Ergodicity in Natural Fault Systems

— Attempts to understand the physics of earthquakes over the past decade generally have focused on applying methods and theories developed based upon phase transitions, materials science, and percolation theory to a variety of numerical simulations of extended fault networks. This recent work suggests that fault systems can be interpreted as mean-field threshold systems in metastable equilibrium (Rundle et al., 1995; Klein et al., 1997; Ferguson et al., 1999), and that these results strongly support the view that seismic activity is highly correlated across many space and time scales within large volumes of the earth’s crust (Rundle et al., 2000; Tiampo et al., 2002). In these systems, the time averaged elastic energy of the system fluctuates around a constant value for some period of time and is punctuated by major events that reorder the system before it settles into another metastable energy well. One way to measure the stability of such a system is to check a quantity called the Thirumalai-Mountain (TM) energy metric (Thirumalai and Mountain, 1993; Klein et al., 1996). In particular, using this metric, we show that the actual California fault system is ergodic in space and time for the period in question, punctuated by the occurrence of large earthquakes, and that, for individual events in the system, there are correlated regions that are a subset of the larger fault network.     

Analysis of GPS Measurements in Eastern Canada Using Principal Component Analysis

Continuous Global Positioning System (CGPS) position time series from eastern North America constrain the pattern and magnitude of regional crustal deformation. Initial analysis delineates consistent uplift patterns, as expected from glacial isostatic adjustment (GIA) predictions, but the associated horizontal deformation is not definitive, in part due to the short time periods for a significant number of the available stations. We employ an eigenpattern decomposition in order to define a unique, finite set of deformation patterns for this continuous GPS data. Similar in nature to the empirical orthogonal functions historically employed in the analysis of atmospheric and oceanographic phenomena, the method derives the eigenvalues and eigenstates from the diagonalization of the correlation matrix using a Karhunen–Loeve expansion (KLE). The KLE technique is used to identify the important modes in both time and space for the CGPS data, modes that potentially include signals such as horizontal and vertical GIA, tectonic strain, and seasonal effects. Here we filter both the vertical and horizontal velocity patterns on different spatiotemporal scales in order to study the potential geophysical sources, after the removal of correlated and random noise. The method is successful in disaggregating the linear vertical signal from more variable and less spatially correlated signals. The vertical and horizontal results are compared to the predictions of the ICE-3G GIA loading model with a number of plausible mantle viscosity profiles. The horizontal velocity analysis allows for qualitative differentiation between several potential GIA models and suggests that, with longer time series, this technique can be employed to remove correlated noise and improve estimates of crustal strain patterns and their sources.     

顾及共性误差的南极半岛地区连续GPS站坐标时间序列分析

共性误差是区域连续GPS网络中存在的一种与时空相关的主要误差源.对区域网络使用空间滤波能够有效减小这种误差并改善坐标时间序列的精度.本文使用GAMIT/GLOBK 10.5软件解算南极半岛区域11个GPS测站2010—2014的数据,各测站独立估计的单天解组成坐标时间序列.利用堆栈法(stacking)、主分量分析法(principal component analysis,简称PCA)和Karhunen-Loeve展开法(KLE)对其进行空间滤波,在利用PCA和KLE方法进行空间滤波时,使用前两个主分量作为共有模式分量.结果表明:三种方法均能有效提取南极半岛区域共性误差,PCA方法的滤波效果明显优于stacking方法,略微优于KLE方法;空间滤波能够有效减小残差时间序列的振幅、功率和RMS;对坐标时间序列进行空间滤波能够有效降低其线性项和周期项误差,从而提高线性项和周期项估计的精度.共性误差的谱分析结果显示在U方向上存在9.4天、13.7天等短周期的信号,推测共性误差组成成分中可能含有与海潮相关的误差源.     

利用GRACE卫星重力资料解算气候驱动的地表周年垂直形变

卫星重力和GPS测量技术可以监测地表流体(大气、海洋和陆地水)质量季节性迁移引起的地表周年形变;与陆地水等地表流体模型综合模拟的地表形变相比,卫星重力的形变监测结果避免了模型的精度不确定性带来的误差.本文利用前60阶GRACE卫星时变重力资料和“去相关”、组合滤波两类滤波方法分别解算了中国及邻区的地表季节性垂直形变,并与区内42个GPS台站上观测到的季节性信号进行了比较,发现采用“去相关”滤波方法处理后的结果优于采用组合滤波处理后的结果.文中采用“去相关”滤波方法,GRACE解算的周年垂直形变的振幅、相位和GPS结果总体上一致;少数站上GRACE和GPS得到的振幅或相位相差较大,主要因素可能与GPS解算策略、GPS观测资料的连续性或局部大气、水文过程等地球物理因素有关.在中国及邻区的陆地上GRACE解算的周年垂直形变的振幅最小值出现在TASH台站东南,约1×10^-3 m;最大值出现在恒河-澜沧江流域,可达10×10^-3 m.文中的结果证实了在中国及邻区可以用GRACE卫星重力这种新手段监测大尺度的地表周年垂直形变.     

