to model the tsunami propagation across the Pacific Ocean, especially towards Nuku Hiva. While the source model taken from the body-wave inversion yields computed tsunami waves systematically too low with respect to observations (on the central Pacific Ocean DART buoy as on the Polynesian tide gauge), the source model established from the surface-wave inversion is more efficient to fit the observations, confirming that the tsunami is sensitive to the low frequency component of the source. Finally we also discuss the modeling of the late tsunami arrivals in Taiohae Bay using several friction coefficients for the sea bottom.     

Earthquake Source Zones in Northeast India: Seismic Tomography, Fractal Dimension and b Value Mapping

We have imaged earthquake source zones beneath the northeast India region by seismic tomography, fractal dimension and b value mapping. 3D P-wave velocity (Vp) structure is imaged by the Local Earthquake Tomography (LET) method. High precision P-wave (3,494) and S-wave (3,064) travel times of 980 selected earthquakes, m _d ≥ 2.5, are used. The events were recorded by 77 temporary/permanent seismic stations in the region during 1993–1999. By the LET method simultaneous inversion is made for precise location of the events as well as for 3D seismic imaging of the velocity structure. Fractal dimension and seismic b value has been estimated using the 980 LET relocated epicenters. A prominent northwest–southeast low Vp structure is imaged between the Shillong Plateau and Mikir hills; that reflects the Kopili fault. At the fault end, a high-Vp structure is imaged at a depth of 40 km; this is inferred to be the source zone for high seismic activity along this fault. A similar high Vp seismic source zone is imaged beneath the Shillong Plateau at 30 km depth. Both of the source zones have high fractal dimension, from 1.80 to 1.90, indicating that most of the earthquake associated fractures are approaching a 2D space. The spatial fractal dimension variation map has revealed the seismogenic structures and the crustal heterogeneities in the region. The seismic b value in northeast India is found to vary from 0.6 to 1.0. Higher b value contours are obtained along the Kopili fault (~1.0), and in the Shillong Plateau (~0.9) The correlation coefficient between the fractal dimension and b value is found to be 0.79, indicating that the correlation is positive and significant. To the south of Shillong Plateau, a low Vp structure is interpreted as thick (~20 km) sediments in the Bengal basin, with almost no seismic activity in the basin.     

Three‐dimensional potential field data inversion with L0 quasinorm sparse constraints

The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.     

Earthquake source parameters and scaling relationships in Hungary (central Pannonian basin)

Fifty earthquakes that occurred in Hungary (central part of the Pannonian basin) with local magnitude $M_\textrm{L}$ ranging from 0.8 to 4.5 have been analyzed. The digital seismograms used in this study were recorded by six permanent broadband stations and 20 short-period ones at hypocentral distances between 10 and 327 km. The displacement spectra for P- and SH-waves were analyzed according to Brune’s source model. Observed spectra were corrected for path-dependent attenuation effects using an independent regional estimate of the quality factor Q _S . To correct spectra for near-surface attenuation, the κ parameter was calculated, obtaining it from waveforms recorded at short epicentral distances. The values of the κ parameter vary between 0.01 and 0.06 s with a mean of 0.03 s for P-waves and between 0.01 and 0.09 s with a mean of 0.04 s for SH-waves. After correction for attenuation effects, spectral parameters (corner frequency and low-frequency spectral level) were estimated by a grid search algorithm. The obtained seismic moments range from 4.21×10¹¹ to 3.41×10¹⁵ Nm (1.7?≤?M _w ?≤?4.3). The source radii are between 125 and 1,343 m. Stress drop values vary between 0.14 and 32.4 bars with a logarithmic mean of 2.59 bars (1 bar = 10⁵ Pa). From the results, a linear relationship between local and moment magnitudes has been established. The obtained scaling relations show slight evidence of self-similarity violation. However, due to the high scatter of our data, the existence of self-similarity cannot be excluded.     

