Control strategy for variable damping element considering near‐future excitation influence

A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment t_k, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at t_k and the final state at t_k+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd.     

LINEAR QUADRATIC REGULATOR FOR STRUCTURE UNDER ON-LINE PREDICTED FUTURE SEISMIC EXCITATION

A predictive-adaptive (PA) control algorithm has been developed for a structure under a seismic excitation. This algorithm analyses information of an observed seismic excitation, estimates future structural responses and determines the control force for the structure, based on the linear quadratic regulator. That is, at a given moment t_k: (1) seismic excitation information is converted to an autoregressive model, which forms the state equation for the excitation; (2) the identification model is combined with the structural model to build a state equation in an augmented space; (3) the weighted quadratic norm of the state vector and the future control force is formed as a cost function for estimating future responses; (4) the Ricatti equation is solved to find the optimum value of the cost function; and (5) the optimum gain matrix is obtained, and the control force is determined. The PA algorithm is not restricted to one type of control system, but can be applied to both an active driver system and an active tendon system. Its effectiveness is confirmed by numerical experiments for 1DOF and 3DOF structural models under sine and seismic excitations.     

A study on the characteristics of the information dimension D 1 of the temporal and spatial distributions of earthquakes in an active fault zone

The research of the information dimension (D ₁) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D ₀). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD ₁=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD ₁(t _N)=0.1363 (for the north section) andD ₁(t _S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD ₁(K _N)=1.053 (for the north section) andD ₁(K _S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 372–379, 1991. This paper is sponsored by the Chinese Joint Seismological Science Foundation. The English version is improved by Zhenwen An.     

CPT-based seismic stability assessment of a hazardous waste site

In areas of high seismicity, seismic stability often controls hazardous and solid waste landfill closure design. The undrained shear strength (S_u) of the waste mass is fundamental to seismic slope stability analyses. The value of S_u for hazardous waste fill is often difficult to characterize. The physical and chemical natures of the waste fill typically preclude laboratory testing of the materials. In certain cases, Cone Penetration Test (CPT) soundings can provide a viable technique for evaluation of S_u provided that the cone shear strength factor N_k can be established. If hazardous waste materials laboratory testing is not an option, N_k may be evaluated based upon results of non-intrusive in situ testing. This paper presents a case history of the seismic stability assessment of a hazardous waste site in which N_k was established from the results of non-intrusive Spectral Analysis of Surface Waves (SASW) soundings and empirical correlations to shear strength of soils. Generalization of the proposed methodology to other sites should be done with caution owing to variability among the parameters used in the analyses.     

基于速率-状态依从摩擦定律的前郭震群余震活动率及模型参数相关性研究

基于速率-状态依从摩擦定律的地震活动率时空预测模型,以同震库伦应力变化作为模型初始应力扰动,模拟了2013年吉林前郭MS5.8震群的余震活动率变化。考虑模型参数相关性,在模拟中采用2种不同的拟合方案,一是余震持续时间t_a不固定条件下的拟合,二是余震持续时间t_a固定条件下的拟合。结果显示,t_a不固定条件下的拟合方式可获得较好的AIC评价,适用于震后早期的趋势判定; t_a固定条件下的拟合计算耗时更短,拟合误差更小,理论模拟结果与前郭震群实际地震时序特征更为吻合。采用该方案对截至2016年10月24日的余震活动率变化进行了回溯性预测检验,结果显示模型预期的余震日频次与实际记录呈较好的正相关关系。研究还发现,主震破裂面附近的同震应力影区导致震后早期模型预测值相对于实际偏低,说明前郭序列余震活动可能还存在其他触发机制。     

The design of visco‐acoustic weighted L1‐error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L ₁ ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L ₁ ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L ₄ ‐norm and L_∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L ₁ ‐error method enhances the resolution and results in practically stable images.     

A study on the characteristics of the information dimensionD 1 of the temporal and spatial distributions of earthquakes in an active fault zone

The research of the information dimension (D ₁) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D ₀). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD ₁=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD ₁(t _N)=0.1363 (for the north section) andD ₁(t _S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD ₁(K _N)=1.053 (for the north section) andD ₁(K _S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction.     

An empirical earthquake prediction model

We have monitored seismic activity induced by impoundment of Lake Jocassee in northwest South Carolina for about two years. Low-level shallow activity was recorded. The larger felt events (2.0 ? M_L ? 2.6) were found to be associated with precursory changes in one or more of the following; number of events, t_S/t_p ratio values and radon concentrations in groundwater.The microearthquakes in the precursory period were accurately located in time and space, and their location pattern was used to develop an empirical earthquake prediction model.The precursory period consists of two phases; α-phase or a period of slow (or no) increase in seismicity, and β-phase, a period when the activity increase is more rapid. The main shock was found to be located within a cluster, a “target” area defined by the location of events in the β-phase. There is a general absence of seismic activity in the “target” area in the α-phase. The main shock occurred soon after a period of quiescence in the seismic activity in the β-phase. The magnitude of the shock, M_L is given by: M_L = 2 log D ? 0.07, where D is the duration of the precursory period in days.The model was successfully tested with data for a magnitude 2.3 event on February 23, 1977 which was also accompanied by radon and t_s/t_p anomalies.     

