Modeling of spatially correlated,site-reflected,and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.     

Hydrology and change

Abstract

Since “panta rhei” was pronounced by Heraclitus, hydrology and the objects it studies, such as rivers and lakes, have offered grounds to observe and understand change and flux. Change occurs on all time scales, from minute to geological, but our limited senses and life span, as well as the short time window of instrumental observations, restrict our perception to the most apparent daily to yearly variations. As a result, our typical modelling practices assume that natural changes are just a short-term “noise” superimposed on the daily and annual cycles in a scene that is static and invariant in the long run. According to this perception, only an exceptional and extraordinary forcing can produce a long-term change. The hydrologist H.E. Hurst, studying the long flow records of the Nile and other geophysical time series, was the first to observe a natural behaviour, named after him, related to multi-scale change, as well as its implications in engineering designs. Essentially, this behaviour manifests that long-term changes are much more frequent and intense than commonly perceived and, simultaneously, that the future states are much more uncertain and unpredictable on long time horizons than implied by standard approaches. Surprisingly, however, the implications of multi-scale change have not been assimilated in geophysical sciences. A change of perspective is thus needed, in which change and uncertainty are essential parts.

Editor Z.W. Kundzewicz

Citation Koutsoyiannis, D., 2013. Hydrology and change. Hydrological Sciences Journal, 58 (6), 1177–1197.     

Three distinct reversing modes in the geodynamo

The data that describe the long-term reversing behavior of the geodynamo show strong and sudden changes in magnetic reversal frequency. This concerns both the onset and the end of superchrons and most probably the occurrence of episodes characterized by extreme geomagnetic reversal frequency (>10–15 rev./Myr). To account for the complexity observed in geomagnetic reversal frequency evolution, we propose a simple scenario in which the geodynamo operates in three distinct reversing modes: i—a “normal” reversing mode generating geomagnetic polarity reversals according to a stationary random process, with on average a reversal rate of ～3 rev./Myr; ii—a non-reversing “superchron” mode characterizing long time intervals without reversal; iii—a hyper-active reversing mode characterized by an extreme geomagnetic reversal frequency. The transitions between the different reversing modes would be sudden, i.e., on the Myr time scale. Following previous studies, we suggest that in the past, the occurrence of these transitions has been modulated by thermal conditions at the core-mantle boundary governed by mantle dynamics. It might also be possible that they were more frequent during the Precambrian, before the nucleation of the inner core, because of a stronger influence on geodynamo activity of the thermal conditions at the core-mantle boundary.     

Space- and Time-Dependent Probabilities for Earthquake Fault Systems from Numerical Simulations: Feasibility Study and First Results

In weather forecasting, current and past observational data are routinely assimilated into numerical simulations to produce ensemble forecasts of future events in a process termed “model steering”. Here we describe a similar approach that is motivated by analyses of previous forecasts of the Working Group on California Earthquake Probabilities (WGCEP). Our approach is adapted to the problem of earthquake forecasting using topologically realistic numerical simulations for the strike-slip fault system in California. By systematically comparing simulation data to observed paleoseismic data, a series of spatial probability density functions (PDFs) can be computed that describe the probable locations of future large earthquakes. We develop this approach and show examples of PDFs associated with magnitude M > 6.5 and M > 7.0 earthquakes in California.     

地震预测预报经验的积累

根据《中国震例》所载1966年至1985年以来，全国Ms≥5.0的58次中强地震的《震例》研究成果，从应用的角度出发，探讨了动态跟踪预测未来中强地震活动“时”、“空”、“强”的活动规律，得出如下启示1)利用地震的前兆总体演变过程的阶段性以探讨定量预测其“活动时段”；2)利用地震的前兆总体分布图象以探讨定量预测其“活动空间”；3)利用地震的前兆环的规模以粗略地预估其未来强震的“活动强度”。还初步探讨了利用它们的“场”、“源”演变的关联性，提出文中一些作法的物理意义之所在。     

