Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Regime interplay: the case of biodiversity and climate change

In this paper, the interplay between the biodiversity and climate change regimes is examined in the context of a case study. An understanding of how the regimes interact is crucial to their successful operation, since it provides insight into how policy options might be drawn up to create synergy rather than conflict among the respective regimes’ objectives. Despite the increasing importance of the study of regime interplay, due to its potential influence on regime effectiveness, there is limited understanding of why regimes interact and how their interplay may affect their successful operation, since few empirical studies have been conducted in this area. By analysing the causes of the regime interplay and the potential effects thereof, this paper draws policy implications regarding how the interacting regimes might be better co-ordinated to create synergy.     

Influence of the total atmospheric optical depth and cloud cover on solar irradiance components

Broadband solar irradiance data obtained in the spectral range 400–940 nm at Kwangju, South Korea from 1999–2000 have been analyzed to investigate the effects of cloud cover and atmospheric optical depth on solar radiation components. Results from measurements indicate that the percentage of direct and diffuse horizontal components of solar irradiance depend largely on total optical depth (TOD) and cloud cover. During summer and spring, the percentages of diffuse solar irradiance relative to the global irradiance were 5.0% and 4.9% as compared to 2.2% and 3.0% during winter and autumn. The diffuse solar irradiance is higher than the direct in spring and summer by 24.2%, and 40.6%, respectively, which may largely be attributed to the attenuation (scattering) of radiation by heavy dust pollution and large cloud amount. In cloud-free conditions with cloud cover ≤2/10, the fraction of the direct and diffuse components were 66.0% and 34.0%, respectively, with a mean daily global irradiance value of 7.92±2.91 MJ m⁻² day⁻¹. However, under cloudy conditions (with cloud cover ≥8/10), the diffuse and direct fractions were 97.9% and 2.2% of the global component, respectively. The annual mean TOD under cloudless conditions (cloud cover≤2/10) yields 0.74±0.33 and increased to as much as 3.15±0.67 under cloudy conditions with cloud amount ≥8/10. An empirical formula is derived for estimating the diffuse and direct components of horizontal solar irradiance by considering the total atmospheric optical depth (TOD). Results from statistical models are shown for the estimation of solar irradiance components as a function of TOD with sufficient accuracy as indicated by low standard error for each solar zenith angle (SZA).     

Similarities between strike-slip faults at different scales and a simple age determining method for active faults

Abstract Several differently scaled strike‐slip faults were examined. The faults shared many geometric features, such as secondary fractures and linkage structures (damage zones). Differences in fault style were not related to specific scale ranges. However, it was recognized that differences in style may occur in different tectonic settings (e.g. dilational/contractional relays or wall/linkage/tip zones), different locations along the master fault or different fault evolution stages. Fractal dimensions were compared for two faults (Gozo and San Andreas), which supports the idea of self‐similarity. Fractal dimensions for traces of faults and fractures of damage zones were higher (D ～1.35) than for the main fault traces (D ～1.005) because of increased complexity due to secondary faults and fractures. Based on the statistical analysis of another fault evolution study, single event movements in earthquake faults typically have a maximum earthquake slip : rupture length ratio of approximately 10^?4, although this has only been established for large earthquake faults because of limited data. Most geological faults have a much higher maximum cumulative displacement : fault length ratio; that is, approximately 10^?2 to 10^?1 (e.g. Gozo, ～10^?2; San Andreas, ～10^?1). The final cumulative displacement on a fault is produced by accumulation of slip along ruptures. Hence, using the available information from earthquake faults, such as earthquake slip, recurrence interval, maximum cumulative displacement and fault length, the approximate age of active faults can be estimated. The lower limit of estimated active fault age is expressed with maximum cumulative displacement, earthquake slip and recurrence interval as T ? (d_max /u) · I(M).     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

On the Effects of Non-planar Geometry for Blind Thrust Faults on Strong Ground Motion

— We quantify the effects of complex fault geometry on low-frequency (<1 Hz) strong ground motion using numerical modeling of dynamic rupture. Our tests include the computation of synthetic seismograms for several simple rupture scenarios with planar and curved fault approximations of the 1994 Northridge earthquake. We use the boundary integral equation method (BIEM) to compute the dynamic rupture process, which includes the normal stress effects along the curved fault geometries. The wave propagation and computation of synthetic seismograms are modeled using a fourth-order finite-difference method (FDM). The near-field ground motion is significantly affected by the acceleration, deceleration and arrest of rupture due to the curvature of the faults, as well as the variation in directivity of the rupture. For example, a 6-km-long hanging-wall or footwall splay with a maximum offset of 1 km can change 1-Hz peak velocities by up to a factor of 2-3 near the fault. Our tests suggest that the differences in waveform are larger on the hanging wall compared to those on the footwall, although the differences in amplitude are larger in the forward rupture direction (footwall). The results imply that kinematic ground motion estimates may be biased by the omission of dynamic rupture effects and even relatively gentle variation in fault geometry, and even for long-period waves.     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

Probabilistic approach for active control of structures: experimental verification

In our previous study (Earthquake Engineering and Structural Dynamics 2003; 32 :2301), we have developed a probabilistic algorithm for active control of structures. In the probabilistic control algorithm, the control force is determined by the probability that the structural energy exceeds a specified target critical energy, and the direction of a control force is determined by the Lyapunov controller design method. In this paper, an experimental verification of the proposed probabilistic control algorithm is presented. A three‐story test structure equipped with an active mass driver (AMD) has been used. The effectiveness of the control algorithm has been examined by exciting the test structure using a sinusoidal signal, a scaled El Centro earthquake and a broadband Gaussian white noise; and, especially, experiments on control have been performed under different conditions to that of system identification in order to prove the stability and robustness of the proposed control algorithm. The experimental results indicate that the probabilistic control algorithm can achieve a significant response reduction under various types of ground excitations even when the modeling error exists. Copyright © 2004 John Wiley & Sons, Ltd.