Review Paper: A semi‐empirical model of strain sensitivity for 4D seismic interpretation

We reformulate the original model of Hatchell and Bourne and Røste, Stovas and Landrø that couples fractional velocity change to subsurface strain via a fundamental constant R. The new model combines elastic compressibility of a dual‐porosity system for a sand–shale mixture with horizontal planes of inter‐granular weakness. The majority of observed R‐factor magnitudes from post‐stack 4D seismic data in both the reservoir and overburden can thus be explained. R is predicted to depend strongly on lithology and also initial strain state. The model is also extended to predict the observed angle‐dependence of time‐lapse time‐shifts from pre‐stack data. An expression for the gradient of time‐shift with incidence angle is obtained in terms of the background V_P/V_S, and also the ratio of tangential to normal compliances B_T/B_N representing loss or creation of inter‐granular coupling. If accurately estimated from data, this compliance ratio can be used as an additional parameter to assess the post‐production state of the overburden. It is concluded that whilst R remains the over‐arching parameter controlling the magnitude of time‐shifts measured from 4D seismic data, B_T/B_N is a subtler parameter that may also prove of future value.     

Prediction of rockburst probability given seismic energy and factors defined by the expert method of hazard evaluation (MRG)

In this paper we suggest that conditional estimator/predictor of rockburst probability (and rockburst hazard, P ^T (t)) can be approximated with the formula P ^T (t) = P ₁(θ ₁)…P _N (θ _N )·P _dyn ^T (t), where P _dyn ^T (t) is a time-dependent probability of rockburst given only the predicted seismic energy parameters, while P _i (θ _i ) are amplifying coefficients due to local geologic and mining conditions, as defined by the Expert Method of (rockburst) Hazard Evaluation (MRG) known in the Polish mining industry. All the elements of the formula are (approximately) calculable (on-line) and the resulting P ^T value satisfies inequalities 0 ≤ P ^T (t) ≤ 1. As a result, the hazard space (0–1) can be always divided into smaller subspaces (e.g., 0–10⁻⁵, 10⁻⁵–10⁻⁴, 10⁻⁴–10⁻³, 10⁻³–1), possibly named with symbols (e.g., A, B, C, D, …) called “hazard states” — which saves the prediction users from worrying of probabilities. The estimator P ^T can be interpreted as a formal statement of (reformulated) Comprehensive Method of Rockburst State of Hazard Evaluation, well known in Polish mining industry. The estimator P ^T is natural, logically consistent and physically interpretable. Due to full formalization, it can be easily generalized, incorporating relevant information from other sources/methods.     

Real-time prediction of near-future seismic excitation adapting AR model to preceding information

This paper examines a real-time prediction method, aimed at application in active structural control. The examined method applies preceding seismic excitation information at a certain moment to a time-variant AutoRegressive (AR) model and uses it to predict near-future excitation information. The performances of this method and appropriate identification parameters are examined by numerical experiments. In fact, the results of these experiments show that a time-variant AR model with appropriate identification parameters has little change in low-frequency components despite change in AR coefficients. The performance of a fixed-coefficient AR model is thus examined. The results show that even a fixed-coefficient AR model can sufficiently predict 0·05-s-future excitation information. Copyright © 1999 John Wiley & Sons Ltd.     

Time-frequency analysis of seismic excitation and estimates of attenuation parameters for the Friuli (Italy) local earthquakes

Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude (M_L ? 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ²_e(t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ²_e(t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings (l), or the equivalent diffusivity coefficient (d) and turbidity (g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ～ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ～ 5 km for the strong interaction model to ～ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as (σ²_e)_max ～ R^?ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.     

THE ESTIMATION OF SIGNAL SPECTRA AND RELATED QUANTITIES BY MEANS OF THE MULTIPLE COHERENCE FUNCTION *

A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χ_j(t), from a set of traces, can be broken down into two stationary components: a signal sequence, α_j(t) *s(t—τ_j), which correlates from trace to trace, and an incoherent noise sequence, n_j(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χ_j(t) =α_j(t) * s(t—τ_j) +n_j(t) where the signal wavelet α_j(t), the lag (moveout) of the signal τ_j, and the noise sequence n_j(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented. The method requires the calculation of the multiple coherence function γ_j(f) of each trace. γ_j(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρ_j(f) by where K_j(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix. Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described. Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.     