再论地震大小的度量

本文是针对迄今为止中国在地震大小的度量方面存在的主要问题撰写的。 在阐明地震大小物理含义的基础上, 首先指出由震源辐射能量E_R出发所定义的传统震级标度M_L, m_b(m_B), M_S都存在着“以偏概全”, “震级饱和”和M_L震级标度的“局限性”, 以及不同标度的震级之间不可相互换算等问题。 而由在地震破裂的整个过程中震源区“等效力”所做的功出发导出的地震矩M₀是对地震大小最科学的度量。 为继续应用“震级”这一术语来描述地震的大小, 由M₀所定义的矩震级标度M_W不仅克服了传统震级标度存在的各种问题, 而且适用对不同大小、 不同震中距、 不同震源深度地震大小的度量。 因此近20年已被国际地震学界普遍采用。 最后强调推进地震大小的度量与国际接轨是推进中国地震科技现代化必须解决的重要基础性工作, 不仅有利于国际地震科技交流合作, 而且有助于增强防震减灾工作的科学性。     

Seismic microzoning from synthetic ground motion earthquake scenarios parameters: The case study of the city of Catania (Italy)

The city of Catania (Italy) in the South-Eastern Sicily has been affected in past times by several destroying earthquakes with high values of estimated magnitude. The seismogenic area to the south of Volcano Etna, known as Iblean Area, is placed between the African and the Euro-Asiatic plates on the west of the Ibleo-Maltese escarpment, to the south of the Graben of the Sicilian channel and on the east of the overlapping front of Gela. Basing on the seismic history of Catania, the following earthquake scenarios have been considered: the “Val di Noto” earthquake of January 11, 1693 (with intensity X-XI on MCS scale, magnitude M_W=7.41 and epicentral distance of about 13 km); the “Etna” earthquake of February 20, 1818 (with intensity IX on MCS scale, magnitude M_W=6.23 and epicentral distance of about 10 km). The soil response analysis at the surface, in terms of time history and response spectra, has been obtained by 1-D equivalent linear models for about 1200 borings location available in the data-bank of the central area of Catania of about 50 km², using deterministic design scenario earthquakes as input at the conventional bedrock.Seismic microzoning maps of the city of Catania have been obtained in terms of different peak ground acceleration at the surface and in terms of amplification ratios for given values of frequency.     

Investigations into critical earthquake load models within deterministic and probabilistic frameworks

This paper deals with the determination of critical earthquake load models for linear structures subjected to single‐point seismic inputs. The primary objective of this study is to examine the realism in critical excitations and critical responses vis a vis the framework adopted for the study and constraints that these excitations are taken to satisfy. Two alternative approaches are investigated. In the first approach, the critical earthquake is expressed in terms of a Fourier series that is modulated by an enveloping function that imparts transient nature to the inputs. The Fourier coefficients are taken to be deterministic and are constrained to satisfy specified upper and lower bounds. Estimates on these bounds, for a given site, are obtained by analysing past earthquake records from the same site or similar sites. The unknown Fourier coefficients are determined such that the response of a given structure is maximized subjected to these bounds and additional constraints on intensity, peak ground acceleration, peak ground velocity and peak ground displacement. In the second approach, the critical earthquake is modelled as a partially specified non‐stationary Gaussian random process which is defined in terms of a stationary random process of unknown power spectral density (psd) function modulated by a deterministic envelope function. The input is constrained to possess specified variance and average zero crossing rate. Additionally, a new constraint in terms of entropy rate representing the expected level of disorder in the excitation is also imposed. The unknown psd function of the stationary part of the input is determined so that the response of a given structure is maximized. The optimization problem in both these approaches is solved by using sequential quadratic programming method. The procedures developed are illustrated by considering the seismic response of a tall chimney and an earth dam. It is concluded that the imposition of lower and upper bounds on Fourier coefficients in the first approach and constraints on amount of disorder in the second approach are crucial in arriving at realistic critical excitations. Copyright © 2002 John Wiley & Sons, Ltd.     