Determination of source,path and site parameters based on non-linear inversion of accelerometric data in Greece

Source, propagation path and site conditions are the factors affecting seismic ground motion. Consequently, recordings acquired at a seismic station are formed by the convolution of these three factors. In this work S-wave acceleration Fourier spectra of earthquakes recorded at local and regional scale, by the ITSAK accelerometric network for the period 2010–2016, are modeled as a product of source, propagation path (including geometric and anelastic attenuation) and site effects. The data set consists of 136 crustal earthquakes occurred in the broader Aegean area, with magnitudes 4.2?≤?M_w?≤?6.5 and epicentral distances 20 km?≤?R?≤?350 km, recorded at 112 broadband accelerometric stations installed at sites with various geologic conditions. Based on this data set, an iterative Gauss–Newton inversion method to solve the non-linear problem and retrieve the different terms of source, propagation path and site, is applied. This method uses an initial input model trying to find the best and at the same time a stable solution for the inverted parameters, which are, moment magnitude (M_w), corner frequency (f_c), attenuation quality factor (Q_s?=?Q_of^α), slope of the geometric attenuation (1/R^γ) and site transfer function (S(f)). The initial values of the starting model can be either known from other studies or inferred within a reasonable range. Depending on the level of knowledge on these input parameters, the associated standard deviation can be adjusted (large values for unknown parameters or small values for parameters which are well constrained). Results of the analyses exhibit satisfactory agreement of estimated source parameters with those proposed by seismological centers in Greece and propagation path properties similar to the ones determined in relevant previous studies for the same region. In addition, the site transfer functions obtained by the non-linear inversion are comparable with those calculated for the same sites using either standard spectral ratio or horizontal-to-vertical spectral ration (HVSR—receiver function) techniques. The aforementioned results are encouraging for reliable earthquake source parameters, propagation path properties and site effect assessment, in areas of intermediate to high seismicity.     

Source parameters of seismic events potentially associated with damage in block 33/34 of the Kiirunavaara mine (Sweden)

Forty-six mining-induced seismic events with moment magnitude between ?1.2 and 2.1 that possibly caused damage were studied. The events occurred between 2008 and 2013 at mining level 850–1350 m in the Kiirunavaara Mine (Sweden). Hypocenter locations were refined using from 6 to 130 sensors at distances of up to 1400 m. The source parameters of the events were re-estimated using spectral analysis with a standard Brune model (slope ?2). The radiated energy for the studied events varied from 4.7 × 10^?1 to 3.8 × 10⁷ J, the source radii from 4 to 110 m, the apparent stress from 6.2 × 10² to 1.1 × 10⁶ Pa, energy ratio (E _s/E _p) from 1.2 to 126, and apparent volume from 1.8 × 10³ to 1.1 × 10⁷ m³. 90% of the events were located in the footwall, close to the ore contact. The events were classified as shear/fault slip (FS) or non-shear (NS) based on the E _s/E _p ratio (>10 or <10). Out of 46 events 15 events were classified as NS located almost in the whole range between 840 and 1360 m, including many events below the production. The rest 31 FS events were concentrated mostly around the production levels and slightly below them. The relationships between some source parameters and seismic moment/moment magnitude showed dependence on the type of the source mechanism. The energy and the apparent stress were found to be three times larger for FS events than for NS events.     

Source parameters of the 27th of June 2015 Gulf of Aqaba earthquake

On the 27 June 2015, at 15:34:03 UTC, a moderate-sized earthquake of M _w 5.0 occurred in the Gulf of Aqaba. Using teleseismic P waves, the focal mechanism of the mainshock was investigated by two techniques. The first technique used the polarities of the first P wave onsets, and the second technique was based on the normalized waveform modeling technique. The results showed that the extension stress has a NE orientation with a shallow southward plunge while the compression stress has a NW trend with a nearly shallow westward plunge, obtaining a strike-slip mechanism. This result agrees well with the typical consequence of crustal deformation resulting from the ongoing extensional to shear stress regime in the Gulf of Aqaba (NE-SW extension and NW-SE compression). The grid search method over a range of focal depths indicates an optimum solution at 15 ± 1 km. To identify the causative fault plane, the aftershock hypocenters were relocated using the local waveform data and the double-difference technique. Considering the fault trends, the spatial distribution of relocated aftershocks demarcated a NS-oriented causative fault, in consistence with one of the nodal planes of the focal mechanism solution, emphasizing the dominant stress regime in the region. Following the Brune model, the estimates of source parameters exhibited fault lengths of 0.29 ≤ L ≤ 2.48 km, moment magnitudes of 3.0 ≤ M _w ≤ 5.0, and stress drops of 0.14 ≤ Δσ < 1.14 MPa, indicating a source scaling similar to the tectonic earthquakes related to plate boundaries.     