Seismotectonic Model and CN Earthquake Prediction in Italy

—The choice of the regions is essential in the application of the algorithm CN, therefore a seismotectonic criterion for their definition is tested. In order to take into account the geodynamic complexity characterising the Italian peninsula, we established to strictly follow the seismotectonic zones, including in each region only zones with similar seismogenic behaviour and the transitional zones connected to them. Three regions have been successfully defined in this way, corresponding approximately to the North, Centre and South of Italy. The reduction of the space-time uncertainty and the increase of the stability of prediction results obtained with this regionalisation, with respect to the previous applications of CN in Italy (Keilis-Borok et al., 1990; Costa et al., 1995, 1996), can be interpreted as a validation of the seismotectonic model.     

Seasonal Water Storage Variations as Impacted by Water Abstractions: Comparing the Output of a Global Hydrological Model with GRACE and GPS Observations

Better quantification of continental water storage variations is expected to improve our understanding of water flows, including evapotranspiration, runoff and river discharge as well as human water abstractions. For the first time, total water storage (TWS) on the land area of the globe as computed by the global water model WaterGAP (Water Global Assessment and Prognosis) was compared to both gravity recovery and climate experiment (GRACE) and global positioning system (GPS) observations. The GRACE satellites sense the effect of TWS on the dynamic gravity field of the Earth. GPS reference points are displaced due to crustal deformation caused by time-varying TWS. Unfortunately, the worldwide coverage of the GPS tracking network is irregular, while GRACE provides global coverage albeit with low spatial resolution. Detrended TWS time series were analyzed by determining scaling factors for mean annual amplitude (f _GRACE) and time series of monthly TWS (f _GPS). Both GRACE and GPS indicate that WaterGAP underestimates seasonal variations of TWS on most of the land area of the globe. In addition, seasonal maximum TWS occurs 1 month earlier according to WaterGAP than according to GRACE on most land areas. While WaterGAP TWS is sensitive to the applied climate input data, none of the two data sets result in a clearly better fit to the observations. Due to the low number of GPS sites, GPS observations are less useful for validating global hydrological models than GRACE observations, but they serve to support the validity of GRACE TWS as observational target for hydrological modeling. For unknown reasons, WaterGAP appears to fit better to GPS than to GRACE. Both GPS and GRACE data, however, are rather uncertain due to a number of reasons, in particular in dry regions. It is not possible to benefit from either GPS or GRACE observations to monitor and quantify human water abstractions if only detrended (seasonal) TWS variations are considered. Regarding GRACE, this is mainly caused by the attenuation of the TWS differences between water abstraction variants due to the filtering required for GRACE TWS. Regarding GPS, station density is too low. Only if water abstractions lead to long-term changes in TWS by depletion or restoration of water storage in groundwater or large surface water bodies, GRACE may be used to support the quantification of human water abstractions.     

利用GPS与GRACE监测陆地水负荷导致的季节性水平形变：以喜马拉雅山地区为例

地表陆地水负荷变化是引起重力场和地壳形变呈现季节性特征的主要因素,并且能够利用地表及空间大地测量技术对其进行有效的监测.本文通过对质量负荷形变效应的理论模拟,描述了水平分量的形变指向以及垂直与水平分量的幅值比可以提高对负荷区域的辨别程度,并且联合GPS坐标时间序列及GRACE模型对喜马拉雅山地区的季节性负荷形变进行了详细对比分析,研究结果显示两者垂直分量的季节性变化具有较好的一致性,且GPS周年项幅值要大于GRACE.而由GRACE解算得到的水平分量结果表明该地区季节性形变主要受东南亚及印度东北部地区的陆地水负荷控制,位于喜马拉雅山地区多数GPS台站的垂直分量及北向分量的初相位与GRACE模型解算结果相近,而部分GPS台站的东向分量与GRACE模型存在明显不同,由此导致GPS与GRACE监测到的形变指向存在差异.通过对GRACE估算精度以及GPS垂直与水平分量幅值比的深入分析,发现GPS对局部周边地区的河流、谷地及农田灌溉等负荷变化造成的形变效应较为敏感,而GRACE由于截断阶次及平滑滤波等影响因素,不仅造成在水平分量上的分辨率远低于垂直分量,而且整体估算精度要低于GPS观测得到的形变信息.     