A vortex-tube model of eddies in the inertial range

Abstract

A vortex-tube geometry of the cascade of energy to small-scale eddies, in the inertial range of fully-developed turbulence, is proposed. The model is a special case of the beta model of Frisch, Sulem and Nelkin (1978). We require that the cascade conserve the principal invariants of inviscid, incompressible flow, namely volume, topological knottedness, circulation, and, at discrete times marking the termination of steps in the cascade, energy. The process terminates in a finite time, as in any beta model, leaving behind a self-similar network of “inactive” tubes. We associate a self-similar scaling dimension D with the structure, equal to the Hausdorff dimension of the set of “active” tubes at the termination of the cascade. Because circulation Λ plays a key role in the analysis of the cascade, we refer to these vortex-tube geometries as “gamma models”. The viewpoint throughout is entirely deterministic.

We describe two examples of gamma models. In the ring geometry, an eddy is a vortex ring, and the cascade produces “rings upon rings”, so we allow cutting and fusing of tubes while conserving total helicity. In the preferred helical model, no cutting is needed, and the cascade produces an infinite progression of braided “coils upon coils”. We suggest that latter geometry as a candidate for the topology of a singularity of the inviscid limit of a Navier-Stokes flow, when modeled by discrete vortex tubes.

A crucial ingredient of a gamma model, not explicitly present in a beta model, is the possibility of “splitting” a vortex tube into sub-tubes carrying smaller circulation. We suggest a dynamical basis for this process, as an instability of tubes whose cores violate the Rayleigh criterion.

The parameters describing a gamma model are not uniquely determined by our study, but there is a “simplest” helical gamma model, involving minimal splitting and distortion of tubes. The dimension D of the structure is 13/5, with a scale factor Λ = 2^?5/4. This value of D agrees with that suggested by Hentschel and Procaccia (1982), by analogy with established results for certain branched polymers.     

Evaluating direct and indirect evidence of climatic change by Hölder regularity and order pattern in time series

The several competing reconstructions of Northern Hemisphere temperature variability exists with partly conflicting evidence. Here we considered a specific problem of choosing “the best” reconstruction, in a frame of assumptions, that they are produced by smooth dynamical system as well as instrumental time series. Using some sophisticated measures of similarity, we could not match to all existing hemispheric paleoclimate reconstructions with hypothesis about any deterministic system which can produced its as typical projection of their trajectories. The results cast doubt on the conventional techniques frequently used to reconstruct past climate variability.     

Seasonal temperature extremes in Potsdam

The awareness of global warming is well established and results from the observations made on thousands of stations. This paper complements the large-scale results by examining a long time-series of high-quality temperature data from the Secular Meteorological Station in Potsdam, where observation records over the last 117 years, i.e., from January 1893 are available. Tendencies of change in seasonal temperature-related climate extremes are demonstrated. “Cold” extremes have become less frequent and less severe than in the past, while “warm” extremes have become more frequent and more severe. Moreover, the interval of the occurrence of frost has been decreasing, while the interval of the occurrence of hot days has been increasing. However, many changes are not statistically significant, since the variability of temperature indices at the Potsdam station has been very strong.     

A sample reconstruction method based on a modified reservoir index for flood frequency analysis of non-stationary hydrological series

Flood extremes, affected by climate change and intense human activities, exhibit non-stationary characteristics. As a result, the stationarity assumption of traditional flood frequency analysis (FFA) cannot be satisfied. Generally, the impacts of human activities, especially water conservancy projects (i.e., reservoirs), on extreme flood series are much greater than those of climate change; therefore, new FFA methods must be developed to address the non-stationary flood extremes associated with large numbers of reservoirs. In this study, a new sample reconstruction method is proposed to convert the reservoir-influenced annual maximum flow (AMF) series from non-stationary to stationary, thus warranting the feasibility of the traditional FFA approach for non-stationary cases. To be more specifically, a modified reservoir index (MRI(t)) is proposed and the original non-stationary AMF series are converted to stationary series by multiplying by a scalar factor 1/(1 ? MRI(t)), and thus traditional FFA can be adopted. Besides, Bayesian theory was applied to analyze the effect of uncertainty on the designed reconstructed AMF. As an example, the proposed method was applied to observations from Huangzhuang station located on the Hanjiang River. The original AMF observations from Huangzhuang displayed nonstationarity for the continuous construction of reservoirs in the basin. After applying the new method of sample reconstruction, the original AMF observations became stationary, and the designed AMFs were estimated using the reconstructed series and compared with those estimated based on the original observation series. In addition, Bayesian theory is adopted to quantify the uncertainty of designed reconstructed AMF and provide the expectation of the sampling distribution.     