基于地质统计先验信息的储层物性参数同步反演

本文提出的储层物性参数同步反演是一种高分辨率的非线性反演方法,该方法综合利用岩石物理和地质统计先验信息,在贝叶斯理论框架下,首先通过变差结构分析得到合理的变差函数,进而利用快速傅里叶滑动平均模拟算法（Fast Fourier TransformMoving Average,FFT-MA）和逐渐变形算法（Gradual Deformation Method,GDM）得到基于地质统计学的储层物性参数先验信息,然后根据统计岩石物理模型建立弹性参数与储层物性参数之间的关系,构建似然函数,最终利用Metropolis算法实现后验概率密度的抽样,得到物性参数反演结果。并将此方法处理了中国陆上探区的一块实际资料,本方法的反演结果具有较高的分辨率,与测井数据吻合度较高;由于可以直接反演储层物性参数,避免了误差的累积,大大减少了不确定性的传递,且计算效率较高。     

A study on the uncertainties of the centroid depth of the 2013 Lushan earthquake from teleseimic body wave data

Centroid depth of earthquakes is essential for seismic hazard mitigation. But, various studies provided different solutions for the centroid depth of the damaging 2013 Lushan earthquake, thus hindering further studies of the earthquake processes. To resolve its centroid depth and assess the uncertainties, we apply the teleseismic cut and paste method to invert for centroid depth with teleseismic body waves in the epicentral distance of 30°–90°. We performed the inversion for P waves only as well the case of both P and SH waves and found that both cases lead to depth solutions with difference less than 0.5 km. We also investigated the effects on depth inversion from azimuth gap of seismic stations, source duration, and corner frequency of filter. These various tests show that even azimuthal distribution of seismic stations is helpful for accurate depth inversion. It is also found that estimate of centroid depth is sensitive to source duration. Moreover, the depth is biased to larger values when corner frequency of low-pass filter is very low. The uncertainty in the velocity model can also generate some error in the depth estimation (~1.0 km).With all the above factors considered, the centroid depth of Lushan earthquake is proposed to be around 12 km, with uncertainty about 2 km.     

(T2,D)二维核磁共振测井混合反演方法与参数影响分析

一维核磁共振(1D NMR)测井技术在流体识别中具有一定的局限性.二维核磁共振(2D NMR)测井能同时测量到多孔介质中横向弛豫时间(T₂)和扩散系数(D)等信息,利用这两个参数区分流体性质,较一维核磁共振测井技术具有明显的优越性.针对梯度场下的2D NMR测井弛豫机理和数学模型,提出了适用于求解大型稀疏矩阵方程的反演方法-基于非负最小二乘法(LSQR)和截断奇异值分解(TSVD)法的混合算法.为验证方法的有效性,先根据多回波观测模式合成回波串数据,然后再用混合反演算法进行反演,反演得到横向弛豫时间(T₂)和扩散系数(D),并构建T₂-D二维谱图.结果对比表明,该混合反演算法得到的T₂-D二维谱与流体模型一致性好,计算精度均比单一反演方法有较大改善,表明该混合反演方法可用于油气储集层2D NMR测井的反演和流体识别.此外,分别对油水同层和气水同层模型进行了正演模拟和反演实验, 系统考察了不同磁场梯度、不同回波间隔组合对反演效果的影响,为2D NMR参数设计提供依据.     

Stress Release and Source Scaling of the 2010–2011 Canterbury,New Zealand Earthquake Sequence from Spectral Inversion of Ground Motion Data

The Canterbury earthquake sequence beginning with the 2010 M _W 7.2 Darfield earthquake is one of the most notable and well-recorded crustal earthquake sequences in a low-strain-rate region worldwide and as such provides a unique opportunity to better understand earthquake source physics and ground motion generation in such a tectonic setting. Ground motions during this sequence ranged up to extreme values of 2.2 g, recorded during the February 2011 M _W 6.2 event beneath the city of Christchurch. A better understanding of the seismic source signature of this sequence, in particular the stress release and its scaling with earthquake size, is crucial for future ground motion prediction and hazard assessment in Canterbury, but also of high interest for other low-to-moderate seismicity regions where high-quality records of large earthquakes are lacking. Here we present a source parameter study of more than 200 events of the Canterbury sequence, covering the magnitude range M _W 3–7.2. Source spectra were derived using a generalized spectral inversion technique and found to be well characterized by the ω ^?2 source model. We find that stress drops range between 1 and 20 MPa with a median value of 5 MPa, which is a factor of 5 larger than the median stress drop previously estimated with the same method for crustal earthquakes in much more seismically active Japan. Stress drop scaling with earthquake size is nearly self-similar, and we identify lateral variations throughout Canterbury, in particular high stress drops at the fault edges of the two major events, the M _W 7.2 Darfield and M _W 6.2 Christchurch earthquakes.