Postseismic Deformation Following the 1994 Northridge Earthquake Identified Using the Localized Hartley Transform Filter

Here we present a new mathematical tool, the localized Hartley (HL) transform (Hartley, 1942; Bracewell, 1990), that allows for the filtering of 1-D time series through the identification of the power at various spatial and temporal wavelengths. Its application to and the associated results are presented from its application to continuous Global Positioning System (GPS) data from southern California for the time period 1994 through 2006. The HL transform filter removes the high-frequency components of the data and effectively isolates the longer period signal. This long-period signal is modeled as time-dependent postseismic deformation using the viscoelastic-gravitational model of Fernández and Rundle (2004) for six stations selected for their proximity to the Northridge earthquake. The x-, y-, and z-components of the postseismic deformation are compared to the filtered data. Results suggest that this long-period deformation is a result of postseismic relaxation and that the HL transform filter provides an important new technique for the filtering of geophysical data consisting of the superposition of the effects of numerous complex sources at a variety of spatial and temporal scales.     

A Quantitative Assessment of DInSAR Measurements of Interseismic Deformation: The Southern San Andreas Fault Case Study

We investigate the capabilities and limitations of the Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques, in particular of the Small BAseline Subset (SBAS) approach, to measure surface deformation in active seismogenetic areas. The DInSAR analysis of low-amplitude, long-wavelength deformation, such as that due to interseismic strain accumulation, is limited by intrinsic trade-offs between deformation signals and orbital uncertainties of SAR platforms in their contributions to the interferometric phases, the latter being typically well approximated by phase ramps. Such trade-offs can be substantially reduced by employing auxiliary measurements of the long-wavelength velocity field. We use continuous Global Positioning System (GPS) measurements from a properly distributed set of stations to perform a pre-filtering operation of the available DInSAR interferograms. In particular, the GPS measurements are used to estimate the secular velocity signal, approximated by a spatial ramp within the azimuth-range radar imaging plane; the phase ramps derived from the GPS data are then subtracted from the available set of DInSAR interferograms. This pre-filtering step allows us to compensate for the major component of the long-wavelength range change that, within the SBAS procedure, might be wrongly interpreted and filtered out as orbital phase ramps. With this correction, the final results are obtained by simply adding the pre-filtered long-wavelength deformation signal to the SBAS retrieved time series. The proposed approach has been applied to a set of ERS-1/2 SAR data acquired during the 1992–2006 time interval over a 200?×?200?km area around the Coachella Valley section of the San Andreas Fault in Southern California, USA. We present results of the comparison between the SBAS and the Line Of Sight (LOS)—projected GPS time series of the USGC/PBO network, as well as the mean LOS velocity fields derived using SBAS, GPS and stacking techniques. Our analysis demonstrates the effectiveness of the presented approach and provides a quantitative assessment of the accuracy of DInSAR measurements of interseismic deformation in a tectonically active area.     

中国大陆构造块体的现今活动和变形

在重新对 1998年和 2 0 0 0年的中国地壳运动观测网络基准站和基本站的 2期观测资料进行预处理的基础上 ,得到了ITRF97坐标框架下 ,参考时刻分别为 1998年 9月 5日和 2 0 0 0年 6月 8日 ,分布在全国各主要构造块体上的 79个GPS站的坐标和协方差矩阵。分别以中国岩石圈动力学地图集 (马杏垣 ,1989)中的中国大陆主要构造单元 (称之为亚板块 )和张培震等 ( 2 0 0 2 )给出的中国主要活动块体为格架 ,用笔者提出的 1种推广了的QUAD方法对中国大陆的 2 0个主要构造块体逐个进行判别检验。那些现今无明显相对运动的相邻块体则被归并起来 ,从而确定了活动块体和它们的边界。采用刚体运动 +块体均匀应变 +局部变形的模型作为描述中国大陆构造块体的现今活动和变形的模型。求出了有明显相对运动块体的欧拉运动矢量和块体的整体均匀变形参数、各块体内部的不均匀局部变形以及活动边界的活动方式和强度。在此基础上 ,除了一般地指出中国大陆地壳运动西强东弱的特征之外 ,还对西部主要活动块体和边界活动强弱给出了定量比较结果 ,从而为强震危险区的判别提供了形变背景依据     