Estimating the energy of seismotectonic deformations in the lithosphere of the Baikal Rift Zone

Estimation and comparison of the energy of seismotectonic deformations in the lithosphere of the Baikal Rift Zone (BRZ) based on observations of large (M ≥ 6) earthquakes for the period of instrumental recording (1950–2002), for a historical period lasting 210 years (1740–1949), and inferred from palaeo-seismological materials for the past 2000 years, all indicate that the hypothesis of a stationary seismic process is appropriate for the region. The locations of maxima of the density of seismotectonic strain energy released during the time intervals under investigation show that most of the failures in the lithosphere occurred approximately in the same areas, which may be interpreted as stress concentrators. The isolines of increased density for the energy of seismotectonic deformations align themselves along the rift features from southwest to northeast in the Baikal region and this allows one to treat the BRZ lithosphere as an extended zone of enhanced, inhomogeneous, energy release of endogenous geotectonic processes. We assessed the power of the seismotectonic processes that reflect the release of endogenous energy through earthquakes. Identification of areas with deficits in the energy of seismotectonic deformations (“energy gaps”) is an important step toward long-term solution of seismic-safety problems for the Baikal region.     

中长期地震预测中的PI算法改进研究及应用

图像信息学PI(Pattern Informatics)算法是一种基于统计物理学的地震预测新方法, 近年来得到了较大发展。 本文探索把此方法与地震活动性网格点密集值方法相结合, 并尝试用于华北地区中长期地震预测。 在预测中, 使用1970—2011年M_L≥3.0区域地震目录, 针对M_S≥5.0预测“目标震级”, 采用15年尺度的地震目录滑动时间窗, 均为3年尺度的地震活动“异常学习”时段和“预测时间窗”, 结合一定时空及震级范围内地震的数量和震中分布因素, 进行地震危险性概率计算。 对该方法的预测效果使用Molchan图表法进行统计检验。 结果表明, 此方法在某些方面优于PI算法, 且在地震趋势分析和中长期预测方面有较好的应用潜力。     

Mitigation of Oceanic Tidal Aliasing Errors in Space and Time Simultaneously Using Different Repeat Sub-Satellite Tracks from Pendulum-Type Gravimetric Mission Candidate

This contribution investigates two different ways for mitigating the aliasing errors in ocean tides. This is done, on the one hand, by sampling the satellite observations in another direction using the pendulum satellite mission configuration. On the other hand, a mitigation of the temporal aliasing errors in the ocean tides can be achieved by using a suitable repeat period of the sub-satellite tracks.The findings show, firstly, that it is very beneficial for minimizing the aliasing errors in ocean tides to use pendulum configuration; secondly, optimizing the orbital parameter to get shorter repeat orbit mode can be effective in minimizing the aliasing errors. This paper recommends the pendulum as a candidate for future gravity mission to be launched in longer repeating orbit mode with shorter “sub-cycle” repeat periods to improve the temporal resolution of the satellite mission.     