Field scale impacts of spatially correlated relative permeability in heterogeneous multiphase systems

Two-dimensional numerical simulations of two-phase (DNAPL-water) flow in spatially correlated random fields demonstrate the influence of nonwetting phase (NWP) relative permeability–saturation (k_r,N–S_W) relationships correlated to porous media intrinsic permeability (k). Both the volume of porous media invaded by the NWP and the length of time during which the NWP is migrating are under predicted if k_r,N–k correlation is not accounted for in the model formulation. Not accounting for the k_r,N–k correlation resulted in under predicting the volume of porous media invaded by up to approximately 10%, which is likely not significant for many practical applications. However, not accounting for the k_r,N–k correlation resulted in under predicting field scale migration times by up to a factor of 4, which is likely significant in that the migration times are on the order of years to several decades for the DNAPL (1,2-DCE) considered in this study. The under prediction of migration times was greater for lower permeability aquifers.     

Seismic Interevent Time: A Spatial Scaling and Multifractality

The optimal scaling problem for the time t(L × L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L × L) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our theoretical deductions are corroborated by California seismicity with magnitude M ≥ 2. In other words, the population of waiting time distributions for L = 10–100 km provides positive information on the multifractal nature of seismicity, which impedes the population to be converted into a unified law by scaling. This study is a follow-up of our analysis of power/unified laws for seismicity (see Pure and Applied Geophysics 162 (2005), 1135 and GJI 162 (2005), 899).     

Turbulent viscosity optimized by data assimilation

As an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a three-dimensional oceanic circulation model. The optimal control method, described for a 3-D primitive equation model, involves the minimization of a cost function that quantifies the discrepancies between the simulations and the observations. An iterative algorithm is obtained via the adjoint model resolution. In a first experiment, a k ± L model is used to simulate the one-dimensional development of inertial oscillations resulting from a wind stress at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosity is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimensional schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event.     

山东长岛地区地震波非弹性衰减Q值、场地响应及震源参数研究

利用山东台网记录的长岛震群2017年2月14日—9月1日期间的波形与震相资料研究长岛地区非弹性衰减系数,得到该地区介质平均Q值与频率f的关系式为Q(f)=363.9f1.374 1。采用Moya等[1]提出的利用遗传算法联合反演得到长岛周边台站的场地响应,根据Brune模型震源参数计算公式求解长岛震群序列地震震源参数。结果显示,各个震源参数之间均存在一定的相关关系,地震矩随ML震级的增大而增加,地震矩与破裂半径R之间存在半对数关系,拐角频率fc随地震矩的增大而减少;长岛地震序列的应力降数值普遍偏小,最大不超过0.9MPa,这意味着长岛震源区整体构造应力较低,也可能指示长岛震群为低摩擦应力的断层作用;震源参数随时间的变化方面,整体而言,长岛震群地震应力降变化起伏很大,在M4.1地震发生前,拐角频率与应力降均发生快速下降后随即翻转上升的现象,证明在M4.1地震发生前震源区整体应力的挤压逐渐增强。     

Lp-NORM DECONVOLUTION1

The purpose of deconvolution is to retrieve the reflectivity from seismic data. To do this requires an estimate of the seismic wavelet, which in some techniques is estimated simultaneously with the reflectivity, and in others is assumed known. The most popular deconvolution technique is inverse filtering. It has the property that the deconvolved reflectivity is band-limited. Band-limitation implies that reflectors are not sharply resolved, which can lead to serious interpretation problems in detailed delineation. To overcome the adverse effects of band-limitation, various alternatives for inverse filtering have been proposed. One class of alternatives is L_p-norm deconvolution, L₁norm deconvolution being the best-known of this class. We show that for an exact convolutional forward model and statistically independent reflectivity and additive noise, the maximum likelihood estimate of the reflectivity can be obtained by L_p-norm deconvolution for a range of multivariate probability density functions of the reflectivity and the noise. The L_∞-norm corresponds to a uniform distribution, the L₂-norm to a Gaussian distribution, the L₁-norm to an exponential distribution and the L₀-norm to a variable that is sparsely distributed. For instance, if we assume sparse and spiky reflectivity and Gaussian noise with zero mean, the L_p-norm deconvolution problem is solved best by minimizing the L₀-norm of the reflectivity and the L₂-norm of the noise. However, the L₀-norm is difficult to implement in an algorithm. From a practical point of view, the frequency-domain mixed-norm method that minimizes the L₁norm of the reflectivity and the L₂-norm of the noise is the best alternative. L_p-norm deconvolution can be stated in both time and frequency-domain. We show that both approaches are only equivalent for the case when the noise is minimized with the L₂-norm. Finally, some L_p-norm deconvolution methods are compared on synthetic and field data. For the practical examples, the wide range of possible L_p-norm deconvolution methods is narrowed down to three methods with p= 1 and/or 2. Given the assumptions of sparsely distributed reflectivity and Gaussian noise, we conclude that the mixed L₁norm (reflectivity) L₂-norm (noise) performs best. However, the problems inherent to single-trace deconvolution techniques, for example the problem of generating spurious events, remain. For practical application, a greater problem is that only the main, well-separated events are properly resolved.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.