A statistical description on the wind-coherent responses of sea surface heights off the US West Coast

Local and remote wind-coherent responses of sea surface heights (SSHs) off the US West Coast (USWC) are described with statistical and analytical models. The wind transfer functions are statistically derived from surface wind stress at National Data Buoy Center (NDBC) buoys, located within 50 km from the shoreline, and detided SSHs (SSH anomalies; SSHAs) at shoreline tide gauges for 15 years (1995 to 2009) using linear regression in the frequency domain. A two-dimensional analytical model constrained by the coastal boundary provides a dynamical framework to interpret the data-derived statistical model. Although both transfer functions agree well at low frequency [σ ≤ 0.4 cycles per day (cpd)], they appear to be inconsistent at high frequency (σ ≥ 0.8 cpd; e.g., diurnal and its harmonic frequencies) because of incoherent signals between wind stress and SSHAs as well as their low signal-to-noise ratios. A multivariate regression analysis using wind stress at multiple wind buoys is implemented with a modified expectation maximization. The cross-validated skill increases and becomes saturated as the number of regression basis functions increases, demonstrating the influence of local and remote winds. The skill computed from all available winds off the USWC has a maximum as 0.1 in southern California, 0.2 to 0.3 in central California, and 0.3 to 0.5 in northern California, Oregon, and Washington. The residual SSHAs, incoherent components with all available coastal wind stress off the USWC, still contain poleward propagating signals, considered as components forced by remote winds outside of the domain.     

Basin patterns of upper ocean warming for 1993–2009

A previous study (Lyman et al., Nature 465:334–337, 2010) showed a robust warming signal of the global upper ocean (0–700 m). They examined several sources of uncertainty that contribute to differences among heat content estimations. However, their focus was limited to globally averaged estimation. This study presents the spatial pattern of the global heat content change based on observed gridded datasets (Levitus et al., Geophys Res Lett 36:L07608, 2009). The western Pacific, Atlantic, and Indian Oceans showed significant warming trends, whereas eastern Pacific and some areas of the Gulf Stream experienced negative trends during 1993–2009. Steady warming trend was obtained from the first EOF mode when El Nino and Southern Oscillation (ENSO)-related signals were removed. This result implies that the rapid increase in heat content of the upper ocean around 2000–2005 is not related to a sampling transition from XBT to Argo observations but is associated with a natural variability dominated by strong ENSO-related signals.     

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     

Ten-antenna prototype of a radio heliograph based on the Siberian Solar Radio Telescope

An upgrade of the Siberian Solar Radio Telescope (SSRT) [Smolkov et al., 1986; Grechnev et al., 2003] to a multiwave radio heliograph has been started. The radio heliograph being created will be designed mainly to measure coronal magnetic fields, to determine the locations of solar-flare energy release, and to investigate coronal mass ejections. These tasks define the parameters of next-generation radio heliographs. A high spatial resolution, a high image acquisition rate, and a high sensitivity are required simultaneously. All these parameters should be realized in the widest possible frequency range—from fractions to tens of GHz). The expected parameters of the future SSRT-based radio heliograph are listed below: spatial resolution 12″–24″, temporal resolution 0.02–1.0 s, frequency range 4–8 GHz, sensitivity up to 100 K, left-hand and right-hand circular polarizations, data rate 0.5–20 Mb s⁻¹ (normal and flare modes). In this paper, we describe the broadband antennas, analog optical data transmission lines, and correlator used in the 10-antenna radio heliograph prototype.     

Crustal deformation before the 2008 Wenchuan MS8.0 earthquake studied using GPS data

We used GPS velocities from approximately 700 stations in western China to study the crustal deformation before the Wenchuan M_S8.0 earthquake. The processing methods included analyses of the strain rate field, inversion of fault locking and the GPS velocity profiles. The GPS strain rate in the E-W direction in the Qinghai-Tibet block shows that extensional deformation was dominant in the western region of the block (west of 92.5° E), while compressive deformation predominated in the eastern region of the block (from 92.5° E to 100° E). On a regional scale, the hypocentral region of the Wenchuan earthquake was located at the edge of an intense compression deformation zone of about 1.9 × 10⁻⁸/a in an east-west direction. The characteristic deformation in the seismogenic fault was compressive with a dextral component. The compression deformation rate was greater in the fault's western region than in its eastern region, and the strain accumulation was very slow on the fault scale. The results of a fault locking inversion show that the locking fraction and slip deficit was greater in the middle-northern section of the seismogenic fault than in the southern section. The GPS velocity profile before the Wenchuan earthquake shows that the compression deformation was smaller than the dextral deformation, which is asymmetrical with respect to the distribution of co-seismic displacement. These deformation characteristics should provide some clues to the Wenchuan earthquake which occurred in the later period of the earthquake cycle.     

Large-scale travelling atmospheric disturbances in the night ionosphere during the solar–terrestrial event of 23 May 2002

This paper examines the night of 23 May 2002 as observed by a large number of Australian ionosondes (19) as well as others situated in New Guinea, Indonesia and China. The arrival of a solar Coronal Mass Ejection (CME) and subsequent negative Bz turnings in the solar wind resulted in a magnetic storm with two bursts of energy inputs into the auroral zones. The energy depositions produced two successive rise and falls in ionospheric height over a 300 km height range within the period 12.30–21.00 UT. The two events were seen in the night-side hemisphere by all ionosondes at Southeast Asian longitudes in the southern hemisphere, as well as in the northern hemisphere. In this paper, the simultaneity and spatial variability of these events is investigated. The first event, after an initial expansion towards the equator, ended with a retreat in the area of height rise back towards the auroral zone. The second event was of greater complexity and did not show such a steady variation in rise and fall times with latitude. Such events are often described as large-scale travelling atmospheric/ionospheric disturbances (LTADs or LTIDs). In the southern hemisphere, the front of the initial height rise was found to move at a speed up to 1300 m/s as was also measured by Tsugawa et al. [2006. Geomagnetic conjugate observations of large-scale travelling ionospheric disturbances using GPS networks in Japan and Australia. Journal of Geophysical Research 111, A02302] from small changes in GPS TEC. The front was uniform across the widest longitudinal range of observation (52° or 5360 km).The relationship between the subsequent fall in ionospheric height and an associated temporary increase in foF2 was found to be consistent with previous observations. Ionospheric drivers that move ionization up and down magnetic field lines are suggested as the common cause of the relationship between foF2 and height.     

基于GPS和GRACE数据的三维地表形变的比较及地球物理解释

GPS技术能以高空间和高时间分辨率监测地表形变.但由于测量原理的不同,GPS监测的地表形变与GRACE存在差异.本文比较了ITRF2008-GPS残差序列与基于CSR的RL05版本的GRACE球谐系数的地表形变序列的差异.结果表明,GPS和GRACE的周年变化在高程方向上具有较好的一致性,但水平方向的差异明显.重点分析了影响GPS/GRACE地表形变差异(尤其是水平方向)的三个因素:不同GPS站时间序列间的不确定性,热弹性形变和区域形变.GPS站地表形变本身的不确定度在一定程度上导致了GPS/GRACE间的差异(特别是水平方向).结合热弹性形变理论指出,由温度变化引起的热弹性形变也是导致GPS/GRACE的南北方向差异的主要原因之一.因此利用GPS数据研究地表质量负载时,必须消除热弹性形变的影响.区域负载对GPS/GRACE水平方向差异的影响也是不可忽略的,特别是对欧洲区域.     

Ergodicity and Earthquake Catalogs: Forecast Testing and Resulting Implications

Recently the equilibrium property of ergodicity was identified in an earthquake fault system (Tiampo et al., Phys. Rev. Lett. 91, 238501, 2003; Phys. Rev. E 75, 066107, 2007). Ergodicity in this context not only requires that the system is stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages when studying their behavior in space and time. In this work we show that this property can be used to identify those regions of parameter space which are stationary when applied to the seismicity of two naturally-occurring earthquake fault networks. We apply this measure to one particular seismicity-based forecasting tool, the Pattern Informatics index (Tiampo et al., Europhys. Lett. 60, 481–487, 2002; Rundle et al., Proc. National Acad. Sci., U.S.A., Suppl. 1, 99, 2463, 2002), in order to test the hypothesis that the identification of ergodic regions can be used to improve and optimize forecasts that rely on historic seismicity catalogs. We also apply the same measure to synthetic catalogs in order to better understand the physical process that affects this accuracy. We show that, in particular, ergodic regions defined by magnitude and time period provide more reliable forecasts of future events in both natural and synthetic catalogs, and that these improvements can be directly related to specific features or properties of the catalogs that impact the behavior of their spatial and temporal statistics.     

On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case

In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers (e.g., Fernández and Rundle, 1994a,b; Fernández et al., 1997, 2005a; Tiampo et al., 2004; Charco et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational field equations.