Oscillatory regime of aftershocks of the 1984 Ddzhirgatal earthquake: Implications for the internal dynamics of an unstable geological system

On the basis of seismological and geological evidence, the aftereffect region of the strong Dzhirgatal earthquake is localized as a real physical object. The time dependence of the number of aftershocks of this earthquake is best described by a simple hyperbolic law (p = 1, or the Omori law), which is well consistent with the ideas of self-similarity of the material fracture and the development of the seismotectonic process. Features characteristic of the evolution of self-similar systems are recognizable in the dynamics of the aftershock flow and parameters of seismotectonic deformation (STD) calculated from focal mechanisms of aftershocks. The evidence for this is the Feigenbaum inverse cascade in predominant frequencies of variations in the numbers of aftershocks and “catastrophes” in the form of an increase in the variability of STD parameters at the time moments when the corresponding predominant periods abruptly change. In this way, the term “catastrophe,” speculative with respect to the geophysical medium, acquires real meaning as a set of observable changes in the dynamics of STD parameters and the flow of aftershocks that occur over a fairly short time compared to the entire duration of the aftershock series.     

Techniques for assessing water infrastructure for nonstationary extreme events: a review

Statistical and physically-based methods have been used for designing and assessing water infrastructure such as spillways and stormwater drainage systems. Traditional approaches assume that hydrological processes evolve in an environment where the hydrological cycle is stationary over time. However, in recent years, it has become increasingly evident that in many areas of the world the foregoing assumption may no longer apply, due to the effect of anthropogenic and climatic induced stressors that cause nonstationary conditions. This has attracted the attention of national and international agencies, research institutions, academia, and practicing water specialists, which has led to developing new techniques that may be useful in those cases where there is good evidence and attribution of nonstationarity. We review the various techniques proposed in the field and point out some of the challenges ahead in future developments and applications. Our review emphasizes hydrological design to protect against extreme events such as floods and low flows.     

An Approximation to Sparse-Spike Reflectivity Using the Gold Deconvolution Method

Wiener deconvolution is generally used to improve resolution of the seismic sections, although it has several important assumptions. I propose a new method named Gold deconvolution to obtain Earth’s sparse-spike reflectivity series. The method uses a recursive approach and requires the source waveform to be known, which is termed as Deterministic Gold deconvolution. In the case of the unknown wavelet, it is estimated from seismic data and the process is then termed as Statistical Gold deconvolution. In addition to the minimum phase, Gold deconvolution method also works for zero and mixed phase wavelets even on the noisy seismic data. The proposed method makes no assumption on the phase of the input wavelet, however, it needs the following assumptions to produce satisfactory results: (1) source waveform is known, if not, it should be estimated from seismic data, (2) source wavelet is stationary at least within a specified time gate, (3) input seismic data is zero offset and does not contain multiples, and (4) Earth consists of sparse spike reflectivity series. When applied in small time and space windows, the Gold deconvolution algorithm overcomes nonstationarity of the input wavelet. The algorithm uses several thousands of iterations, and generally a higher number of iterations produces better results. Since the wavelet is extracted from the seismogram itself for the Statistical Gold deconvolution case, the Gold deconvolution algorithm should be applied via constant-length windows both in time and space directions to overcome the nonstationarity of the wavelet in the input seismograms. The method can be extended into a two-dimensional case to obtain time-and-space dependent reflectivity, although I use one-dimensional Gold deconvolution in a trace-by-trace basis. The method is effective in areas where small-scale bright spots exist and it can also be used to locate thin reservoirs. Since the method produces better results for the Deterministic Gold deconvolution case, it can be used for the deterministic deconvolution of the data sets with known source waveforms such as land Vibroseis records and marine CHIRP systems.     

Incorporating the spatio-temporal distribution of rainfall and basin geomorphology into nonlinear analyses of streamflow dynamics

Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been given to the nonlinear dependencies of the two and especially on how the spatio-temporal distribution of rainfall affects the nonlinear dynamics of streamflow at flood time scales. In this paper, a methodology is presented which simultaneously considers streamflow series, spatio-temporal structure of precipitation and catchment geomorphology into a nonlinear analysis of streamflow dynamics. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic spatially extended system rather than a deterministic multivariate one. The methodology is applied to two basins in Central North America using 6-hour streamflow data and radar images for a period of 5 years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between streamflow dynamics and the spatio-temporal dynamics of precipitation; (b) study how streamflow predictability is affected by the trade-offs between the level of detail necessary to explain the spatial variability of rainfall and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) streamflow predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology.